Computational Methods in Nuclear Radiation Shielding and Dosimetry 1536185272, 9781536185270

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PHYSICS RESEARCH AND TECHNOLOGY

COMPUTATIONAL METHODS IN NUCLEAR RADIATION SHIELDING AND DOSIMETRY

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PHYSICS RESEARCH AND TECHNOLOGY

COMPUTATIONAL METHODS IN NUCLEAR RADIATION SHIELDING AND DOSIMETRY KULWINDER SINGH MANN AND

V. P. SINGH EDITORS

Copyright © 2020 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470

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NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the Publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data Names: Mann, Kulwinder Singh, editor. | Singh, V. P. (Nuclear physicist), editor. Title: Computational methods in nuclear radiation shielding and dosimetry / Kulwinder Singh Mann (author), D.A.V. College, Bathinda, Punjab, India, V.P. Singh (author), Department of Physics, Kamatak University, India. Description: New York : Nova Science Publishers, [2020] | Series: Physics research and technology | Includes bibliographical references and index. | Identifiers: LCCN 2020039652 (print) | LCCN 2020039653 (ebook) | ISBN 9781536185270 (hardcover) | ISBN 9781536186611 (adobe pdf) Subjects: LCSH: Radiation dosimetry. | Shielding (Radiation)--Mathematics. Classification: LCC QC795.32.R3 C65 2020 (print) | LCC QC795.32.R3 (ebook) | DDC 612/.014480287--dc23 LC record available at https://lccn.loc.gov/2020039652 LC ebook record available at https://lccn.loc.gov/2020039653

Published by Nova Science Publishers, Inc. † New York

This book is dedicated to our families

Editors K. S. Mann, PhD V. P. Singh, PhD

CONTENTS Preface Chapter 1

Chapter 2

xi RIPM-Toolkit: A Computer Program to Investigate Double-Layered Gamma-Ray Shielding Enclosures Sukhmanjit Singh Mann and Kulwinder Singh Mann FLUKA: A Competent Code for Shielding Characteristics Amandeep Sharma

1

39

Chapter 3

Basic Quantities for Photon Shielding Calculations Suffian Mohamad Tajudin

65

Chapter 4

Ambient Dose Buildup Factors Oyeleke Olarinoye

87

Chapter 5

Calculation of Buildup Factors Using Taylor’s Approximation for Multi-Layered Shields Nisha Raj

113

viii Chapter 6

Chapter 7

Contents Novel Materials for Dosimetry and Shielding Radiation Mayra Guadalupe Garcia-Reyna, Hector Rene Vega-Carrillo, Victor Martin-Hernandez Davila, Antonio Baltazar-Raigosa and Maria Del Rosario Martinez-Blanco Phantom Based Computational Models for Dose Calculation in Medicine Shashi Bala and Ashwani Koul

151

183

Chapter 8

Dosimetry in Computed Tomography Joel Vazquez-Bañuelos, Guillermo Eduardo Campillo-Rivera, Claudia Angelica Marquez-Mata, Claudia Villalpando-Hernandez, Angel Garcia-Duran and Hector Rene Vega-Carrillo

211

Chapter 9

Dosimetry in the Area of Dentistry Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos, Claudia Villalpando-Hernandez, Claudia Angelica Marquez-Mata, Angel Garcia-Duran, Eduardo Medrano-Cortes and Hector Rene Vega-Carrillo

243

Chapter 10

Evaluation of Some Ignimbrite Rocks as Gamma Radiation Shıeldıng Material: A FLUKA Simulation Study E. Kavaz, M. Dal, Z. Kuluöztürk and N. Demir

Chapter 11

Investigation of Gamma-Ray Shielding Parameters of Marbles Nilgün Demir, Zehra Nur Kuluöztürk, Murat Dal and Bünyamin Aygün

277

293

Contents Chapter 12

Chapter 13

Radiation Shielding Characteristics of Bulk Amorphous Metals for Gamma Rays, Charged and Uncharged Particles Ufuk Perişanoğlu Detection Features of Borate-Based Thermoluminescent Dosimeters Carina Oliva Torres-Cortes, Hector Rene Vega-Carrillo, Antonio Baltazar-Raigosa and Luis Hernandez-Adame

ix

313

331

About the Editors

357

Index

359

PREFACE This book describes the mushrooming applications of gamma-rays as radiological diagnostic tools used for scientific research and medical diagnostics. The aim behind the compilation of this book is to provide collective knowledge and experience of various computational techniques required for the evaluation of gamma-ray shielding parameters. These gamma-ray shielding parameters are useful for investigations of radiation protection and dosimetry. The book has been divided into thirteen chapters, arranged in a systematic order. The first chapter describes a new computer code designed with SVM for suggesting the arrangement of layers in the design of double-layered shielding enclosures. The second chapter provides detailed information about FLUKA-toolkit. The next three chapters, i.e., chapters 3 to 5, illustrate the significance of buildup factors in shielding calculations. Chapters 6 to 9 explain about dosimetric-calculations required for medical diagnostics. The next four chapters viz. chapters 10 to 13 describe the applications of various techniques in the investigation and evaluation of shielding parameters of some building materials. This book focuses on various computer codes such as FLUKA, GEANT4, EGS5, XCOM, Phy-X, BMIX, ASFIT, and ANSI. The topics such as multilayered shielding, Dose calculation with SVM, Phantom based computational models, and nuclear safety aspects have been discussed in detail. We have included the chapters after the standard peer-review process to improve the

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Kulwinder Singh Mann and V. P. Singh

book's quality of knowledge. It is essential to mention here that we have tried to utilize the free time of authors because of the worldwide lockdown caused by the spread of COVID-19. This book will serve as an excellent selflearning tool for researchers working in radiological protection, nuclear physics, and chemistry. Respective authors are solely responsible for any plagiarism, copyright issues, and any conflict in their respective chapters after the publication. We have informed all the authors about publicationethics to remove the plagiarism and copyright issue. The credit of the compilation of this book goes to authors, and family-support obtained by us. The cooperation provided by the NOVA Science Publication house helps a lot to complete this book. We are grateful to Google for helping in creating Chapter-Submission-Portal with a free Google-Forms facility. Editors July 2020

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 1

RIPM-TOOLKIT: A COMPUTER PROGRAM TO INVESTIGATE DOUBLE-LAYERED GAMMA-RAY SHIELDING ENCLOSURES Sukhmanjit Singh Mann1,* and Kulwinder Singh Mann2 1

Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, India 2 Depetment of Physics, D.A.V. College, Bathinda, Punjab, India

ABSTRACT The construction of gamma-ray shielding enclosures at nuclear establishments is mandatory for the safety concerns from ionising radiation. Recently, it has been established that heterogeneous enclosures offer better gamma-ray shielding behaviour (GSB) than homogeneous enclosures. For most of the periodic table elements, the NIST provides standard databases of many photon interaction cross-sections in a wide energy range. We dedicate the present work to investigating the GSB of *

Corresponding Author’s Email: [email protected].

2

Sukhmanjit Singh Mann and Kulwinder Singh Mann some shielding enclosures using the dominance of the fundamental photon interactions. The Support Vector Machine has been used for classification of the standard interaction cross-sections for the major photon interactions viz. Photoelectric absorption (PE), Compton Scattering (CS), and Pair production (PP). Further, the Support Vector Machine (SVM) has been used to investigate and design a computer program (RIPM-toolkit). The RIPM-toolkit predicts the dominating photon interaction process with excellent accuracy (99.77%) and predicting the required GSB of the shielding enclosure. The toolkit has been validated for its calculation accuracy, using the Monte Carlo simulation based on FLUKA code and standard materials. It has been concluded that the double-layered shielding enclosures made from PET as low-Z, and three high-Z materials (NBS concrete, Pb, W) offers the best GSB in a wider energy range.

Keywords: radiation shielding, shielding parameter, shielding design, shielding effectiveness, cross-section

INTRODUCTION The gamma-ray leakage is one of the biggest problems that nuclear engineers are trying to solve by constructing effective shielding enclosures for nuclear establishments. The unpleasant past experiences of various nuclear accidents indicated the importance of effective GSE. By including the most recent nuclear accident, Fukushima (Japan), until now, about 63 major nuclear accidents have been recorded. After the Three Mile Island (TMI) accident, many parameters have been introduced for the analysis of the GSB of a given shielding structure. The parameters like effective atomic number (Zeff), effective electron density (Nel), and photon buildup factor (BUF) are termed as gamma-ray shielding parameters (GSP). These GSP have been used to investigate the GSB of nuclear structure. According to Web of Science and Scopus, in the previous two decades, a plethora of research papers had been published on the topic of gamma-ray shielding. These research papers published with various keywords like mass attenuation coefficient (MAC), Zeff, Nel, and BUF. Many computer codes, toolkits, and software have been developed for the said purpose. This worldwide trend indicates that researchers are continuously working to solve

RIPM-Toolkit

3

the problem of gamma-ray leakage from nuclear establishments. By compiling the collected wisdom of nuclear radiations, safety standards have been proposed by many organisations like IAEA, ICRP, NCRP, DAE. The primary aim behind the proposed standards is to keep the exposure of radiations below the safe limit [1, 2]. From the bitter past experiences of nuclear accidents, we have learned a crucial lesson that the chances of accidental leakage of radioactivity from nuclear establishments cannot be neglected. Such an accident demands immediate protection of the local public from nuclear radiation exposures. Additionally, the rapidly increasing number of nuclear weapons poses a significant threat of nuclear disaster. So, to face such undesirable situations, the only instantaneous safety alternative left to isolate the affected public is by keeping them inside the prebuilt nuclear radiation protection shelter (NRPS) [3]. The GSB of NRPS can be evaluated from its GSP. Fundamental gamma-ray interactions viz. PE, CS, and PP, are responsible for its attenuation and useful to decide GSB of the shielding enclosure. The GSB of GSE depends on the nature of the material used in it. But for heterogeneous GSE, it depends on the arrangement of different materials. Moreover, the GSB of any material can be evaluated from its various shielding parameters such as mass attenuation coefficient, optical thickness, BUF. These parameters are an explicit function of gamma-ray energy (E) and effective atomic number (Zeff) of the material. The Zeff value depends on the probability of various photon interaction processes with the material, which is described by the respective cross-section parameter. In this work an attempt has been made to investigate the GSB of double-layered heterogeneous shields (DLHS) using a powerful algorithm the SVM (Support Vector Machine). Radiation Interaction Predictor for Materials (RIPM-toolkit), self-designed computer program provides GSB of shielding enclosures in the wide energy range 1 keV-1 GeV. The toolkit is useful in designing DLHS with required GSB.

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

THEORY AND BACKGROUND

Figure 1. Variation of the theoretical cross-section values for PE, CS, PP and total with energy.

Gamma-ray photons interact with matter via absorption or scattering phenomenon. Magnitude of these interactions depends on corresponding interaction-probabilities. However, the quantitative description of each interaction probability is described by the interaction cross-section (σ). The total MAC of shielding material for gamma rays is the sum of its partial attenuation coefficients for some fundamental interactions (PE, CS, and PP). Magnitude of the partial MAC depends on the respective cross-section. Total MAC is the most widely used parameter for shielding investigation of

RIPM-Toolkit

5

materials. Figure 1 illustrates the variations of partial and total cross-sections with the photon energy for some periodic table elements. Davisson and Evans [4] beautifully depicts the collected information regarding variations of partial interaction cross-sections with energy and atomic numbers, in EZ graph. Almost similar graphs have been reproduced (Figure 2) in the present investigation with the help of designed toolkit. This graph is useful to decide the dominating photon interaction with the shielding material.

Figure 2. The E-Z graph for three major gamma-ray interactions viz. PE, CS and PP for first 100 elements of the periodic table.

PARAMETERS AND DATABASE Mass Attenuation Coefficient, MAC The process of listing the measured values of MAC has been started since 1907 [5]. The database of MAC thus obtained has been updated and corrected many times [6-9]. The most recent update in it is by Chadwick et al. [9] for photon energy range 10 eV-13.5 GeV. Hubbell and Seltzer [10]

6

Sukhmanjit Singh Mann and Kulwinder Singh Mann

compiled the MAC database for wide energy range 1keV–20 MeV. Hubbell [11-12] listed the uncertainties in the MAC database. Chantler [13] pointed out the higher values of uncertainties in MAC, particularly for photon energy below 4 keV. The work in this direction is still in progress to find out MAC values of different compounds and mixtures in the wider energy range. Recently, measured values of MAC for many types of materials like tissues, human organs, marbles, concretes, amino acids, boron compounds, oxide films, polymer and plastic materials have been reported [14-23].

Effective Atomic Number, Zeff The effective atomic number (Zeff) is another useful parameter for the gamma-ray shielding analysis of building materials. The concept of Zeff has been introduced by Hine [24] to quantify the GSB of material. He described that the Zeff of multi-element material does not represent by a single number for various types of gamma-ray interactions. Thus, Zeff value depends on the material’s chemical composition as well as on the energy of the incident photon. For a mono-energetic gamma-ray photon, the Zeff of a multi-element material can be computed by following formula [25]:

Z eff 

 n A MAC  A  n Z MAC  i i

i

i

i

i i

(1)

i

i

Where ni represents the number of atoms, Ai is the atomic weight, Zi is the atomic number, and MAC represents total mass attenuation coefficient for the ith constituent element of the material.

BUF White (1950) has discovered about the contribution of scattered photons in the measured value of MAC of water for gamma rays emitted from Co-

RIPM-Toolkit

7

60. He thus introduced the concept of BUF for correcting the calculations for MAC [26]. After, TMI nuclear accident the importance of BUF in GSB analysis has been highlighted, thereby the American Nuclear Society (ANS) included the BUF in ANS standard [27]. The detailed computational procedure for BUF and required parameters for many elements of the periodic table have been listed in the ANS standard.

Computer Program, Software, and Toolkits Berger and Hubbell [28] have developed a computer program, XCOM using FORTRAN-77. It computes MAC and interaction cross-sections of multi-element materials at any energy between 1keV to 100 GeV. Nowotny has designed another similar computer program, XMuDat [29], for computations of Zeff and MAC. Gerward et al. have transferred the DOSbased programme, XCOM, to GUI based computer software, WinXCom [30, 31]. Okunade [32] has provided another computer program for calculation of mass energy absorption coefficients of material. For the computation of additional parameters than MAC and Zeff, some other computer programs have been developed, such as Auto-Zeff [33], Direct-Zeff software [34], ZXCOM software [35], GRIC-toolkit [22], GRIC2-toolkit [23], Zeff-toolkit [36]. In the last decade, a plethora of research papers have been published by citing ANS-standards [27] for the computation of BUF. Some computer programs such as BUF-toolkit [37], DLEBF-Toolkit [38], BXCOM-software [39], and PSD-software [40] have been developed for computation of BUF by using the ANS-standards [27].

MATERIAL AND METHODS Five samples of standard polymeric materials and one sample of standard building material (concrete) have been chosen for the investigation. Reason behind selection of polymeric materials is that they belong to a lowZ group of materials. Their reproducibility is the second reason for the

8

Sukhmanjit Singh Mann and Kulwinder Singh Mann

selection. Moreover, combinations of concrete with the polymeric materials can produce double-layered heterogeneous shield (DHLS) with a significant difference in Zeff values of the materials. The difference in Zeff of both materials of DLHS helps to investigate its effect on the GSB. The chemical composition and symbols used for the chosen sample-materials have been listed in Table 1. Table 1. Materials used for standardisation of RIPM-toolkit [48, 27] S. Material No.

Symbol Chemical composition (by wt. fraction)

Density (g/cm3 ) 0.95

1

Polymethyl methacrylate PMMA H (0.08054); C (0.59985); O (0.31961)

2

Polysulfone

PSU

H (0.05011); C (0.73282); O (0.14462); S (0.07246)

1.24

3

Polyvinyl chloride

PVC

H (0.04838); C (0.38436); O (0.56726)

1.30

4

Polyethylene terephtalate PET

H (0.04196); C (0.62502); O (0.33302)

1.40

5

Polytetrafluoroethylene

PTFE

C (0.24018); F (0.75982)

2.20

6

NBS Concrete

NBSC

H (0.00560); O (0.49800); Na (0.01710); Mg (0.00240); Al (0.04560); Si (0.31600); S (0.00120); K (0.01920); Ca (0.08260)

2.35

Support Vector Machine, SVM SVM algorithm [41] has been used widely in many scientific applications such as diagnostics [42], security [43], signature, and speech recognition [44]. It is a special type of algorithm that helps to classify rawdata by creating hyper-planes in a multidimensional-space that splits the data into different classes. It utilises iterative-training algorithm to minimise errors and construct an optimal hyperplane. The training provides two types of output. The first type is the normal-coefficient vector of a hyperplane that separates the data into two classes, whereas the second type is a bias term that is the offset of the hyperplane along its normal-vector. After the completion of the training stage, the hyperplane consisting of both types of output starts predicting the data for new observations with the help of a prediction-function. The prediction-function based on the probability of

RIPM-Toolkit

9

predicted-data for both the classes. The accuracy of SVM depends on many factors, such as the selection of the kernel and related parameters, the regularisation parameter, size, and the quality of the chosen training data.

RIPM-Toolkit SVM algorithm based computer program, Radiation Interaction Predictor for Materials-RIPM-toolkit, has been designed for the present investigation. The interface of the toolkit has been described in Figure 3. It requires the input of the photon energy in MeV and chemical composition of the sample (by weight fraction). The toolkit thus predicts the dominating type of photon interaction with the sample at selected energy. It uses X-ray or gamma-ray cross-section databases [10, 13, 6] for the prediction.

Figure 3. The interface of the RIPM-Toolkit.

Thus, SVM classifies the data and helps in taking a decision boundary to maximise the separation between random data points (large margin classifier). It uses various similarity-functions to create different features. Mathematical functions satisfying Mercer's Theorem are termed as kernels.

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

These kernels reduce computational steps, thus making their operation very fast. Gaussian-kernel has been used in the RIPM-toolkit. The cost function of SVM is listed in Eq. (2):





 





 12 

J ( )  C i 1 y (i ) cos t1  T f (i )  1  y (i ) cos t  T f (i )  m

m

 j2

j 1

(2)

Here, C is the regularisation parameter, f(i)=exp[(||x-l(i) ||2)/2σ2] and l(i) = x(i) for the Gaussian-kernel and similarly for other kernels [45]. The Octave code used for training the data and plotting of the graph has been provided as Appendix-A in the supplementary file. About 8500 examples have been used for training purposes based on dominating photon interactions. The toolkit has achieved a high training accuracy of 99.77%.

Formulation of the Toolkit The toolkit has been programmed in the Octave language. It uses LIBSVM software and SVM to classify the database [46]. It plots the E-Z graph (Figure 2) from the database [10, 13, 6]. Figure 4 shows the input window of the toolkit, which requires information regarding the samplematerial. The output window described in Figure 5, provides the information about the dominating photon interaction process with samples at chosen photon energy. Additionally, it computes the total MAC, Zeff, and Nel of the sample for gamma rays. The main programme code of RIPM-toolkit has been provided as Appendix-B in the supplementary file.

Figure 4. The command window of RIPM-toolkit waiting for the input about nature of the sample.

RIPM-Toolkit

11

Operating Procedure of the Toolkit RIPM-toolkit accepts input data of the sample-material as its chemical composition and incident photon energy (in MeV). Output windows of the toolkit have been described in Figure 5 and Figure 6.

Figure 5. The output window of RIPM-toolkit for element, Ga at various energy values.

Figure 6. The output window of RIPM-toolkit for mixture, H2O at various energy values.

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

Validation of the Toolkit Dominating interaction prediction efficiency of the toolkit depends on its ability to compute Zeff accurately. FLUKA software [47-48] has been used for validation purposes of the toolkit. The computed values of Zeff for the chosen samples with the toolkit and FLUKA software have been listed in Table 2. Excellent agreement between both the results validates the designed toolkit for Zeff calculations. Table 2. Standardisation of the RIPM-toolkit for computation of effective atomic number, Zeff E (MeV)

Computational Method

RIPM-Toolkit 5.95E-02 FLUKAa % Relative RIPM-Toolkit 8.09E-02 FLUKAa % Relative RIPM-Toolkit 1.41E-01 FLUKAa % Relative RIPM-Toolkit 3.57E-01 FLUKAa % Relative RIPM-Toolkit 6.62E-01 FLUKAa % Relative RIPM-Toolkit 8.35E-01 FLUKAa % Relative RIPM-Toolkit 1.17E+00 FLUKAa % Relative RIPM-Toolkit 1.33E+00 FLUKAa % Relative

PMMA

PSU

PVC

PET PTFE NBSC

3.70 4.78 8.26 4.65 8.11 11.52 3.70 4.74 8.09 4.70 8.10 11.28 0.03 0.85 2.04 -1.13 0.17 2.05 3.61 4.40 6.60 4.56 8.03 10.06 3.63 4.48 6.73 4.63 8.06 10.25 -0.52 -1.69 -1.91 -1.56 -0.42 -1.96 3.60 4.35 5.89 4.55 8.01 9.72 3.58 4.34 5.72 4.58 8.02 9.43 0.59 0.15 2.98 -0.72 -0.10 2.97 3.60 4.30 5.35 4.54 8.00 9.33 3.56 4.30 5.41 4.56 8.01 9.44 1.07 -0.09 -1.13 -0.36 -0.13 -1.12 3.60 4.30 5.33 4.54 8.00 9.32 3.56 4.29 5.38 4.56 8.01 9.40 1.10 0.14 -0.84 -0.33 -0.13 -0.83 3.60 4.30 5.33 4.54 8.00 9.32 3.56 4.29 5.38 4.56 8.01 9.40 1.11 0.14 -0.86 -0.33 -0.12 -0.86 3.60 4.30 5.33 4.55 8.00 9.32 3.56 4.29 5.38 4.56 8.01 9.40 1.12 0.14 -0.87 -0.33 -0.13 -0.85 3.60 4.30 5.34 4.55 8.00 9.32 3.56 4.29 5.38 4.56 8.01 9.40 1.13 0.16 -0.83 -0.31 -0.12 -0.82

a: Computed by Monte-Carlo Code-FLUKA [48]

RIPM-Toolkit

13

Graph has been plotted between Zeff and Log10E to decide the dominating gamma-ray interaction with the sample-material. Figure 7 describes the energy variations of various partial MACs computed by WinXCom programme, Zeff values calculated by RIPM-toolkit, and the regions of dominance (RoD) for the fundamental interactions predicted by the toolkit for PET (one of the chosen polymeric material). From Figure 7a, it is clear that energy RoD predicted by the toolkit shows good agreement with corresponding partial MACs computed by WinXCom software. Figure 7 indicates similar agreements of RoD predicted by RIPM-toolkit and WinXCom program for other chosen samples. So, the toolkit has been validated for computation of Zeff by FLUKA, and the prediction of energy RoD for major gamma-ray interaction processes by WinXCom software. The above validation indicated that the RIMP-toolkit could be used to investigate GSB of the sample-material with full confidence. 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 10 RoD by PE -5 10 (RIPM-Toolkit) -6 10 -7 10 RIPM-Toolkit -8 10 Zeff -9 10 WinXCom -10 10 CS -11 10 PE -12 10 PP -13 10 -4 -3 -2 10 10 10

7.5

PMMA

6.5 6.0 5.5 5.0

5

10

4

10

3

10

2

10

1

10

0

10

-1

10

-2

10

-3

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-11

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-12

10

-13

10

4.5 4.0 3.5 RoD by CS (RIPM-Toolkit) -1

10

10

0

10

1

E (MeV) Figure 7. (Continued).

7.0

RoD by PP (RIPM-Toolkit)

Zeff

2 -1

(cm g )

5

10

10

2

10

3

10

4

10

5

3.0

10

10 10

-1

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

2 -1

(cm g )

5

10 4 10 PSU 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 10 RoD by PE -5 10 (RIPM-Toolkit) -6 10 -7 10 -8 RIPM-Toolkit 10 Zeff -9 10 WinXCom -10 10 CS -11 10 PE -12 RoD by CS 10 PP -13 (RIPM-Toolkit) 10 -4 -3 -2 -1 0 1 10 10 10 10 10 10

RoD by PP

10

5

10

4

10

3

10

2

10.5

10

1

10.0

10

0

9.5

(RIPM-Toolkit)

9.0 8.5 8.0 7.5 7.0

Zeff

14

6.5 6.0

-3

10

-4

10

-5

10

-6

10

-7

10

-8

10

-9

10

-10

10

-11

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-12

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-13 -4

10

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-5

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-7

5.0 4.5 4.0

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5

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6

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-8

10

-9

10

5

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4

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2 1

10 1 10 0 10

16

10

-1

RoD by PP

10

-2

(RIPM-Toolkit)

10

-3

10

-4

10

-5

10

-6

10

-7

10

-8

10

-9

14

12

10

Zeff

2 -1

(cm g )

Figure 7. (Continued).

10

5.5

5

E (MeV)

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-2

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Sukhmanjit Singh Mann and Kulwinder Singh Mann 10 4 10 NBSC 3 10 RoD by PP 2 (RIPM-Toolkit) 10 1 10 0 10 -1 10 -2 10 -3 10 -4 RoD by PE 10 (RIPM-Toolkit) -5 10 -6 10 -7 10 RIPM-Toolkit -8 10 Zeff -9 WinXCom 10 CS -10 10 RoD by CS PE -11 10 (RIPM-Toolkit) PP -12 10 -4 -3 -2 -1 0 1 2 3 4 10 10 10 10 10 10 10 10 10 E (MeV)

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RESULTS AND DISCUSSION It is evident from Figure 2 that for majority of periodic table elements, the PE is dominating for photon energies (E) below 0.01 MeV, the PP starts dominating for photon energies above 10 MeV, and in the energy range, 0.01-10 MeV, the CS is dominating [21]. According to Siegbahn, [49] the PE cross-section (σPE) is proportional to Z5/E3.5, CS cross-section (σCS) is proportional to Z/E. While the threshold energy for PP is 1.02 MeV, and for photon energy above 1.02 MeV, the PP cross-section (σPP) is proportional to Z2.(lnE). In other words, the PP starts contributing to the total MAC of the sample for E>1.02 MeV. Three fundamental photon interactions phenomena viz. PE, CS, and PP collectively responsible for attenuation of gamma rays traversing through the material. However, the relative contributions of these phenomena to the total MAC varies with Zeff and E values. Thus, the E-Z graph helps to understand the dependence of three cross-sections viz. σPE,

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Figure 7. The validation of RIPM-toolkit using WinXCom programme for the chosen standard samples.

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RIPM-Toolkit

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σCS and σPP on both Z and E. The Figure 2 shows the relative dependence of these cross-sections on Zeff and E similar to that explained by Evans [50]. By carefully observing the plotted graph (Figure 2) following observations have been noted. The sinusoidal variations in boundary-line between region of dominance of PE (shaded in green colour) and region with dominance of CS (shaded in red colour). This variation seems to be due to the presence of various energy absorption edges of K-shells [13]. This is the additional information to previously available E-Z graphs by Evans [50]. For the chosen sample-material, computed Zeff value at incident photon energy (E) can be used to find the dominating photon interaction process from the graph (Figure 2), as explained in the following examples. Example-1: For Ga (Z=31) at three energies (E) 0.01, 1.00 and 100.00 MeV, the log10E values become -2, 0 and 2, respectively. The points (-2, 31), (0, 31) and (2, 31) on the E-Z graph (Figure 2), representing these combinations of the example. It is clear from Figure 2 that the point (-2, 31) lies in the green area of the graph, representing that the PE is dominating photon interaction. The point (0, 31) lies in the red-region of the graph, indicating that CS is the dominating photon interaction. However, the point (2, 31) lies in the blue-region of the graph, indicating that the PP is dominating photon interaction. Example-2: For Be (Z=4) at the same three values E. The points (-2, 4), (0, 4), and (2, 4) of the E-Z graph (Figure 2) thus provides the desired information regarding the dominating photon interactions. The RIPM-toolkit replicates this manually checked procedure to find the dominating photon interaction process by using SVM. After training the toolkit, it provides information regarding the dominating photon interaction process with 99.77% accuracy. Thus, the toolkit saves lots of effort and time, minimises the chances of gross-errors, and helps in providing quick decision for the arrangement of the chosen materials for designing efficient DLHS. Mann et al. [51] have established that the orientation of materials in DLHS such that low-Z material followed by high-Z (LZFHZ) offers better GSB than its reverse orientation, i.e., HZFLZ. Table 3 describes all the dominance-possibilities of the photon interactions in both the layers of DLHS and respective GSB

18

Sukhmanjit Singh Mann and Kulwinder Singh Mann

for the mono-energetic gamma rays. The GSB of DLHS has been described with the star-ratings. For the full energy range (1 keV-1 GeV), the output of the toolkit as dominating photon interaction for the chosen samples has been listed in Table 4. It is evident from Table 4 that for all the selected materials, the PE is dominating for the photon energy range (1 keV-80.9 keV), the PP is dominating for photon energies above 20 MeV, and the CS is dominating between these energy ranges. Table 5 describes the GSB for double-layered shielding enclosures made from combinations of the chosen five polymeric samples with standard concrete in both LZFHZ and HZFLZ orientations. Table 3. Quantification of GSB for DLHS using dominance of the three interaction processes for both materials (moving from source towards detector) S. No.

Dominating interaction process for two materials a

Gamma-Ray Shielding Behavior (GSB)

Layer 1

Layer 2

1

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PE

Excellent

2

PE

PE

Very Good

3

PE

CS

Good

4

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PP

Average

5

PP

PE

Average

6

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PP

Bad

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CS

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PP

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CS

Terrible

Star Rating of GSB of the DLHS

Further, testing of the toolkit, three types of other high-Z materials viz. Telluride glass, Lead (Pb), and Tungsten (W) [52, 53] have been analysed. The results have been listed in Tables 6-9. From Table 6, it has been concluded that for all these high-Z samples, the PE is dominating for the energy range (1 keV-357 keV), the PP is dominating for the energies above 10 MeV, and the CS is eclipsing between these energy ranges. The evaluation of double-layered shielding enclosures has been made as per the scheme provided in Table 3. The enclosures have been made from combinations of the chosen samples of low-Z polymeric materials and each of the high-Z material viz. Telluride Glass, Lead, and Tungsten respectively.

RIPM-Toolkit

19

The shielding efficacy of the double-layered shielding enclosures have been described in Tables 7-9. It established that the toolkit is capable of predicting the dominating energy range for different types of photon interactions with the chosen sample. It has been concluded that in the energy range 0.662-5 MeV no combination can provide acceptable GSB. This seems be because of the dominance of CS in both layers. For the energies below this region the dominance of PE in high-Z layer results in better GSB. On the upper side of energy, the dominance of PP absorption of gamma photons results in improving the GSB. Thus, GSB of given enclosure be determined by gamma photon energy. Table 4. Description of dominance of various photon interactions with energy for the chosen samples Energy PMMA (MeV) 1.00E-03 PE 1.00E-02 PE 2.00E-02 CS 3.00E-02 CS 4.00E-02 CS 5.00E-02 CS 5.95E-02 CS 8.09E-02 CS 1.41E-01 CS 3.57E-01 CS 6.62E-01 CS 8.35E-01 CS 1.17E+00 CS 1.33E+00 CS 1.50E+00 CS 2.00E+00 CS 5.00E+00 CS 1.00E+01 CS 2.00E+01 CS 3.00E+01 CS 4.00E+01 CS 5.00E+01 PP 1.00E+02 PP 1.00E+03 PP 1.00E+04 PP 1.00E+05 PP 1.00E+06 PP

PSU PE PE PE CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS PP PP PP PP PP PP

PVC PE PE PE PE CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP

PET PE PE CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS PP PP PP PP PP PP

PTFE PE PE PE PE CS CS CS CS CS CS CS CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP

NBSC PE PE PE PE PE PE PE PE CS CS CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP

PE: Photo electric absorption, CS: Compton Scattering; PP: Pair production.

20

Sukhmanjit Singh Mann and Kulwinder Singh Mann Table 5. The GSB for double-layered shielding enclosures made from combinations of the chosen polymeric materials with the concrete as LZFHZ and HZFLZ orientations

Energy (MeV) 1.00E-03 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 5.95E-02 8.09E-02 1.41E-01 3.57E-01 6.62E-01 8.35E-01 1.17E+00 1.33E+00 1.50E+00 2.00E+00 5.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

LZFHZ HZFLZ PMMA- PSU- PVC- PET- PTFE- NBSC- NBSC- NBSC- NBSC- NBSCNBSC NBSC NBSC NBSC NBSC PMM PSU PVC PET PTFE A V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. Best V.G. V.G. Best V.G. Good V.G. V.G. Good V.G. Best Best V.G. Best V.G. Good Good V.G. Good V.G. Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Bad Worse Worse Worse Worse Worse Bad Bad Worst Bad Worst Worse Worse Worst Worse Worst Bad Bad Worst Bad Worst Worse Worse Worst Worse Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst

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Table 6. Description of GSB for some Telluride glasses, Lead and Tungsten using RIPM-toolkit [52, 53] Energy Mo20 Te80 (MeV) 1.00E-03 PE 1.00E-02 PE 2.00E-02 PE 3.00E-02 PE 4.00E-02 PE 5.00E-02 PE 5.95E-02 PE 8.09E-02 PE 1.41E-01 PE 3.57E-01 CS 6.62E-01 CS 8.35E-01 CS 1.17E+00 CS 1.33E+00 CS 1.50E+00 CS 2.00E+00 CS 5.00E+00 CS 1.00E+01 PP 2.00E+01 PP 3.00E+01 PP 4.00E+01 PP 5.00E+01 PP 1.00E+02 PP 1.00E+03 PP 1.00E+04 PP 1.00E+05 PP 1.00E+06 PP

Mo30 Te70 PE PE PE PE PE PE PE PE PE CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP PP

Mo40 Te60 PE PE PE PE PE PE PE PE PE CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP PP

Mo50 Te50 PE PE PE PE PE PE PE PE PE CS CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP PP

Pb PE PE PE PE PE PE PE PE PE PE CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP PP PP

W PE PE PE PE PE PE PE PE PE PE CS CS CS CS CS CS CS PP PP PP PP PP PP PP PP PP PP

22

Sukhmanjit Singh Mann and Kulwinder Singh Mann Table 7. The GSB for double-layered shielding enclosures made from combinations of the chosen samples of five polymeric materials and Telluride Glass sample (Mo20Te80) as LZFHZ and HZFLZ orientations Energy (MeV) 1.00E-03 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 5.95E-02 8.09E-02 1.41E-01 3.57E-01 6.62E-01 8.35E-01 1.17E+00 1.33E+00 1.50E+00 2.00E+00 5.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

LZFHZ HZFLZ PMMA-PSU- PVC- PET- PTFE- TG- TG- TG- TG- TGTG TG TG TG TG PMM PSU PVC PET PTFE V.G. V.G. V.G. V.G. V.G. A V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. V.G. Best V.G. V.G. Best V.G. Good V.G. V.G. Good V.G. Best Best V.G. Best V.G. Good Good V.G. Good V.G. Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Best Best Best Best Best Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Bad Worse Worse Worse Worse Worse Bad Bad Bad Bad Bad Worse Worse Worse Worse Worse Bad Bad Worst Bad Worst Worse Worse Worst Worse Worst Bad Bad Worst Bad Worst Worse Worse Worst Worse Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst Worst

V.G.: Very Good; TG: Telluride Glass

For better GSB of DLHS, it has been established [51] that for monoenergetic photons, if the CS is dominating in layer-1 of the DLHS, then it results in lowering the value of DLEBF (Double-Layered Exposure Buildup Factor). The absorption of scattered photons in the 2nd layer of the shield by either of the PE and PP results in lowering the values of DLEBF. Moreover,

RIPM-Toolkit

23

the CS in the first layer results in the scattered photons moving in different directions, which causes increase of the interaction time for the scattered photons with the material of the 2nd layer. Thereby increases the chances of photon absorption in the 2nd layer. Thus, the value of DLEBF gets reduced.

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Figure 8. Variation of MACs, computed RIPM-toolkit for the chosen samples.

Additionally, as indicated by Figure 2 that for E≤ 0.01 MeV, the DLHS is effective as the PE interaction dominates for the high-Z material of the shield. For the high energy region (E > 0.01 MeV), the PE starts decreasing, which affects the GSB of the DLHS. At high energy, the required GSB of the shield may be achieved by increasing its thickness. Further, the increased value of thickness for the shield introduces a new problem of multiple scattering of photons. Thus, for energy regions (E > 0.01 MeV), the concept of BUF has to be included for investigation of GSB or GSE. For any GSE, the involvement of BUF makes its GSB’s investigation more complex. Alternatively, the triple layered heterogeneous shield (TLHS) seems to

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

provide better GSB than DLHS, provided that the third layer should be made from a very high-Z material. From Figure 2, it is evident that the energy difference between the boundaries which separates the RoD for PE and PP from the CS starts reducing with the increase of the atomic number (Z). In other words, the dominating energy range for the CS gets contracted with the rise in Zeff value. It has concluded that for making effective GSE for photon energies above 0.01 MeV, comparatively high-Z materials required as compared to photon energy lower than 0.01 MeV. In other words, for photon energy above 0.01 MeV, three-layered heterogeneous shields offer better GSB than DLHS. The orientation of materials in TLHS should be such that the third layer from the incident side, should be made from the substance of the highest value of Zeff. 25 PMMA PSU PVC PET PTFE NBS Concrete

20

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RIPM-Toolkit

25

Table 8. The GSB for double-layered shielding enclosures made from combinations of the chosen samples of five polymeric materials and Lead (Pb) as LZFHZ and HZFLZ orientations Energy (MeV)

LZFHZ HZFLZ PMMA- PSU- PVC- PET- PTFE- PbPb- Pb- PbPb Pb Pb Pb Pb PMMA PSU PVC PET

PbPTFE

1.00E-03 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 5.95E-02 8.09E-02 1.41E-01 3.57E-01 6.62E-01 8.35E-01 1.17E+00 1.33E+00 1.50E+00 2.00E+00 5.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

V.G. V.G. Best Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worse Worse Worse Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Bad Bad Bad Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. Best Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Bad Bad Bad Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. Good Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worse Worse Worse Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. Good Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

V.G.: Very Good; Pb: Lead

Figure 8 describes the variation in the MACs of the chosen samples with energy. It is evident from the exception that the sample PTFE offers the least values of MACs for the selected energy range. Figure 9 describes the changes in Zeff graphically for the chosen samples. It is clear from the graph that the sample PTFE offers the highest value of Zeff in comparison to the

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Sukhmanjit Singh Mann and Kulwinder Singh Mann

other chosen polymeric materials. Figure 10 describes the variations of computed values of electron density, Nel, for the chosen samples. PTFE also offers the highest value of the effective electron density for the photon energy above 0.4 MeV. Thus, it has been concluded that the GSB investigation with the help of Zeff and Nel seems easier than that of MAC for lower energy photons. Table 9. The GSB for double-layered shielding enclosures made from combinations of the chosen samples of five polymeric materials and Tungsten (W) as LZFHZ and HZFLZ orientations Energy (MeV)

LZFHZ HZFLZ PMMA- PSU- PVC- PET- PTFE- WWWWW W W W W PMMA PSU PVC PET

WPTFE

1.00E-03 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 5.95E-02 8.09E-02 1.41E-01 3.57E-01 6.62E-01 8.35E-01 1.17E+00 1.33E+00 1.50E+00 2.00E+00 5.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

V.G. V.G. Best Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worse Worse Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Worst Bad Bad Worst Worst Worst Worst Worst Worst Worst Worst

V.G.: Very Good; W: Tungsten

V.G. V.G. Best Best Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Worst Bad Bad Bad Bad Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Best Best Best Best Best Best Worst Worst Worst Worst Worst Worst Worst Bad Bad Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. Good Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

V.G. V.G. V.G. V.G. Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worse Worse Worst Worst Worst Worst Worst Worst Worst Worst

V.G. V.G. Good Good Good Good Good Good Good Good Worst Worst Worst Worst Worst Worst Worst Worse Worse Worse Worse Worst Worst Worst Worst Worst Worst

RIPM-Toolkit

27

4.00

PMMA PSU PVC PET PTFE NBSC

3.75

3.50

23

Nel (x 10 )

3.25

3.00

2.75

2.50

2.25 0.0

0.2

0.4

0.6 0.8 E (MeV)

1.0

1.2

1.4

Figure 10. Variation of Nel values, computed RIPM-toolkit for the chosen samples.

CONCLUSION It has been concluded that the SVM based computer program, RIPMtoolkit provides information regarding gamma-ray shielding behaviour (GSB) of the double-layered shielding enclosures. High prediction accuracy (99.77%) of the toolkit for the dominating photon interaction processes has been exploited to decide the GSB of double layer shielding enclosures. Both absorption and scattering phenomena influenced the GSB of an enclosure. It has been noticed that in a double-layered enclosure if gamma photon interacts dominantly via CS followed by PE then the enclosure offers the best GSB. But, if gamma photon interacts dominantly via CS in both layers of the enclosure then it offers the worst GSB. Whereas, other dominances provide the GSB in between these two extreme cases. The double-layered

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shielding enclosures made from a polymeric material and NBS concrete offer the best GSB only in the LZFHZ orientations. The best GSB offers only for gamma energies at which PE dominates in the second layer of the enclosures. It has been concluded that the double-layered enclosures made from PET with NBS Concrete, Telluride Glass, Lead, and Tungsten offer the best GSB in a wider energy range as compared to the other four polymeric materials’ combinations. The developed toolkit will be useful in the selection of materials for designing effective shielding enclosures.

ACKNOWLEDGMENTS Authors are thankful to Dr. Chih-Chung and Chih-Jen Lin for providing LIBSVM: a library for SVMs, and to Ms. Baljit Kaur (Lecturer in Physics) for the proofreading contribution to this chapter.

APPENDIX A Train_and_plot_data function [Emu,Esigma,Zmu,Zsigma,model] = train_and_plot_data(); data = load('final_data.txt'); data(:,1) = log10(data(:,1)); E_vec = data(:,1); Z_vec = 1:(size(data,2)-1); [f1 Emu Esigma] = featureNormalise(data(:,1)); [f2 Zmu Zsigma] = featureNormalise(Z_vec); hold on; fprintf("\nPlotting data..\n"); posdata = data(:,2:size(data,2)); [oneposr oneposc] = find(posdata==1); [twoposr twoposc] = find(posdata==2); [threeposr threeposc] = find(posdata==3); plot(E_vec(oneposr),Z_vec(oneposc),'r*','MarkerSize',10); plot(E_vec(twoposr),Z_vec(twoposc),'go','MarkerSize',10);

RIPM-Toolkit plot(E_vec(threeposr),Z_vec(threeposc),'b+','MarkerSize',7); ylabel("Z"); xlabel("log10E"); h = legend('Compton Scattering','Photoelectric effect','Pair Production'); set(gca,"fontsise",16); set(h,"fontsise",16); hold off; X = repmat(f1,[size(posdata,2) 1]); Zfeat = []; for i=1:size(posdata,2) Zfeat = [Zfeat;repmat(f2(i),[length(f1) 1])]; endfor X = [Zfeat X]; y = posdata(:); curr_dir = pwd(); libr_dir = strcat(pwd(),'\libsvm-3.23\libsvm-3.23\matlab'); cd(libr_dir); fprintf("\nTraining data using LIBSVM..\n"); model = svmtrain(y,X,'-t 2 -c 15 -g 0.8 -q'); fprintf("\nTraining finished..\n"); res = svmpredict(y,X,model); cd(curr_dir); %acc = sum(res==y)/length(y); endfunction

APPENDIX B Main Programme clear; clc; close all; [Emu Esigma Zmu Zsigma model] = train_and_plot_data(); cont_val = 1; fprintf('\nNote: The output is more accurate for the energy range 0.001 MeV 100000 MeV\n'); element_names = importdata('elements.txt'); atomic_masses = load('Atomic_masses.txt'); while cont_val

29

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userans = input("\nEnter e for element and m for mixture: ","s"); if (userans == "e") Z_input = 1; while Z_input; user_element = input("\nEnter the symbol of the element: ","s"); Z = find(strcmp(user_element,element_names)); if size(Z,1) == 1 Z_input = 0; Zfeat = (Z-Zmu)/Zsigma; E_input = 1; while E_input user_energy = input("\nEnter the energy of photon(MeV): ","s"); E = str2double(user_energy); if E != NaN Efeat = (log10(E)-Emu)/Esigma; cur_dir = pwd(); lib_dir = strcat(pwd(),'\libsvm-3.23\libsvm-3.23\matlab'); cd(lib_dir); predicted_class = svmpredict(0,[Zfeat Efeat],model,'-q'); cd(cur_dir); if predicted_class == 1 fprintf("\nMajority of photons will experience Compton Scattering\n"); else if predicted_class == 2 fprintf("\nMajority of photons will experience Photoelectic Effect\n"); else if predicted_class == 3 fprintf("\nMajority of photons will experience Pair Production\n"); endif endif endif user_decision = yes_or_no("\nDo you want to check it for another energy? "); if user_decision E_input = 1; else E_input = 0;

RIPM-Toolkit user_decision = yes_or_no("\nDo you want to enter another? "); if not(user_decision) cont_val = 0; endif endif else fprintf("\nPlease enter a valid energy value in MeV\n"); endif endwhile else fprintf("\nPlease enter a valid element symbol\n"); endif endwhile else if userans == "m" num_elements_input=1; while num_elements_input mix_num_elements = input("\nEnter number of elements: ","s"); mix_num_elements = floor(str2num(mix_num_elements)); if size(mix_num_elements,1) == 1 & mix_num_elements>0 num_elements_input = 0; mix_elements = zeros(num_elements_input,3); for i=1:mix_num_elements element_input = 1; while element_input element = input(strcat("\nEnter symbol of element number"," ",num2str(i)," : "),"s"); Z = find(strcmp(element,element_names)); if size(Z,1) == 1 if Z>109 fprintf("\nPlease enter elements with Z=110 are not available\n"); else element_input = 0; mix_elements(i,1) = Z; mix_elements(i,2) = atomic_masses(Z); atomicity_input = 1;

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while atomicity_input atomicity = input(strcat("\nEnter atomicity of element number"," ",num2str(i)," : "),"s"); atomicity = floor(str2num(atomicity)); if size(atomicity,1) == 1 mix_elements(i,3) = atomicity; atomicity_input = 0; else fprintf("\nPlease enter valid atomicity\n"); endif endwhile endif else fprintf("\nPlease enter a valid element symbol\n"); endif endwhile endfor Zeq = calculateZeq(mix_elements); fprintf("\nEquivalent Atomic number of the sample: %f\n",Zeq); Zfeat = (Zeq-Zmu)/Zsigma; E_input = 1; while E_input user_energy = input("\nEnter energy of photon(MeV): ","s"); E = str2double(user_energy); if E!=NaN Efeat = (log10(E) - Emu)/Esigma; cur_dir = pwd(); lib_dir = strcat(pwd(),'\libsvm-3.23\libsvm-3.23\matlab'); cd(lib_dir); predicted_class = svmpredict(0,[Zfeat Efeat],model,'-q'); cd(cur_dir); if predicted_class == 1 fprintf("\nMajority of photons will experience Compton Scattering\n"); else if predicted_class == 2 fprintf("\nMajority of photons will experience Photoelectic Effect\n"); else

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if predicted_class == 3 fprintf("\nMajority of photons will experience Pair Production\n"); endif endif endif user_decision = yes_or_no("\nDo you want to check it for another energy? "); if user_decision E_input = 1; else E_input = 0; user_decision = yes_or_no("\nDo you want to enter another? "); if not(user_decision) cont_val = 0; endif endif else fprintf("\nPlease Enter valid energy(MeV)\n"); endif endwhile else fprintf("\nPlease enter valid number of elements\n"); endif endwhile else fprintf("\nPlease enter e or m\n"); endif endif endwhile

REFERENCES [1]

ICRP Publication 60, “Recommendations of the International Commission on Radiological Protection,” Pergamon Press, Elmsford, NY, 1990.

34 [2] [3] [4] [5] [6]

[7]

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[9]

[10]

[11] [12]

[13]

Sukhmanjit Singh Mann and Kulwinder Singh Mann NCRP Report No. 116, “National Council on Radiation Protection and Measurements,” Bethesda, Maryland, 1993. Fallout Protection, “What to know and do about nuclear attack,” Department of defense-office of civil defence, USA, 1961. Davisson, C.M., Evans, R.D., “Gamma-Ray absorption coefficients,” Rev. Mod. Phys.24, pp. 79-107., 1952. Barkla, C.G., Sadler, C.A., “The absorption of Röntgen rays,” Phil. Mag., 17, pp. 739-760., 1909. Chadwick, M.B., Oblozinsky P., Herman M., et al., “ENDF/B-VII.0: Next generation evaluated nuclear data library for nuclear science and technology,” Nucl. Data Sheets 107, pp. 2931–3060, 2006. Hubbell, J.H., “Bibliography of photon total cross-section (attenuation coefficient) measurements 10 eV to 13.5GeV,” NISTIR 5437, pp. 1907–1993., 1994. Hubbell, J.H., “Experimentally measured total X-ray attenuation coefficients extracted from previously unprocessed documents,” NIST photon and charged particle data centre NISTIR 5893, 1996. Hubbell, J.H., “Summary of existing information on the incoherent scattering of photons, particularly on the validity of the use of the incoherent scattering function,” Radiat. Phys. Chem., 50, pp. 113– 124., 1997. Hubbell, J.H., Seltzer, S.M., “Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients 1 keV to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest,” NISTIR 5632., 1995. Hubbell, J.H., “Review of photon interaction cross-section data in the medical and biological context,” Phys. Med. Biol., 44, pp. 1–22., 1999. Hubbell, J.H., “Experimentally measured total X-ray attenuation coefficients extracted from previously unprocessed documents held by the NIST Photon and Charged Particle Data Centre,” NISTIR 7163, 2004. Chantler, C.T., “New theoretical investigation resolving discrepancies of atomic form factors and attenuation coefficients in the near-edge soft X-ray regime,” Radiat. Phys. Chem., 61, pp. 343–345, 2001.

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[14] Shivaramu, “Effective atomic numbers for photon energy absorption and photon attenuation of tissues from human organs,” Med. Dosim., 27, pp. 1–9., 2002. [15] Akkurt, I., Kilincarslan, S., Basyigit, C., “The photon attenuation coefficients of barite, marble and limra,” Ann. Nucl. Energy, 31(5), pp. 577–582., 2004. [16] Akkurt, I., Basyigit, C., Kilincarslan, S., Mavi, B., “The shielding of γ-rays by concretes produced with barite,” Prog. Nucl. Energy, 46, pp. 1–11., 2005. [17] Manohara, S.R., Hanagodimath, S.M., “Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1 keV–100 GeV,” Nucl. Instrum. Methods B, 258, pp. 321-328., 2007. [18] Içelli, O., Mann, K.S., Yalçın, Z., Orak, S., Karakaya, V., “Investigation of shielding properties of some boron compounds,” Annals of Nuclear Energy, 55, pp. 341–350, 2013. [19] Sahin, A., and Un, Y., “Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores,” Nucl. Instrum. Methods B, 269, pp. 1506-1511, 2011. [20] Kurudirek, M., Sardari, D., Khaledi, N., Cakır, C., Mann, K.S., “Investigation of X- and gamma-ray photons buildup in some neutron shielding materials using G-P fitting approximation,” Ann. Nucl. Energy, 53, pp. 485–491, 2013. [21] Kavanoz, H.B., Yagci, O., Yalçın, Z., Içelli, O., Altındal, A., Okutan, M., Mann, K.S., “Photon parameters for γ-rays sensing properties of some thick oxide films,” Vacuum, 101, pp. 238-245, 2014. [22] Mann, K.S., Rani, A., Heer, M.S., “Shielding behaviours of some polymer and plastic materials for gamma rays,” Radiat. Phys. Chem., 106, pp. 247-254, 2015. [23] Mann, K.S., Heer, M.S., Rani, A., “Effect of Low-Z absorber‫׳‬s thickness on gamma-ray shielding parameters,” Nucl. Instrum. Methods A, 797, pp. 19-28, 2015.

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[24] Hine, G., “The effective atomic numbers of materials for various gamma-ray interactions,” Phy. Rev., 85, pp. 725-737, 1952. [25] Manohara, S.R., Hanagodimath, S.M., Gerward, L., “Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates,” Phys. Med. Biol., 53, pp. 377-386, 2008. [26] White, G.R., “The penetration and diffusion of 60Co gamma rays in water using spherical geometry,” Phys. Rev., 80 (2), pp. 154-156, 1950. [27] ANSI/ANS 6.4.3, “Gamma-ray attenuation coefficients and buildup factors for engineering materials,” American Nuclear Society, LaGrange Park, Illinois, 1991. [28] Berger, M.J., Hubbell, J.H., “XCOM: Photon cross- sections database, Web version1.2,” Natl. Ins. Standards Tech., Gaithersburg, MD 20899, originally published as NBSIR, 87, 3597., 1987. [29] Nowotny, R., “XMuDat: Photon attenuation data on PC.,” IAEA Report IAEA-NDS 195, 1998. [30] Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., “X-ray absorption in matter, Reengineering XCOM,” Radiat. Phys. Chem., 60, pp. 23-24, 2001. [31] Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., “WinXCom – A programme for calculating X-ray attenuation coefficients,” Radiat. Phys. Chem., 71, pp. 653–654., 2004. [32] Okunade, A., “Parameters and computer software for the evaluation of mass attenuation,” Journal of Medical Physics, 32, pp. 124-132., 2007. [33] Taylor, M.L., Smith, R.L., Dossing, F., Franich, R.D., “Robust calculation of effective atomic numbers: The Auto-Zeff software,” Med. Phys. 39 (4), pp. 1769-1778, 2012. [34] Un, A., and Caner, T., “The Direct-Zeff software for direct calculation of mass ate nuation coefficient, effective atomic number and effective electron number,” Ann. Nucl. Energy, 65, pp. 158–165, 2014. [35] Eyecioglu, O., Karabul, Y., El-Khayatt, A.M., İçelli, O., “ZXCOM: a software for computation of radiation sensing attributes,” Radiation Effects and Defects in Solids,171:11-12, pp. 965-977, 2016.

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[36] Mann, K.S., Heer, M.S., Rani, A., “The Study of the Compaction Effect on Gamma-Ray Shielding,” International Journal of Pure and Applied Physics, 13(1), pp. 96-99, 2017. [37] Mann, K.S., Heer, M.S., Rani, A., “Gamma-ray double-layered transmission exposure buildup factors of some engineering materials, a comparative study,” Radiat. Phys. Chem., vol. 125, pp. 27–40, 2016. [38] Mann, K.S., “Measurement of exposure buildup factors: The influence of scattered photons on gamma-ray attenuation coefficients,” Nucl. Instrum. Methods A, 877, pp. 1-8, 2018. [39] Eyecioǧlu, Ö., El-Khayatt, A.M., Karabul, Y., Çağlar, M., Toker, O., İçelli, O., “BXCOM: a software for computation of radiation sensing,” Radiation Effects and Defects in Solids, 174:5-6, pp. 506-518, 2019. [40] Şakar, E., Özpolat, O.F., Alim, B., Sayyed, M.I., Kurudirek, M, “PhyX/PSD: Development of a User Friendly Online Software for Calculation of Parameters Relevant to Radiation Shielding and Dosimetry.” Radiation Physics and Chemistry,” Radiation Physics and Chemistry, 166, pp. 108496, 2020. [41] Vapnik, V., Lerner, A., “Pattern recognition using generalised portrait method.,” Autom. Rem. Contr., pp. 24, 774–780., 1963. [42] Furey, T.E.A., “Support vector machine classification and validation of cancer,” Bioinformatics, pp. 16, 906–914., 2000. [43] Heisele, B., Serre, T., Prentice, S., Poggio, T., “Hierarchical classification and feature reduction for fast face detection with support vector machines,” Pattern Recogn, pp. 36, 2007-2017, 2003. [44] Simon, T., Daphne, K., “Support vector machine active learning with applications to text classification.,” J. Mach. Learn. Res., pp. 45–66., 2001. [45] Grigorev, A., “Support Vector Machines,” 2013. [Online]. [46] Chih-Chung Chang and Chih-Jen Lin, “LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2:27:1--27:27,” 2011. [Online]. Available: http://www. csie.ntu.edu.tw/~cjlin/libsvm. [47] Battistoni, G., Boehlen, T., Cerutti, F., et al., “Overview of the FLUKA code,” Annal. Nucl. Ener., no. 82, pp. 10–18, 2015.

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[48] Sharma, A., Singh, B., Sandhu, B.S., “Investigation of photon interaction parameters of polymeric materials using Monte Carlo simulation,” Chinese Journal of Physics, 60, pp. 709-719, 2019. [49] Siegbahn, K., Alpha, Beta and Gamma-Ray Spectroscopy, NorthHolland, Netherlands: Amsterdam, 1965. [50] Evans, R.D., The Atomic Nucleus, New York: McGraw-Hil, 1955. [51] Mann, K.S., Heer, M.S., Rani, A., “Gamma-ray double-layered transmission exposure buildup factors of some engineering materials, a comparative study,” Radiat. Phys. Chem., 125, pp. 27–40, 2016. [52] Al-Buriahi, M S, Mann, K.S, “Radiation shielding investigations for selected tellurite based glasses belonging to the TNW system,” Materials Research Express, vol. 6, no. 10. [53] Abu AlRoos, N.J., Amin, N.A.B., Zainon, R., “Conventional and new lead-free radiation shielding materials for radiation protection in nuclear medicine: A review,” Radiat. Phys. Chem., vol. 165, no. 108439, 2019. [54] Campbell, W.M., Campbell, J.P., Reynolds, D.A., Singer, E., TorresCarrasquillo, P.A., “Support vector machines for speaker and language recognition.,” Comput., pp. 20, 210–229., 2006. [55] Mann, K.S., Heer, M.S., Rani, A, “Investigation of clay bricks for storage facilities of radioactive-wastage,” Appl. Clay Sci., 119, pp. 249–256, 2016.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 2

FLUKA: A COMPETENT CODE FOR SHIELDING CHARACTERISTICS Amandeep Sharma* Department of Physics, Akal University Talwandi Sabo (Bathinda), Punjab, India

ABSTRACT The present chapter aimed to report the validation of FLUKA Monte Carlo code for estimation of various shielding parameters. The appropriate method to examine new shielding materials, having capacity to keep the radiations at minimum permissible level, is literally crucial for the safety of the general public as well as the workers who are occupationally exposed to penetrating radiations. The capability, geometry layout, scoring commands of FLUKA along with computed values of mass attenuation coefficients, mean free paths, half value layers and effective atomic numbers have been approved by making the comparison with experimental, Geant4 and XCOM reference databases. The new composite materials like heavy metal based glass systems (MoO3-B2O3-Bi2O3, Li2OB2O3-P2O5-TeO2), polymeric materials (Bakelite, Polypropylene, *

Corresponding Author’s Email: [email protected].

40

Amandeep Sharma Polysulfone, Polystyrene, Polyethylene terephthalate, Polytetrafluoroethylene) and polyester concretes (BiClO: 5-20%) have been considered for their usefulness as alternative shielding materials. The shielding competence of chosen materials has been reported over useful Gamma-ray energy range, between 59.5 – 1408 keV, for designing of new radiation protection set-ups. The good agreement among the FLUKA outputs and other available methods validates FLUKA’s high competency for shielding investigations, particularly when it is hard to arrange an experiment. Based upon the computation of different parameters, it is concluded that the samples namely MoBBi-4, LiBPTe-40, BiClO (20%) and Polytetrafluoroethylene (PTFE) are the best shielding compositions among the respective categories of examined materials.

Keywords: radiation shielding, gamma photons, FLUKA simulations

INTRODUCTION The Monte Carlo methods involve calculating the probable or average behaviour of a system by observing the outcomes of a large number of trials at a game of chance that simulates the physical events accountable for the behaviour. Every trial of the game of possibility is played out on a computer according to the values of a series of random numbers. Monte Carlo based computations are a standard method in basic as well as many emerging areas of research. Such simulations are essential to construct forecasts about real experiments. Computations in radiation related fields are becoming more and more accepted with development of new simulation methods. Monte Carlo based methods play an increasingly vital role in modelling the interaction of radiations/particles with the material of interest. The increasing use of efficient simulations in shielding, dosimetry and other related fields is possible due to the advancement of computer technology and better computational power of modern computers. There are many packages (codes) with various distinctiveness and opportunities, whose execution relies on Monte Carlo methods. The brief features of FLUKA software package, which has been employed for shielding investigations, are described in this chapter. The basic physics, geometry and input/output of FLUKA are reviewed, along with the detailed

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results obtained with code. FLUKA (FLUktuirende KAskade) refers to a general purpose Monte Carlo code that records the simulation of transportation of more than 60 particles (such as electrons, neutrons, neutrino, photons, heavy ions and muons) and is developed with collaboration among CERN and INFN. Its original application was in shielding of accelerator, however in the past years it has been also developed as a tool for covering an extended range of applications spanning from electron and proton accelerator shielding to target design, activation, calorimetry, dosimetry, neutrino physics and radiotherapy etc. (Ballarini et al. [1]; Böhlen et al. [2]; Battistoni et al. [3]). In view of the above capabilities of FLUKA, this chapter reports the validation of FLUKA Monte Carlo code for estimation of shielding features of new composite materials exclusively for gamma rays. The main benefit of the approach is that it permits to investigate various geometries/primary particles without performing high cost experiments. Nowadays, radiation technology is widely used in radiology departments of hospitals, nuclear power plants, nuclear research, agriculture and industry sectors. Since gamma-ray emitting sources are mainly involved in these places therefore it is of crucial importance to protect the humans living/working in close vicinity of these areas from the hazardous effects of highly penetrating radiation. As composition of any shielding material is one of the most effective considerations to protect against dangerous effects of highly energetic radiation. Thereby, determination of various quantities concerned on the passage of ionising radiations through any shielding composition is of critical interest. Heavy metals such as lead are usually used for safety against X-rays or gamma rays as they have high mass densities. However, there are numerous disadvantages related to these conventional materials. The toxic nature of lead, causes adverse effects on human health and environment. Due to metal’s heaviness, low chemical stability and Bremsstrahlung production during electron interaction, it has become a main concern to find new materials that can successfully replace usual lead based shielding materials. Recently, radiation shielding features of many natural or synthetically produced materials, such as clay (Olukotun et al. [4]), concretes (Agar et al.

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[5]; Hernandez-Murillo et al. [6]), glasses (Al-Buriahi et al. [7]), alloys (Akman et al. [8]) and double-layered enclosures (Mann [9]) have been reported by different researchers successfully.

PHYSICS AND CAPABILITY OF FLUKA FOR PHOTON INTERACTIONS In any Monte Carlo code it is possible to assign basic essentials like a database library, the generator of random numbers, the description of geometry etc. FLUKA is able to simulate transportation of various particles (electromagnetic as well as hadronic) varying in energy from few keV (thermal neutrons) to cosmic ray energies in any target material. The code features at intermediate energies make it reliable in treating in the field of dosimetry and radiation protection. The transport of photons and electrons in this code handles all the scattering processes as well, including photon nuclear interactions (Fasso et al. [10]). For every kind of particle, a set of relative effects are taken into account regarding all the possible interactions. The algorithm used by FLUKA for photons is able to depict: 1. Photoelectric effect with detailed interaction on K and L sub-shells, emission of fluorescence photons and Auger electron treatment 2. Pair production with angular distribution of positrons and electrons 3. Coherent (Rayleigh) scattering and incoherent (Compton) scattering by considering binding effects and orbital motion of electrons 4. Polarisation of photons for Photoelectric, Rayleigh and Compton scattering 5. Landau-Pomeranchuk-Migdal pair production suppression 6. Photo Hadron production In FLUKA, the continuous processes (such as energy loss and angular deflections due to Coulomb interactions) and discrete processes (photon interactions, delta-ray production) are treated separately. The strength of this

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code lies in its physical models, the detailed analysis of models implemented in FLUKA can be found elsewhere (Ferrari et al. [11]). The validity of these physical models has been benchmarked against a range of experimental data over a broader energy.

INPUT/OUTPUT IN FLUKA The user according to the set of instructions in the FLUKA fixed format constructs an input file. In FLUKA vocabulary, a line of an input file refers to cards or options utilised by the code. Each card consists of the name, oneline parameter and from one up to six numerical parameters. The input file of simulation is an ASCII file with an extension. inp. The title along with comments is written firstly followed by description of geometry, materials, particle source, detector, biasing scheme, energy cut-offs, initialisation of random number sequence, number of requested histories etc. (Ferrari et al. [11]).

Available Input Options In FLUKA, there are more than 80 commands for the user to arrange the desired input file. A few of the useful options, for the design of a simple simulation set up, are;     

BEAM: defines the beam energy, divergence, particle type BEAMPOS: defines the beam direction and starting point of particles DETECT: scores energy deposition in anti-coincidence and coincidence, on an event by event basis EMF: detailed transportation of photons, positron and electron EMFCUT: decides energy cut-offs for particles or for switching off some interactions

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Amandeep Sharma   

GEOEND: geometry description ends MATERIAL: defines a material along with its properties SOURCE: to invite a user-written source routine

Although there are building scoring cards to estimate requested quantities, FLUKA also has various routines to recover information from different processes. For more difficult situations, generally a dedicated ‘user routine’ is preferred. FLUKA input files consist of a number of data commands, each consisting of one or more lines in the file.

Radiation Source through FLUKA The command BEAM is employed to define particle energy, type, angular divergence and beam profile shape. The energy defined by BEAM is used by the programme to initialise cross-section data. In absence of BEAMPOS, the beam particles are supposed to start from origin and to be directed along the Z-axis. The two commands namely BEAMPOS and BEAM can be placed anywhere but before the START command. Additional features like angle, space, time and more than one type of particles can be defined through user-written subroutine SOURCE.

Geometry Layout An improved version of Combinatorial Geometry (C. G.) package is employed to handle complex geometries. The input for this C. G. must be preceded and followed by GEOBEGIN and GEOEND cards respectively. The bodies in C. G. are defined as convex solid bodies along with extension to include infinite cylinders and planes. Regions are defined as combinations of bodies and each region must be of homogeneous material composition. All the regions must be enclosed by a surrounding blackhole (an infinitely absorbing material to end particle trajectories), limited by a closed body. The size of this body is chosen much bigger than the minimum necessary size

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for further extension of geometry. If the flight of primary particles starts outside the physical geometry, then it may be useful to enclose the actual geometry by a region of ideal vacuum and to have the blackhole region enclosing the vacuum. A typical layout of the target geometry (with different views) surrounded by blackhole region is shown in Figure 1. The region input as well as the body input part must be ended with END card.

Matter Identification An element can either be defined or pre-defined by a MATERIAL card giving its name, atomic weight, atomic number and density etc. A user can either refer to any of the pre-defined material, or override it with a new name and number, or define a new material. If a material is not a single isotope or element but a mixture, compound or alloy is defined by a MATERIAL card plus as many Compound cards as required to express its composition. After assigning all the materials to various geometry regions, it is essential to specify which material each region is made of, by setting a correspondence between material index to region number. This is done by a command named ASSIGNMAT. Another option concerning the definition of materials is MAT-PROP. It is used for a variety of purposes like to describe inhomogeneous or gas materials and to dominate the default average ionisation potential etc.

Energy Cut-Offs The correct tuning of cut-off energies for particles (transported and produced) is another important aspect. Transport cut-offs are set with card EMFCUT for photons, positrons and electrons. This is non-physical and it is provided mainly for a particular purpose where the user wants to switch off selectively a physical process. Due to the difficulty in well defining the range of electrons, EMFCUT assigns transport threshold on a region basis for the particles.

Figure 1. Flair screenshot for a typical geometry (target thickness 1 cm).

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47

Scoring Commands In addition to the output file, many scoring possibilities are available by way of SCORE cards. FLUKA simulations can score particle current, fluence, energy spectra, track length, energy and dose deposition etc. Some of the useful cards being used for this purpose are:   



USRBDX: score average of double differential fluence of a given type of particles in a given region USRBIN: scores the spatial distribution of total fluence or energy deposited in a regular mesh described by user USRYIELD: scores a double differential yield of particles escaping from a surface. The distribution can be with respect to angle and energy or other specific quantities. USRTRACK/USRCOLL: scores average of differential fluence of a given type of particles in a given region

It is worth mentioning here that almost all the FLUKA estimators (USRBIN, USRBDX etc.) give results normalised per primary particle. Thus, they neither depend on the number of cycles nor on the number of primaries in the START card.

FLUKA Output The output of FLUKA consists of standard output, a scratch file, a file with last random number seeds, a file of error messages, number of estimator output files and additional output generated by user through user routine etc. The main/standard output file contains ample of information about the executed run (not limited to): 1. FLUKA banner page and licence information 2. A header mentioning FLUKA version and time of output printing 3. A straight echo of the input commands

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Amandeep Sharma 4. 5. 6. 7. 8. 9.

Basic information of physical models and nuclear data files Matter characteristics regarding multiple scattering Allocation of memory information Ionisation energy losses, Bremsstrahlung and transport threshold Detailed summary of input and scoring Initial energy deposited/lost on every region of simulation

In case of any error during the simulation process, the file with extension .err is helpful to users for rectifying the input. Every error message starts with the name of the routine through which it originated. However, some messages are also printed on the main output.

COMPUTATION AND VALIDATION OF SHIELDING PARAMETERS The important shielding parameters (such as mass attenuation coefficient, half value layer, mean free path and effective atomic number) for some new composite materials obtained with FLUKA has been reported in this section. The validation of FLUKA results for newly developed glass systems, polymeric materials and polyester concretes have been checked against experimental data/Geant4/XCOM database. The brief review of FLUKA based simulations for estimation of shielding parameters of newly developed composites is described below:

Simulation Method FLUKA Monte Carlo code version 2011.2c, installed on Linux Mint 19, has been utilised for the computations of various shielding characteristics. The energy and direction of propagation of transporting photons is conveniently chosen through BEAM command. A cubic sample-material was designed through Flair (Vlachoudis [12]), by setting photons

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49

propagating along the Z-axis. A beam of 105 Gamma particles with selected momentum/energy were incident during a typical run on shielding material of desired composition. The designed cubic composite material causes the attenuation of the incident photons. In the present work, the minimum and maximum limits of the sample boundaries were set at -5 cm and +5 cm each for X as well as Y directions (shown in Figure 2). This results in 10 cm height as well as breadth of material under investigation, with desired (variable) thickness. The attenuation results with the assistance of USRBDX score card, appropriate to define a detector for fluence estimation, have been obtained for five cycles with respect to material thicknesses chosen. A MATERIAL card as well as Compound card has been used to simulate a typical composition of shielding material. All simulation data obtained by FLUKA code were reported with less than 1% uncertainty.

Figure 2. Target geometry chosen for simulations.

FLUKA and Experimental Data of MoO3-B2O3-Bi2O3 Glasses The new composite materials (like glass matrices, polyester concretes, polymers etc.) have an increasing attention as innovative and alternatives in radiation protection. In recent years, there are numerous reports on shielding performances as well as structural, mechanical and physical features of new

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glass systems (Al-Buriahi et al. [7]; Sharma et al. [13]). The mass attenuation coefficients of new composite materials chosen for this study has been determined according to Lambert-Beer’s law, I = Ioexp (-μx), where Io and I are incident and transmitted intensity of gamma photons, μ is called the linear attenuation coefficient and x is the thickness (cm) of the material chosen. Sometimes it is effective to use mass attenuation coefficient (μm = μ/ρ), where ρ is the density of concerned material. It equals the probability of quantum interaction with a column of material with crosssection equal one squared cm2 cm and mass of one gram. The composite glass system MoO3-B2O3-Bi2O3 is chosen for estimation of µm values at four different energies by making use of FLUKA and validation of the results have been done by comparing the results with experimental obtained data (details reported by Sharma et al. [13], Sayyed et al. [14]). The simulated and experimental results obtained have been enlisted in Table 1(a) and plotted for MoBBi-1 in Figure 3. Moreover, the relative difference ([FLUKA- Expt]/ Expt * 100) between the FLUKA and experimental values are calculated and are summarised in Table 1(b) and obtained values have been shown through Figure 4. Table 1. (a) Mass attenuation coefficients (cm2/g) of the MoO3-B2O3Bi2O3 glass system obtained through FLUKA and experiment (Sayyed et al. [14]). The values given in round brackets of sample code indicates mol% of MO3, B2O3 and Bi2O3 respectively Glass Sample (mol %) MoBBi-1 (20,50,30) MoBBi-2 (20,45,35) MoBBi-3 (20,40,40) MoBBi-4 (20,35,45)

356 keV 662 keV 1173 keV 1330 keV FLUKA Expt. FLUKA Expt. FLUKA Expt. FLUKA Expt. 0.2213 0.2136 0.0977 0.0977 0.0603 0.0594 0.0553 0.0549 0.2287

0.2201 0.0992

0.0986 0.0604

0.0603 0.0555

0.0554

0.2350

0.2234 0.1005

0.0996 0.0604

0.0605 0.0556

0.0555

0.2397

0.2302 0.1015

0.1011 0.0605

0.0610 0.0555

0.0556

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Table 1. (b) Relative difference (%) between FLUKA experimental data Glass Sample MoBBi-1 MoBBi-2 MoBBi-3 MoBBi-4

356 keV 3.60 3.91 5.19 4.13

662 keV 0 0.61 0.90 0.40

1173 keV 1.52 0.17 -0.17 -0.82

1330 keV 0.73 0.18 0.18 -0.18

Figure 3. Comparison of mass attenuation coefficients of MoO3-B2O3-Bi2O3 glass system (MoBBi-1) obtained through FLUKA and experiment.

The comparison of data shown in Table 1(a), (b) and Figures 3, 4 showed that the µm values obtained through FLUKA are very close with those measured experimentally. Moreover, the relative difference between the two methods is very small in the range of 0-3.6% (for MoBBi-1), 0.17-3.91% (for MoBBi-2), 0.17-5.19% (MoBBi-3) and 0.18-4.13 % (for MoBBi-4) respectively. This small percentage difference, for the samples prepared over the useful energy range, implies that the values of µm can be predicted for the new glass systems utilising the FLUKA simulated geometry without need of actual lab experiment set up. It has also been observed that higher amounts of Bi2O3 results into increase of the values of µm i.e., more attenuation tendency and hence superior is the shielding material in this type of glass composition.

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FLUKA and Geant4 for LiBPTe Glass System The shielding potential of another category of glass system namely borophosph tellurite glasses (100-x) [0.5Li2O-0.1B2O3-0.4P2O5]-xTeO2 (x = 0, 10, 20, 30, 40 mol%) has also been investigated through FLUKA code. In order to validate the FLUKA results against another Monte Carlo code, the µm values obtained through FLUKA were plotted against the results of Geant4. The samples chemical composition and values of µm obtained through FLUKA code is presented in Table 2, along with the results obtained from Geant4 (Askin et al. [15]). It can be observed from Table 2, there is a good agreement between the values of µm obtained by the two simulation codes (i.e., FLUKA and Geant4) for all the samples chosen for the study. As an example, for 60[0.5Li2O-0.1B2O3-0.4P2O5]-40TeO2 glass sample, FLUKA and Geant4 results of µm has been plotted against each other for comparison and the correlation theory confirms the linearity of FLUKA and Geant4 results (Figure 5). The coefficient of correlation (r = 0.998) is very close to 1, which indicates that µm values by FLUAK and Geant4 simulations are in good agreement with each other. The shielding related parameter, contrary to the linear absorption factor, called mean free path (1/μ) is defined as the average distance between the two successive interactions of photons in which the intensity of incident particle is attenuated by the factor of 1/e. This parameter has been computed from linear attenuation coefficient obtained through FLUKA code. Among the investigated tellurite glasses, the sample with 40% mol. fraction of TeO2 (i.e., LiBPTe-40) possesses a minimum value of mean free path at all the selected energies (356, 662, 1173 and 1330 keV). The comparison of mean free path of samples with different amounts of tellurite as a function of photon energy has been shown in Figure 6. Moreover, it has also been observed that the mean free path of ordinary concrete is higher than that of tellurite based glasses, thus they possess better shielding features than ordinary concretes.

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53

Figure 4. Relative difference for FLUKA and experimental results of µm.

Table 2. Comparison of mass attenuation coefficients (cm2/g) of Li2OB2O3P2O5-TeO2 glass system obtained through FLUKA and Geant4 simulations (Askin et al. [15]). The values given in round bracket of sample name are mol % of Li2O, B2O3, P2O5, TeO2 respectively Glass Sample (mol%) LiBPTe-0 (50,10,40,0) LiBPTe-10 (45,9,36,10) LiBPTe-20 (40,8,32,20) LiBPTe-30 (35,7,28,30) LiBPTe-40 (30,6,24,40)

356 keV 662 keV 1173 keV 1330 keV FLUKA Geant4 FLUKA Geant4 FLUKA Geant4 FLUKA Geant4 0.0982 0.1021 0.0756 0.0817 0.0575 0.0554 0.0538 0.0525 0.1171

0.1024

0.0783

0.0756 0.0575

0.0542 0.0536

0.0536

0.1329

0.1080

0.0810

0.0761 0.0576

0.0569 0.0538

0.0503

0.1457

0.1152

0.0834

0.0773 0.0576

0.0552 0.0537

0.0510

0.1576

0.1114

0.0854

0.0733 0.0575

0.0554 0.0539

0.0517

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Figure 5. Linearity between the mass attenuation coefficients for 60 [0.5Li2O 0.1B2O3-0.4P2O5]-40TeO2 sample simulated by FLUKA and Geant4 code.

Figure 6. Comparison of mean free path as a function of energy.

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55

FLUKA and Experimental Data of Polyester Concretes In view of the demand for new lightweight materials, the reinforced unsaturated polyesters, for which filler used is Bismuth (III) Oxychloride, have been examined for their effectiveness as an alternative shielding material with reduced heaviness. The accurate findings of shielding parameters for newly proposed polyester based concretes are quite helpful for the workers to improve their conventional shielding designs. The FLUKA based data for mass attenuation coefficients have been reported for useful gamma photon energy range (covering a wider range of 59.54 – 1408 keV). The polymer concretes with concentration by weight 5%, 10%, 15%, and 20% of Bi have been prepared (details are available in author’s previous work, Sharma et al. [16]). The detailed elemental compositions of prepared BiClO concretes have been presented in Table 3. The obtained values of µm, both from FLUKA and experiment are given in Table 4a and 4b. The agreement of experimental findings authenticates the FLUKA code for determination of shielding parameters of polyester concrete. The values of important shielding parameters named half value layer (HVL) are also computed, from the relation ln2/μ, for the FLUKA data. From Table 5 and Figure 7, HVL values at different energies, it can be clearly concluded that as the energy values varies from 59.5 keV to 1408 keV, the HVL values confirm an increase. This result implies that with increase of the energy of gamma photons makes them more capable for penetrating through polymer concretes under examination. The results also illustrate that the HVL for the highest density (ρ=1.429 g/cm3) polymer concrete i.e., BiClO (20%) (possessing the highest weight fraction of Bi) is lower than other samples (BiClO (15%), BiClO (10%) and BiClO (5%)). For instance, at 276.3 keV, the thickness of BiClO (5%) is 4.08 cm to reduce the photon intensity to 50%, while BiClO (20%) needs to be 3.04 cm in thickness for the same reduction. Moreover, the HVL for the same two samples (5% and 20%) at 1408 keV are 9.39 cm and 8.74 cm respectively. These values show how the shielding efficiency of the prepared polymer

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concretes, with different Bi content, is inversely proportional to their density. Table 3. The elemental compositions and densities of prepared BiClO concretes Sample BiClO (5%) BiClO (10%) BiClO (15%) BiClO (20%)

Compositions (%) Co C 0.0271 56.9947 0.0260 54.5274 0.0249 52.2649 0.0239 50.1826

O 34.2837 33.0655 31.9484 30.9203

H 4.4475 4.2550 4.0785 3.9160

Bi 3.6309 6.9475 9.9888 12.7878

Cl 0.6160 1.1786 1.6946 2.1694

Density (g/cm3) 1.322 1.383 1.408 1.429

Table 4a. Comparison of µm values of BiClO (5% and 10%) polyester concretes Energy (keV) 59.5 80.9 122.1 136.4 276.3 302.8 356.0 383.8 511.0 661.6 778.9 834.8 867.3 964.1 1085.8 1112.1 1173.2 1212.9 1274.5 1299.1 1332.5 1408.0

BiClO (5%) FLUKA 0.3762 0.2516 0.2718 0.2360 0.1286 0.1172 0.1108 0.1072 0.0925 0.0819 0.0756 0.0724 0.0715 0.0673 0.0643 0.0631 0.0617 0.0605 0.0588 0.0581 0.0576 0.0558

Experimental 0.3787 ± 0.0078 0.2539 ± 0.0052 0.2798 ± 0.0062 0.2467 ± 0.0131 0.1258 ± 0.0046 0.1189 ± 0.0029 0.1067 ± 0.0022 0.1020 ± 0.0033 0.0944 ± 0.0019 0.0804 ± 0.0017 0.0749 ± 0.0020 0.0711 ± 0.0018 0.0729 ± 0.0028 0.0656 ± 0.0015 0.0643 ± 0.0017 0.0610 ± 0.0013 0.0604 ± 0.0013 0.0591 ± 0.0030 0.0616 ± 0.0013 0.0574 ± 0.0022 0.0569 ± 0.0012 0.0530 ± 0.0011

BiClO (10%) FLUKA 0.5480 0.3249 0.3809 0.3180 0.1415 0.1313 0.1174 0.1118 0.0949 0.0827 0.0759 0.0734 0.0720 0.0679 0.0642 0.0632 0.0612 0.0602 0.0589 0.0582 0.0574 0.0558

Experimental 0.5710 ± 0.0118 0.3449 ± 0.0070 0.3690 ± 0.0080 0.3127 ± 0.0155 0.1371 ± 0.0051 0.1274 ± 0.0031 0.1182 ± 0.0025 0.1152 ± 0.0040 0.0965 ± 0.0020 0.0798 ± 0.0016 0.0780 ± 0.0021 0.0751 ± 0.0019 0.0707 ± 0.0026 0.0662 ± 0.0015 0.0642 ± 0.0016 0.0611 ± 0.0013 0.0644 ± 0.0014 0.0598 ± 0.0028 0.0615 ± 0.0013 0.0600 ± 0.0022 0.0557 ± 0.0012 0.0545 ± 0.0011

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Table 4b. Comparison of µm values of BiClO (15% and 20%) polyester concretes Energy (keV) 59.5 80.9 122.1 136.4 276.3 302.8 356.0 383.8 511.0 661.6 778.9 834.8 867.3 964.1 1085.8 1112.1 1173.2 1212.9 1274.5 1299.1 1332.5 1408.0

BiClO (15%) FLUKA 0.6983 0.3954 0.4681 0.3923 0.1520 0.1406 0.1300 0.1166 0.0973 0.0834 0.0764 0.0739 0.0722 0.0684 0.0639 0.0631 0.0614 0.0601 0.0586 0.0581 0.0575 0.0557

Experimental 0.6784 ± 0.0143 0.4148 ± 0.0086 0.4709 ± 0.0108 0.4115 ± 0.0224 0.1458 ± 0.0048 0.1437 ± 0.0036 0.1261 ± 0.0026 0.1167 ± 0.0037 0.0998 ± 0.0021 0.0851 ± 0.0017 0.0766 ± 0.0020 0.0747 ± 0.0018 0.0743 ± 0.0029 0.0663 ± 0.0015 0.0623 ± 0.0016 0.0635 ± 0.0014 0.0605 ± 0.0013 0.0593 ± 0.0028 0.0576 ± 0.0012 0.0567 ± 0.0020 0.0598 ± 0.0012 0.0561 ± 0.0012

BiClO (20%) FLUKA 0.8455 0.4561 0.5762 0.4631 0.1593 0.1484 0.1281 0.1218 0.0989 0.0844 0.0768 0.0739 0.0725 0.0682 0.0638 0.0632 0.0615 0.0603 0.0587 0.0582 0.0571 0.0555

Figure 7. Comparison of HVL for the polymer concretes.

Experimental 0.8273 ± 0.0181 0.4819 ± 0.0104 0.5946 ± 0.0154 0.4423 ± 0.0250 0.1656 ± 0.0055 0.1440 ± 0.0035 0.1253 ± 0.0026 0.1175 ± 0.0043 0.0946 ± 0.0019 0.0848 ± 0.0017 0.0809 ± 0.0021 0.0725 ± 0.0018 0.0746 ± 0.0029 0.0688 ± 0.0015 0.0633 ± 0.0016 0.0616 ± 0.0013 0.0638 ± 0.0013 0.0604 ± 0.0030 0.0572 ± 0.0012 0.0559 ± 0.0022 0.0562 ± 0.0012 0.0548 ± 0.0011

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Therefore, we can state that increasing the Bi content results in increase of concrete density and this leads to managing of the photons attenuating capability of the designed polymer concretes. Moreover, the unsaturated polyester (being quite light material) can be conveniently put into a number of uses like storage and transportation, when compared to other materials. Table 5. Half value layer (in cm) of polyester concretes computed from FLUKA data Energy (keV) 59.5 80.9 122.1 136.4 276.3 302.8 356.0 383.8 511.0 661.6 778.9 834.8 867.3 964.1 1085.8 1112.1 1173.2 1212.9 1274.5 1299.1 1332.5 1408.0

BiClO (5%) 1.39 2.08 1.93 2.22 4.08 4.47 4.73 4.89 5.67 6.40 6.93 7.24 7.34 7.79 8.15 8.31 8.50 8.67 8.91 9.02 9.10 9.39

BiClO(10%) 0.91 1.54 1.32 1.58 3.54 3.82 4.27 4.48 5.28 6.06 6.61 6.83 6.96 7.38 7.81 7.93 8.19 8.32 8.51 8.61 8.72 8.98

BiClO(15%) 0.70 1.24 1.05 1.25 3.24 3.50 3.79 4.22 5.06 5.90 6.44 6.67 6.81 7.19 7.70 7.80 8.01 8.19 8.40 8.47 8.57 8.83

BiClO(20%) 0.57 1.06 0.84 1.05 3.04 3.27 3.79 3.98 4.91 5.74 6.31 6.56 6.69 7.11 7.60 7.67 7.89 8.04 8.26 8.34 8.50 8.74

FLUKA and XCOM Database for Polymers For the validation of FLUKA data, third approaches based upon XCOM computations have also been compared with simulated data of some useful

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59

polymers. Polymers are the most appropriate phantom materials in dosimetry and tissue equivalents for human organs. The specific properties of polymers make them useful for protective coating, nuclear technology and base materials for radiation shielding. Polymers play a critical role in radiological protection of biological structures for X/Gamma rays as they can be effectively used as a host matrix for new shielding compositions. Some commonly used polymers with monomer units and density values are tabulated below (Table 6). Table 6. Abbreviations, monomer units and densities of common polymers Polymer Name Bakelite (PF) Polypropylene (PP) Polysulfone (PSU) Polystyrene (PS) Polyethylene terephtalate (PET) Polytetrafluoroethylene (PTFE)

Monomer C9H9O C3H6 C27H22O4S C8H8 C10H8O4 C2F4

Density (g/cm3) 1.45 0.90 1.24 1.06 1.40 2.20

Lastly, the effective atomic number (Zeff) is another factor that may be considered while designing any shielding composites. The values of Zeff have been calculated from the ratio of total atomic cross-section to total electronic cross-section (Sharma et al. [17]). The Zeff values of selected polymers obtained with FLUKA have been listed in Table 7 and agreed to within 1% of the values achieved with the XCOM database (Berger et al. [18]) shown through the same table. The resultant plots of Zeff, based upon FLUKA data, as a function of gamma energy have been shown in Figure 8. It is observed that Zeff initially decreases slowly and tends to remain almost stable with further increase of photon energy. The values of Zeff after 100 keV are observed as almost constant. Obviously, this is due to the supremacy of Compton scattering process whose cross-section is proportional to Z. Hence, no well defined energy dependence of an effective atomic number was noticed in the range of this energy. Out of the polymers under examination, Polytetra-

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fluoroethylene (PTFE) material possesses the highest value of Zeff and may be considered as the best shielding material among the selected polymers. Table 7. Effective atomic number of various polymers corresponding to different gamma photon energies. The values given correspond to the FLUKA calculations and in round brackets using XCOM database Polymer PTFE PF PET PP PSU PS

Incident photon Energy (keV) 59.5 80.9 140.5 356.5 8.19 8.14 8.10 8.09 (8.10) (8.06) (8.02) (8.01) 3.8 3.65 3.66 3.66 (3.84) (3.79) (3.75) (3.74) 4.72 4.55 4.54 4.53 (4.70) (4.63) (4.58) (4.56) 2.66 2.54 2.56 2.57 (2.72) (2.69) (2.66) (2.65) 4.74 4.38 4.28 4.25 (4.74) (4.48) (4.34) (4.30) 3.51 3.38 3.40 3.41 (3.58) (3.54) (3.51) (3.50)

661.6 8.07 (8.01) 3.69 (3.74) 4.57 (4.56) 2.59 (2.65) 4.28 (4.29) 3.43 (3.50)

834.8 8.09 (8.01) 3.62 (3.73) 4.49 (4.56) 2.54 (2.65) 4.20 (4.29) 3.37 (3.50)

1173.2 8.08 (8.01) 3.62 (3.73) 4.48 (4.56) 2.54 (2.65) 4.21 (4.29) 3.37 (3.50)

Figure 8. Variation of effective atomic number versus photon energies.

1332.5 8.08 (8.01) 3.59 (3.74) 4.46 (4.56) 2.51 (2.65) 4.17 (4.29) 3.34 (3.50)

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CONCLUSION This chapter focused on exploring the competence of FLUKA Monte Carlo code for estimation of shielding /interaction parameters of many new composite materials. The validation of FLUKA for new alternative shielding materials like Bismuth/tellurite based glass systems, polymers and polyester concretes etc. over useful energy range 59.5–1408 keV have been listed in this chapter. The following ending can be drawn from the study: 



 







The validation of FLUKA based shielding computations has been checked against experimental data, Geant4 and XCOM as well. It is found that FLUKA is an influential alternative for estimation of shielding related parameters without worrying about the feasibility of actual experimental set-ups. It may be fairly handy for the investigators seeking the radiation shielding capability of newly developing materials. The FLUKA code offers the user abundant opportunities on carrying out flexible experiments, composition of shielding material and photon energy etc. just based on computer systems. To improve the shielding features for the MoO3-B2O3-Bi2O3glass system, a higher amount of Bi2O3 must be used. LiBPTe-40 composition shows the better shielding feature due to higher content of Tellurium (Te) having uppermost atomic number compared to the other elements present in the samples. It has been observed that concrete having more amount of Bismuth i.e., BiClO (20%) consistently possesses the best photon shielding performance in comparison to samples with lesser amounts of Bismuth. Among the selected polymers Polytetrafluoroethylene (PTFE) is the best shielding polymer due to its highest effective atomic number in comparison to others in the list. The reported results are expected to be valuable in shielding, dosimetry and other radiation related fields.

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[17]

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Mann, K. S. 2019. “Investigation of gamma-ray shielding by double layered enclosures.” Radiation Physics and Chemistry 159: 207-221. Fasso, A., Ferrari, A., Roesler, S. et al. 2003. “The FLUKA code: present applications and future developments.” Talk given at 13th International Conference for Computing in High Energy and Nuclear Physics (CHEP 2003), CA, United States, March 24-28. Ferrari, A., Sala, P. R., Fasso, A. and Ranft, J. 2005. “FLUKA: A multi- particle transport code.” CERN-2005-10. INFN/TC_05/11, SLAC-R-773. Vlachoudis, V. 2009. “FLAIR: A Powerful But User Friendly Graphical Interface for FLUKA.” Proceedings of International Conference on Mathematics, Computational Methods & Reactor Physics, Saratoga Springs, New York, May 3-7. Sharma, A., Sayyed, M. I., Agar, O. and Tekin, H. O. 2019. “Simulation of shielding parameters for TeO2-WO3-GeO2 glasses using FLUKA code.” Results in Physics 13: 102199 (1-8). Sayyed, M. I., Kaky, K. M., Gaikwad, D. K., Agar, O., Gawai, U. P. and Baki, S. O. 2019. “Physical, structural, optical and gamma radiation shielding properties of borate glasses containing heavy metals (Bi2O3/MoO3).” Journal of Non-Crystaline Solids 507: 30– 37. Askin, A., Sayyed, M. I., Sharma, A., Dal M., El-Mallawany, R. and Kacal, M. R. 2019. “Investigation of the gamma-ray shielding parameters of (100-x) [0.5Li2O–0.1B2O3–0.4P2O5]-xTeO2 glasses using Geant4 and FLUKA codes.” Journal of Non-Crystalline Solids 521: 119489 (1-7). Sharma, A., Sayyed, M. I., Agar, O., Kacal, M. R., Polat, H. and Akman, F. 2020. “Photon-shielding performance of bismuth oxychloride-filled polyester concretes.” Materials Chemistry and Physics 241: 122330 (1-9). Sharma, A., Singh, B. and Sandhu, B. S. 2019. “Investigation of photon interaction parameters of polymeric materials using Monte Carlo simulation.” Chinese Journal of Physics 60: 709-719.

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[18] Berger, M. J., Hubbell, J. H., Seltzer S. M. et al. 2010. “XCOM: Photon Cross- Section Database.” NIST Standard Reference Database. http://www.nist.gov/pml/data/xcom/index.cfm.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 3

BASIC QUANTITIES FOR PHOTON SHIELDING CALCULATIONS Suffian Mohamad Tajudin* School of Medical Imaging, Faculty of Health Sciences, Universiti Sultan Zainal Abidin (UniSZA), Kuala Nerus, Terengganu, Malaysia

ABSTRACT The Monte Carlo method is commonly used for the following purposes; dose calculation, detector design, radiation shielding and medical application. There have been extensive efforts to improve the shielding and dose assessment by using Monte Carlo and the journey remains on. In this chapter, the Monte Carlo code called Electron and Gamma Shower version 5 (EGS5 code) for electron and photon transport have been used to simulate how radiation enters the shielding materials when a beam of photons is incident. Calculating the number and average energy of the primary photons, Rayleigh scattered and Compton scattered photons that were passing through a shielding material are important to understand the photon interactions and efficiency of shielding materials. *

Corresponding Author’s Email: [email protected].

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Suffian Mohamad Tajudin For photon dosimetry, the calculation of absorbed dose (Gy) is an important step for the calculation of various radiation dose quantities for its corresponding photon fluence such as ambient dose and effective dose. Ambient dose equivalent is an operational quantity defined by the International Commission on Radiation Units and Measurements (ICRU) body for radiation safety. The ratio of two different photon dose units calculated using EGS5 as a function of photon energy shows that an effective dose is always less than ambient dose equivalent, particularly photons below a hundred keV. Hence, this chapter will examine the concept of dose and various dose calculations irradiated with photons and its adoption in EGS5 code for calculation of dose, either it is transmitted or reflected photons from the shielding material.

Keywords: Monte Carlo method, EGS5 code, photon dosimetry

MONTE CARLO METHOD The use of random numbers in the calculation is typically referred to as the Monte Carlo (MC) method and has come to be an essential simulation method in radiation shielding design. The name of Monte Carlo approach was first brought in 1945 by J. Von Neumann and S. M. Ulam to find out about neutron scattering [1]. The Monte Carlo method is employing random numbers and statistical descriptions to approximate mathematical functions and define the operations of complicated structures [2, 3]. In Monte Carlo, the incident photons on the material are tracked for the point of photon interactions, the type of interactions either absorption or scattering, the direction of scattered photons and else, where random numbers are chosen that are associated with particular probabilities to stipulate the determination outcome. There are many studies for radiation shielding materials that have been performed by Monte Carlo methods such as GEANT4 [4], MNCP [5], FLUKA [6], PENELOPE [7], EGS5 [8] and PHITS [9] codes. According to the Institute of Physics & Engineering in Medicine (IPEM), UK, the design of radiation shielding should also take into the best simulation code to evaluate the shielding adequacy [10].

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By default, shielding for photon radiation could be estimated by the deterministic method. This analytical approach which is known as the point kernel method is faster than the computations method. The technique is relatively easy to perform; however, it may be problematic in a situation where the sources and shielding geometries are complex. With the developments of high speed and improvements in the performance of a computer, the Monte Carlo method had been applied successfully on the shielding problems related to complex shield geometries and energy sources [11, 12]. Its application in medical physics is growing together. However, this does require a good understanding of computer programming and training to reach a solution. As an example, two persons who are running an identical Monte Carlo code to solve the same problem, the obtained results might be different between each other. Several researchers had made an attempt to develop a user friendly and easy to use environment for calculation of photon attenuation such as GRIC-toolkit [13], Simu-Rad [14], µFinder [15] and Phy-X/PSD [16].

Figure 1. Example of simulated geometry for photon attenuation study.

Monte Carlo method of EGS5 code will be mainly employed in this chapter for several examples of calculations relevant to radiation shielding

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and dosimetry. Figure 1 shows an example of a simple geometry modelled in the code for study of photon attenuation; have a shield and the source at a certain distance (cm) from the scoring region or point. As seen in the Figure, if only a few numbers of photons are simulated, the output could be expected to vary widely in much time. By increasing the number of photons, we could then expect the results generally could represent the real one, i.e., the determined dose at the scoring region will be correct. A similar Figure could be generated from [14]. The detail of each type of photons and how they contribute to the dose was explained within this chapter.

VARIOUS DOSE CALCULATIONS IRRADIATED WITH PHOTONS KERMA and Absorbed Dose of Air (Gy) In workplaces close to radiation-generating units and radioactive sources such as accelerators, X-ray tubes, and radioactive nuclei, the radiation produced must be controlled to prevent risks caused by exposure to radiation. Photon dosimetry is indispensable mainly if the incident photon energy is high enough as photons are easily generated as secondary radiation of energetic charged particles and neutrons. At the same time, photons also could be emitted from the activated materials generated by the irradiation of the primary particles. The computational method could be used either to ensure the photon radiation dose is at an acceptable level or to consider a useful building material to shield either low or high energy photons. Various dose quantities for photon radiation dose could be evaluated based on the calculated photon energy fluence. Photon energy was transferred to any materials via various photon interactions. When a non-charge particle, such as photon and neutron, is irradiated to a material, the sum of energy transferred to the charged particle is called KERMA (K). The acronym of KERMA is “Kinetic Energy

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Released in Material”. KERMA in the unit of Gray (Gy) is the sum of kinetic energy to charged particles inside a small volume by neutral particles like photons and neutrons [17]. 𝐾=

∆𝐸𝑡𝑟 ∆𝑚

(1)

in which ∆Etr is kinetic energy transferred to charge particle, and ∆m is the mass of material. The relation between KERMA and mass energy transfer coefficient is,

(2) where ρ, φ, k0 are the density of the material, fluence, and particle energy, respectively. The unit of kerma is J/kg and Gy. When the ratio of Bremsstrahlung photon energy is subtracted from KERMA, it is called “collision KERMA” (KC). Collision KERMA is the total of collision loss energy by charged particles created by the photon. In EGS5 code calculation, collision kerma can be calculated by multiplying photon energy fluence (MeV.cm-2) to the mass energy absorption coefficient of a particular material. Such coefficients prepared mainly at National Institute of Standards and Technology (NIST) by Hubbel et al. [18]. The values for the mass energy absorption coefficients could be found at NIST web site (https://www.nist.gov/pml/X-ray-mass-attenuation-coefficients). Following conversion has been used to convert the unit of MeV/g to Gy; 1.0 MeV = 1.602 x 10-13 J

(3)

1.0 MeV/g = 1.602 x 10-13 (J/MeV) x 1000(g/kg) = 1.602 x 10-10 Gy

(4)

When a material is exposed to radiation, energy is absorbed in the material. Absorbed dose is the mean energy transferred to a small volume

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mass of material by photon. Absorbed energy is related to interactions between radiations and energy. For photons, the main photon interactions like photoelectric absorption, Compton scattering and pair production would strongly depend on the material atomic number (Z). Therefore, the absorbed dose in the unit of Gray (Gy) would be different to a material irradiated. If charged particle equilibrium (CPE) exists, the absorbed dose would equal to collision kerma. CPE situation is when the amount of charged particles escaping from a tiny region and that of an incoming charged particle are the same. In another situation, photon interaction might result in secondary photons that could reach the scoring region or dose point. The dose buildup factor could be defined as the ratio of total photon radiation dose that consisting of the dose from secondary photons at the dose point to the primary photon dose at an identical point. The incident photons that have penetrated the shielding material without reaction are denoted as unscattered transmitted photons as shown earlier in Figure 1. Accordingly, if a point kernel calculation is used rather than a Monte Carlo simulation, the Compton photon contribution is accounted for by the use of buildup factors.

Ambient Dose Equivalent and Effective Dose (Sv) Calculation of absorbed photon energy in some volume of air (air absorbed dose) needs huge events (or called histories in EGS5 code) due to the low interaction probability of air. KERMA approximation was utilised where the mass energy absorption coefficient was multiplied to the energy fluence to yield the collision kerma. Then an ambient dose equivalent (Sv) could be calculated by multiplying the ratio of ambient dose equivalent (Sv) to air absorbed dose (Gy) as shown in Figure 2. The ratio is based on the International Commission on Radiation Units and Measurements (ICRU) Report 47, [19]. According to the definition, the ambient dose equivalent, an ICRUdefined quantity, is the dose by aligned photons field and incident on the ICRU 30 cm diameter spherical phantom that scored at a depth of 1 cm.

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However, the human is not ‘sphere’ and therefore it does not have a strong reason to be defined by the sphere. When the depth of interest is taken as 1 cm, the ambient dose equivalent is intended to be a reasonable estimation of the effective dose (it will be conservative). It has to be noted that the ambient dose equivalent is intended for the purpose of device calibration for radiation dose measurements. This quantity is typically used in personal dosimetry calibration. When the depth is taken as 1 cm, the value of the personal dose equivalent is generally used as an estimator of the effective dose, based on the appropriate calibration of the personal dosimeters in use.

Figure 2. Conversion coefficients from ICRU Report 47 that were adopted in EGS5 code to calculate a coefficient for all photon energies (MeV) by log-log interpolation.

Monte Carlo code is commonly used to calculate ambient dose equivalent values in wide photon energy. The ambient dose equivalent is a convenient construct intentionally selected to yield a conservative approximation of the effective dose. Another dose unit, effective dose, E, which is defined by the International Commission on Radiological Protection (ICRP), is a dose concept associated with radiation health risks. E defined as; 𝐸 = ∑𝑇

𝑊𝑇 ∑𝑅

𝑊𝑅 𝑥 𝐷𝑅

(5)

where WT is the tissue weighting factor for organ T, WR is a radiation weighting factor for radiation type R, and DR is the absorbed dose of organ T due to radiation type R. The effective dose is a quantity that is difficult to determine since it requires knowing the doses to all the significantly

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irradiated organs or tissue in the body. There is no way to make a reasonable measurement of this quantity directly. It is the quantity that would like to evaluate since it is the quantity that is tied most directly to radiation effects. An example of the calculated ratio between effective dose with ambient dose equivalent for photon as shown in Figure 3. The figure shows the ratio of effective dose to the ambient dose equivalent in a wide range of photon energy. Generally, the effective dose is less than the ambient dose equivalent for many energies, especially for photons below 100 keV.

Figure 3. The ratio of two different photon dose units calculated using EGS5 to show the relation between effective dose and ambient dose equivalent as a function of photon energy. AP (Anterior-Posterior) denoted the irradiation geometry consisting of a parallel beam of photon impinging on the front of the air body.

Figure 4 (a) shows the comparison of both dose quantities calculated from fluence across the thickness of 50 cm concrete shielding. The calculated ambient dose was calculated as described earlier by using conversion coefficients provided from ICRU 47, while for the effective dose, the conversion coefficients from fluence based on ICRP 103 (AP irradiation) [20]. Several studies had been done based on the Monte Carlo method to calculate the conversion coefficients for both ambient dose equivalent and effective dose from air kerma for mono-energetic photons [21, 22]. In Figure 4 (b), the effective dose often being much more than 15% lower than the ambient dose equivalent. The ambient dose for photons is higher than the effective dose over wide photon energy because the photon radiation is attenuated as the radiation penetrates the material. Since the

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effective dose is calculated by considering the doses to all the significantly irradiated material, this dose gets reduced as radiation is reduced in intensity through attenuation. The effect of attenuation is confirmed by the fact that the ambient dose equivalent and the effective dose would agree more as photon energy increases.

(a)

(b) Figure 4. Photons can be shielded by degrading dose (effective and ambient dose) with concrete (a). The ratio of both dose quantities was shown in (b).

In the case of photons above 10 MeV, Sato et al. [23] had described in detail that the ambient dose would be lower than the effective dose. Despite the conversion coefficient for the primary incident photon, more studies on conversion coefficient are required, which include the effects of generated

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secondary particles in the air such as electrons and positrons to get the total effective dose for high energy photons. For this purpose, all the conversion coefficients must be evaluated with a material in a vacuum environment. The effective doses at the point of interest then could be calculated by multiplying the conversion coefficients to the particle fluence. Therefore, for shielding design purposes, the use of a single dose quantity of ambient dose equivalent for photon dosimetry is not adequate in a wide photon energy range. However, it has to be noted that when doing area monitoring with portable instruments, the ambient dose equivalent is an appropriate quantity to use to estimate effective dose from instrument measurements. In such a case, the calculated values are comparable in absolute values to the experimentally measured data to validate the process [24, 25]. Nevertheless, both photon dose quantities calculated by the Monte Carlo method, having started with the calculated air kerma as described earlier.

CALCULATING PHOTON FLUENCES BEHIND THE SHIELDING Photon Attenuation The basic ways to understand the behaviour of photon interaction inside the materials is by measuring or calculating the linear attenuation coefficients (µ) of the particular material. The µ values could be easily deduced from the XCOM database [26, 27] for low atomic number (Z) to high Z number materials at any photon energies. To date, there are many studies that have been performed to measure and calculate µ values for shielding materials to get the value of discrepancies with the XCOM database [28, 29, 30, 31, 32 and 33]. It is essential and effective ways to study the fundamental quantity such as photon attenuation for one to verify their measurements or simulations before applying a more complicated shielding geometry.

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The photon attenuation could be represented by the exponential decay equation [33] as; I  e  x , I0

(6)

where I0 and I are the intensity of incident and the attenuated photons, respectively. The material thickness in the unit of cm is denoted as x, and µ is the linear attenuation coefficient in the unit of cm-1. It is also usually identified as the mass attenuation coefficient (µ/ρ) in a unit of cm2 g-1. The attenuation of the photon in the material is determined by the interaction of photons such as photoelectric absorption, pair production, Rayleigh and Compton scattering, dependent on the incident photon energy.

Figure 5. Example result of calculated transmitted photons that pass through the concrete material for Co-60 source to give µ =0.1336 cm-1, which is in agreement with the XCOM value, µ = 0.1338 cm-1.

Figure 5 shows an example of the calculation of transmitted photons as a function of concrete thickness for a pencil beam of Co-60 source. The full square points were fitted with an exponential function as equation (6) to obtain a linear attenuation coefficient (µ) value of 0.1336 cm-1. The

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calculated value has a good agreement within 0.15% with the theory, and such comparison is essential to justify the calculations at other photon energies or for newly developed shielding materials. For such comparison to have a good agreement, only unscattered transmitted photons have to be considered in the Monte Carlo method. The attenuation coefficients generated by XCOM are intended to apply only to the primary photons, so no consideration is given to Compton scattered photons. In a real case, the photons may undergo any interactions within the material and exit the material, as denoted scattered transmitted photons in earlier Figure 1. It could be simply imagined as if the attenuation coefficients will be applied in "good geometry" situations. That means the beam of photons is narrow and the desired quantity to calculate, such as photon fluence and dose at a point that is far enough from the attenuating material. Any Compton scattered photons produced in the material will change direction sufficiently that they will not intercept the point of interest. It has to be noted that this description is only for purposes of definition. In many real situations, the beam might not be narrow, and the attenuator or shielding material may be relatively thick and not far removed from the point of interest. In such cases, the linear attenuation coefficient is still used to predict the penetration of the primary photons through a material. Yet, some Compton scattered photons will likely reach the point of interest as well. These could be accounted for by following such photons in the Monte Carlo simulation. Some of those Compton scattered photons may have contributed to the tally in the receptor volume or area, which would result in a seemingly lower value for the attenuation coefficient. Another scattered photon, which is the Rayleigh scatter, does not result in any energy transfer to charged particles but can contribute to changes in directions of scattered photons, most notably when the incident photons are low in energy. However, it could add a few percent to the value of the attenuation coefficient.

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Fractions of the Transmitted Photons In the Monte Carlo method, each particle could be followed in the code to identify what it has been experienced, such as entering, exiting from, reacting in, and reflected by a certain region. This subtopic is to see the fluence distribution inside and after the shielding material in more detail. The former point is the distribution of photon fluence that penetrated within the material. The latter point is to evaluate the particle fluence either photon, electron or neutron that escape behind the shielding material. While considering attenuation of the incident primary particle, secondary particles might be generated within the material and transmitted and escape behind the shielding material, if the thickness is not enough. Such consideration becomes important, particularly for the incident particles or when the photon energy is very high (~ >20 MeV).

Figure 6. Example fractions of the transmitted photons that escape the concrete shielding either scattered (solid line) or unscattered photons (dashed line). The transmitted total ambient dose is 2.25 Sv.inc.-1.cm-2s-1 while scattered and unscattered dose are 1.83 (82%) and 0.42 (18%) Sv.inc.-1.cm-2s-1, respectively.

Figure 6 shows the incident photons that do not scatter and scattered in the concrete material to the dose that scored in the air region behind the material. In this calculation, the 4π isotropic photons of 0.4 MeV were

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incident on the concrete of 10 cm thickness. As could be seen, most of the incident photons penetrate the concrete with reactions that scattered photons contribute almost 82% of the total dose that pass through the concrete. Unscattered photons of the incident photons with degrading energy have a minimum contribution (18%) in the total dose after a 10 cm concrete. Such estimation is useful particularly for higher energy incident photons to understand how much the incident photons do not scatter or react in the concrete and contribute to the dose in a certain region of the air. The information could help medical physicists to justify an adequate approach of radiation shielding, such as more shielded by denser material is necessary or a combination of two materials.

Figure 7. Klein-Nishina differential cross-sections demonstrated the relationship of the incident photon energies with the Compton scattering angle [39].

CONSIDERATION ON REFLECTED DOSE COMPONENT (MEDICAL PERSPECTIVE) Photon dosimetry is indispensable in designing an irradiation medical facility shielding. The purposes of radiation shielding are to protect the

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patients, the department staff, visitors and the public [35]. As an example, for controlled and public areas, the radiation dose level should be in a reference value range of 0.75 μSv/h and 0.5 μSv/h [36]. While doing the calculations for the required wall thicknesses to protect people outside of the treatment area, it might be necessary to evaluate for the contribution of reflected photons energy fluence and its contribution to the dose. It is important to evaluate the particles that might be reflected by a certain region in designing an irradiation facility shielding, particularly in the medical application where the patient or personnel are within the room during the procedure. From a dose standpoint, there is a need to optimise radiation protection of patients (clinical dosimetry) and medical personnel (occupational dosimetry). Clinical dosimetry is the cornerstone of any dose optimisation attempt. Radiation delivery to cancer patients for radiotherapy could be including leakage and scatter radiation which provides unnecessary additional radiations or dose to other parts of the patient’s body [37]. However, it is generally difficult to predict accurately. The difficulty of implementing to take measures to reduce reflection could be reduced with the aid of the Monte Carlo method. It is known that the calculation of incident radiation toward a surface and reemitted toward a certain point of interest is commonly encountered as a problem in radiation shielding. Tajudin et al. [38] had calculated backscattered photon spectra from different radioactive sources with concrete material as a scatterer to have reflected photon energy up to ~200 keV photons. Figure 7 is a Klein-Nishina differential cross-section that demonstrated the relationship of the incident photon energies with the Compton scattering angle [39]. The higher the energy of the incident photon, the more significant scatter will be in the forward direction. Lower energy photons are more likely to scatter at an angle of higher than 90o, or scatter in the reverse direction, which is called backscatter. According to Compton scattering, the Compton scattered photon energy can be calculated by where; ℎ𝑣 ′ =

ℎ𝑣 1+

ℎ𝑣 𝑚𝑐2

(1−𝑐𝑜𝑠𝜃)

(7)

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where hv is the incident photon energy, hv' is the Compton scattered photon energy, θ is the angle between the incident and Compton scattered photons, and mc2 is equal to 511 keV, which is the electron energy at rest. As described in the Monte Carlo method section, each particle could be assigned with a ‘dedicated’ number to identify those that have been ‘reflected’ by a certain region. As in Figure 8, the photons that enter the shielding material and go out from the region, either backscattered (denoted as reflected) or passed through the concrete region (denoted as transmitted), had been followed in the code. The backscattered photons information such as its photon spectrum and dose that contributed to the tally in the receptor volume or area were scored. As an example, a simple approach is to add some lead to the inner walls to reduce the reflection dose component.

Figure 8. The cross mark denoted the reflected photon spectra from the concrete material for the incident of 1 MeV photon. Adding a thin lead (0.5 cm) that on the photon-facing side of the concrete material could attenuate reflected photon components, particularly below 200 keV photon, as denoted by the squares. The circles and plus marks are present for the transmitted photons.

Figure 8 shows an example of reflected and transmitted photons scored from a 50 cm thickness of concrete as a result of a 1.0 MeV incident photon that emitted in the 4π direction. In the second case, a thin layer of lead with a thickness of 0.5 cm was added on the photon-facing side of the concrete

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material as an ‘inner layer’ to attenuate reflected photons. The average energy of transmitted photons is almost similar for 0.337 MeV and 0.339 MeV, respectively, as denoted by plus and circles marks. The calculated transmitted dose rate for the one with the lead layer is lower within 30%. For the latter point, adding a thin layer of 0.5 cm lead was successfully attenuated the calculated reflected dose rate of almost 80% from 15.7 to 3.5 Sv/inc./cm2/s, as denoted by cross and square marks, respectively. The peak at around 88 keV in the reflected spectra when a lead is added is due to the emission of the Pb-82 K-edge characteristic X-ray. In another example, Tajudin et al. [32] had demonstrated how to reduce reflected photon spectra from the clay material for the Am-241 gamma source by using an iron (Fe-26) element. Whenever necessary, if the added reflected dose is high enough to justify trying to reduce it, then it becomes a matter of cost and convenience in deciding what approach might be best to reduce reflection.

CONCLUSION The Monte Carlo method is a probabilistic approach where selected random numbers associated with particular probabilities are used to stipulate the determination outcome. The results from the Monte Carlo method are much affected by the number of photons, and hence the task of calculating complex shielding geometry was very time-consuming. In shielding design purposes, the main index to determine the effectiveness of shielding is not the photon fluence, but the photon dose either is an ambient dose equivalent or effective dose in the unit of Sievert (Sv). Nevertheless, both dose quantities having started with the calculated air kerma as the absorbed dose is the only physical quantity related to dose. There is no physical dose that is defined for photon fluence. The Monte Carlo method is reliable and accurate in developing specialised shielding approaches. However, most of the available Monte Carlo methods are for experienced users and do require considerable training time to use. This approach requires more time so that an optimal solution

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could be reached than the deterministic methods. In the last section, a reflected dose component had also been discussed from a medical application point of view. As an example, the walls closest to the source could likely be the most significant contributors to the scattered radiation at the patient location. In such a case, it is necessary to reduce the reflected photons in order to reduce the effective dose to the patient.

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Ulam, Stanislaw M. 1990. Analogies Between Analogies: The Mathematical Reports of S. M. Ulam and His Los Alamos Collaborators. University of California Press, Berkeley. Harrison, Robert L. 2009. “Introduction to Monte Carlo Simulation.” In AIP Conference Proceedings 1204:17-21. Nicholas, Metropolis, and Ulam, Stanislaw M. 1949. “The Monte Carlo Method.” Journal of the American Statistical Association 44:335-341. Agostinelli, S., Allison, J., Amako, K., Apostolakis, J., Araujo, H., et al. 2003. “GEANT4 - A Simulation Toolkit.” Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 506:250-303. Arthur, Forster R., Cox, Lawrence J., Barrett, Richard F., Booth, Thomas E., Briesmeister, Judith F., Brown, Forrest B., et al. 2004. “MCNPTM Version 5.” Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms 213: 82-86. Ferrari, Alfredo, Sala, Paola R, Fasso, Alberto, and Johannes, Ranft. 2005. FLUKA: A Multi-Particle Transport Code. Stanford Linear Accelerator Centre, Stanford University, Stanford, California. Salvat, Francesc, Jose, Fernández-Varea M., Acosta, Eduardo, and Sempau, Joseph. 2001. Penelope - A code system for Monte Carlo Simulation of Electron and Photon Transport. Nuclear Energy

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Agency, Organisation for Economic Co-operation and Development, Barcelona, Spain. Hirayama, Hideo, Namito, Yoshihito, Alex, F. Bielajew, Scott, J. Wilderman, and Walter, R. Nelson. 2005. The EGS5 Code System. Stanford Linear Accelerator Centre, Stanford University, Stanford, California. Tatsuhiko, Sato, Koji, Niita, Norihiro, Matsuda, Shintaro, Hashimoto, Yosuke, Iwamoto, Shusaku, Noda, Tatsuhiko, Ogawa, Hiroshi, Iwase, Hiroshi, Nakashima, Tokio, Fukahori, Keisuke, Okumura, Tetsuya, Kai, Satoshi, Chiba, Takuya, Furuta, and Lembit, Sihver. 2013. “Particle and Heavy Ion Transport Code System, PHITS, Version 2.52.” Journal of Nuclear Science and Technology 50:913-923. Patrick, Horton, and David, Eaton. 2017. Design and Shielding of Radiotherapy Treatment Facilities: Institute of Physics and Engineering in Medicine (IPEM) Report 75: Second Edition. Ivan, T. Dimov, and Ognyan, I. Tonev. 1993. “Monte Carlo Algorithms: Performance Analysis for Some Computer Architectures.” Journal of Computational and Applied Mathematics 48:253-277. Ziegenhein, Peter, Pirner, Sven, Cornelis, Ph. Kamerling, and Oelfke, Uwe. 2015. “Fast CPU-based Monte Carlo Simulation for Radiotherapy Dose Calculation.” Physics in Medicine and Biology 60:6097–6111. Mann, Kulwinder S., Rani, Asha, and Heer, Manmohan S. 2015. “Shielding Behaviours of Some Polymer and Plastic Materials for Gamma Rays.” Radiation Physics and Chemistry 106: 247-254. Tajudin, Suffian M, and Aminordin Sabri, Adila H. 2019. SIMU-RAD Programme: A Learning Tool for Radiation (Photons and Charged Particles) Interaction. Polish Journal of Medical Physics and Engineering 25:189-192. Fulvio, Arboccò F. 2020. µFinder: X-ray and Gamma-Ray Mass Attenuation Coefficients Between 1 keV and 100 GeV. Licence: CC BY-NC-ND 4.0. https://doi: 10.13140/RG.2.2.14187.54565/2.

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[16] Şakar, Erdem, Özpolat, Özgur F., Alım, Bunyamin, Mohammed, Abu Al. Sayyed, and Kurudirek, Murat. 2020. “Phy-X/PSD: Development of A User Friendly Online Software for Calculation of Parameters Relevant to Radiation Shielding and Dosimetry. Radiation Physics and Chemistry 166: 108496. [17] Attix, Frank H. 1986. Introduction to Radiological Physics and Radiation Dosimetry. New York: John Wiley. [18] Berger, Martin. J., Hubbell, John H., Seltzer, Stephen M., Chang, John, Coursey, J. S., Sukumar, Rajauria, and Olsen, Karen. (2010). “XCOM: Photon Cross-Section Database (version 1.5).” Accessed May 2020. http://physics.nist.gov/xcom. [19] Katoh, Akira. 1993. “A Brief Introduction of ICRU 47: Measurement of Dose Equivalents from External Photon and Electron Radiations.” Japanese Journal of Health Physics 28:219-227. [20] ICRP. 2007. ICRP Publication 103: The 2007 Recommendations of the International Commission on Radiological Protection. Annals of the ICRP 37:9-34. [21] Saito, Kimiaki, and Petoussi-Henss, Nina. 2014. “Ambient Dose Equivalent Conversion Coefficients for Radionuclides Exponentially Distributed in the Ground.” Journal of Nuclear Science and Technology 51:1274-1287. [22] Hassan, Al Kanti, El Hajjaji, O., Tarek, El Bardouni, Boukhal, Hamid, and Mohammed, Maged. 2020. Conversion Coefficients Calculation of Mono-Energetic Photons from Air KERMA Using Monte Carlo and Analytical Methods. Journal of King Saud University – Science 32:288-293. [23] Sato, Osamu, Yoshizawa, Nobuaki, Takagi, Shunji, Iwai, Satoshi, Uehara, Takashi, Sakamoto, Yukio, Tanaka, Shun-ichi. 1999. “Calculations of Effective Dose and Ambient Dose Equivalent Conversion Coefficients for High Energy Photons.” Journal of Nuclear Science and Technology 36:977-987. [24] Tajudin, Suffian M., Namito, Yoshihito, Sanami, Toshiya, and Hirayama, Hideo. 2014. “Quasi-mono-energetic 200 keV Photon

Basic Quantities for Photon Shielding Calculations

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

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Field Using A Radioactive Source with Backscatter Layout.” Japanese Journal of Applied Physics 53: 116401. Tajudin, Suffian M., Namito, Yoshihito, Sanami, Toshiya, and Hirayama, Hideo. 2013. “Experimental Study of Quasi-Monoenergetic 200 Kev Photon Field Using A Radioactive Source with Backscatter Layout.” Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC), Seoul, pp. 1-6. Hubbell, John H., and Seltzer, Stephen M. 1996. “NIST: X-ray Mass Attenuation Coefficients.” Accessed May 2020. https://www. nist.gov/pml/X-ray-mass-attenuation-coefficients. Berger, Martin. J., Hubbell, John H., Seltzer, Stephen M., Chang, John, Coursey, J. S., Sukumar, Rajauria, and Zucker, D. S. 1998. “XCOM: Photon Cross-Sections Database.” Accessed May 2020. https://doi.org/citeulike-article-id:9783715. Pawar, Pawar P. 2011. Measurement of Mass and Linear Attenuation Coefficients of Gamma Rays of Al for 514, 662 and 1280 keV Photons. Journal of Chemical and Pharmaceutical Research 3:899903. Tekin, Huseyin. O., and Manici, Tugba. 2017. “Simulations of Mass Attenuation Coefficients for Shielding Materials Using the MCNPX Code.” Nuclear Science and Techniques 28:95-98. Zhang, L., Jia, M. C., Gong, J. J., and Xia, W. M. 2017. “Simulation of Photon Attenuation Coefficients for High Effective Shielding Material Lead-Boron Polyethylene.” IOP Conference Series: Earth and Environmental Science 100(1):012137. Ferreira, C. C., Ximenes, R. E., Garcia, C. A. B., Vieira, J. W., and Maia, A. F. 2010. Total Mass Attenuation Coefficient Evaluation of Ten Materials Commonly Used to Simulate Human Tissue. Journal of Physics: Conference Series. 249:012029. Tajudin, Suffian M, Aminordin Sabri, Adila H., Aziz, Mohd Zahri A., Olukotun, Stephen. F., Ojo, Babatunde, and Fasasi, Musbau K. 2019. “Feasibility of Clay Shielding Material for Low Energy Photons (Gamma/X). Nuclear Engineering and Technology 51:1633-1637.

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[33] Tajudin, Suffian M., and Tabbakh, Farshid. 2019. Biological Polymeric Shielding Design for an X-ray Laboratory Using Monte Carlo Codes. Radiological Physics and Technology 12:299–304. [34] Glenn, Frederick Knoll. 2010. Radiation Detection and Measure-ment (4th Edition). New York: John Wiley and Sons, Inc. [35] IAEA. 2019. “Radiation Protection in Brachytherapy”. Accessed Jun 11. https://www.iaea.org/resources/rpop/health-professionals/radio therapy/brachytherapy. [36] Kainz, Kristofer. 2006. “Radiation Oncology Physics: A Handbook for Teachers and Students.” Medical Physics 33:1920. [37] Taylor, Michael, and Kron, Tomas. 2011. “Consideration of The Radiation Dose Delivered Away from The Treatment Field to Patients in Radiotherapy.” Journal of Medical Physics 36(2):59-71. [38] Tajudin, Suffian M., Namito, Yoshihito, Sanami, Toshiya, and Hirayama, Hideo. 2020. “Photon field of ~100–200 keV for Environmental Dosemeter Calibration.” Radiation Protection Dosimetry. https://doi.org/10.1093/rpd/ncz308. [39] Klein, Oskar, and Nishina, Yuichiro. 2014. On the Scattering of Radiation by Free Electrons According to Dirac’s New Relativistic Quantum Dynamics. In the Oskar Klein Memorial Lectures, pp. 253272.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 4

AMBIENT DOSE BUILDUP FACTORS Oyeleke Olarinoye* Department of Physics, Federal University of Technology, Minna, Nigeria

ABSTRACT Accurate dose measurement and shielding calculation are two aspects of quality assurance procedure in all applications of ionising/nuclear radiations. The consideration of the radiation dose buildup factor is very critical in the dose measurement and shielding requirement calculations. The determination of the buildup factor is an important topic in radiation applications. This chapter highlights the concept of photons and neutron dose buildup factors as it affects radiation dosimetry and shielding. The meaning, application, and different ways of measuring and calculating buildup factors have also been discussed. The merits and demerits of each of the methods have been discussed, and the general behaviour of the photon buildup factor regarding energy and depth have been fully highlighted.

Keywords: photons, neutrons, ambient dose, buildup factor, attenuation *

Corresponding Author’s Email: [email protected].

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INTRODUCTION The use of ionising radiations (IR) in different areas of human society has increased over the years. Nowadays, IR emanating from natural radionuclides, artificial radiation machines and radioisotopes are applied in: medicine (for sterilisation, diagnostic and the therapeutic purposes), environmental conservation; agriculture; food processing; archaeological and cultural preservation; radio-tracing in industries; ultrasonic crack verifications in metallic industries; research; electricity production via nuclear reactors amongst others. However, in order to sustain and explore other potential areas of application, radiation protection and dosimetry must be an integral part of the procedures involved in all areas of radiation use. This is a sequel to the deleterious effect uncontrolled exposure to radiation can cause to living tissues. The harmful effect of IR is not limited to living cells, but could also lead to damage to material and cause devices to malfunction. Consequently, the principle of optimisation of procedure geared towards limitation of ambient IR absorbed doses in living tissues, devices and the environment in general is always a focal issue in all fields where IR is adopted for use. This is expected to rule out the occurrence of deterministic effects and cause a reduction in the probable occurrence of stochastic effects in living tissues. Furthermore, it goes a long way towards protecting non-living components and devices from degradation that could arise from exposure to IR above the threshold level of degradation. A good understanding of how different IR interact with different materials (living or otherwise) is fundamental to the estimation of radiation energy deposited (absorbed dose) in such medium, identification of appropriate material and the evaluation of how much of it is required to provide a good radiation protection barrier for different IR of interest. IR comes in different flavours such as energetic electrons (beta rays), protons, heavy ions, neutrons and photons (gamma- and X-rays) with each having distinct energy deposition mechanisms when interacting with a medium. The estimation of absorbed doses for all IR incidents on a target however, simply involves estimating the amount of energy it deposits at a particular point in the interacting medium. Generally, the absorbed dose (𝐷𝑜 (𝑟)) delivered at

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a distance r in air by IR point source of strength S (a measure of particle flux density) is related to the radiation detector response (𝑅𝐷 ) according to 𝑅 𝑆

𝐷 𝐷𝑜 (𝑟) ∝ 4𝜋𝑟 2 . If at the distance r, the radiation is incident on a medium, the

absorbed dose of the IR after passing through a medium of thickness t can be estimated from 𝐷𝑜 (𝑟) based on the equation: 𝐷(𝑡) = 𝐷𝑜 𝑒 −𝛴𝑡

(1)

The parameter 𝛴 is a constant which is a function of the nature of the absorbing medium, radiation type and energy. 𝛴 in general, represents the interaction cross-sections of the IR and indicates the degree of radiation energy loss in the medium of interaction. The use of equation 1 assumes the IR beam to be mono-energetic, parallel and well collimated and that the target medium is thin. Furthermore, it assumes that good geometry is used and that the detector response, (𝑅𝐷 ) which provides a relationship between 𝐷𝑜 and the radiation flux, only responds to uncollided radiation flux collected at t. For most practical purposes, good geometry is rare and some of these assumptions are not valid. In fact, 𝑅𝐷 thus represents scattered flux in addition to uncollided radiation flux. This implies that using equation 1 might introduce significant error in dose estimation. In many radiation applications, error of dose estimation leading to error of judgement could be very costly. In order to avert such error a correction factor is normally used to multiply the equation in the form: 𝐷 ′ (𝑡) = 𝐵𝐷(𝑡)

(2)

The multiplying (correction) factor (𝐵) is called the buildup factor of the IR or the dose parameter of interest in the interacting medium. Thus we have, buildup factor for photons, neutrons, dose, exposure, energy absorption, fluence, KERMA, etc. The 𝐵 value ensures accuracy in dose estimation for different applications and also for the calculation of shielding requirement in radiation protection. The value of 𝐵 is always greater than or equal to unity. Furthermore, 𝐵 depends on radiation type and quality, and

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the absorption depth. Many theoretical and practical approaches have been suggested for the accurate estimation of B for photons and other types of IR. In this chapter, the buildup factors of photons and neutron beams are explained, the different methods of estimating them are presented. The implication of B on dose and shielding calculations for homogeneous and inhomogeneous media are further elucidated.

DOSE BUILDUP FACTOR FOR PHOTONS Linear and Mass Attenuation Coefficients Suppose an isotropic source of mono-energetic photons (S) is placed in a vacuum (or air) at a position x-distance away from a detector (D) as shown Figure 1, the photon dose measured by D due to the primary particles from S can be expressed as: 𝐷𝑜′ (𝑥) =

𝑆𝑅𝐷 ′ 4𝜋𝑥 2

(3)

The above equation enables one to evaluate the absorbed dose in air if the source strength is known and assumes photon absorption is negligible in air. Also, the equation shows that the measured dose obeys the inverse square law due to the geometric decrease of photons collected by the detector with varying distance from source. Now, assuming an absorbing medium (M) of finite thickness t is placed between S and D, the photon dose due to uncollided photons with M collected at D can be given as [1,2]: 𝐷 ′ (𝑥) =

𝑆𝑅𝐷 ′ −𝜇𝑡 𝑒 4𝜋𝑥 2

(4)

Equation 4 assumes point isotropic source of monochromatic and well collimated beam as shown in Figure 2. The factor 𝑒 −𝜇𝑡 is the attenuating factor which accounts for the photons loss (absorbed in M) due their

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collisions with the particles of the absorber. The attenuating factor is a measure of the probability that a source photon does not interact with M before reaching D. The parameter 𝜇 is called the linear attenuation coefficient 𝜇 of M. The 𝜇 depends on photon energy, absorber thickness and its chemical description (e.g., using atomic number). In order to eliminate the thickness or dimension dependence of 𝜇, a similar quantity called the 𝜇 𝜌

mass attenuation coefficient (𝜇𝑚 = ) where 𝜌 is the density of the absorber can be used. Whenever 𝜇𝑚 is used in equation 5, the mass thickness (𝑡𝑚 = 𝜌𝑡) of the absorber is used instead of the linear thickness (t) in order to conserve the dimension of the equation. The unit of the linear attenuation coefficient is cm-1. The linear or mass attenuation coefficient of a material is a measure of the total interaction cross-sections due to different photon interaction processes that take place in the medium as the photons traverse through it. Thus we can write:

Figure 1. Photon transmission in air or vacuum.

Figure 2. Narrow beam (good) geometry for photon transmission.

92

Oyeleke Olarinoye 𝜇𝑚 ∝ 𝜇 ∝ 𝜎𝑡 𝑁

here, 𝑁 =

𝜌𝑁𝐴 𝐴

(5)

is the atomic density of the absorber with density and atomic

mass number 𝜌 and A respectively. 𝑁𝐴 is a constant called the Avogadro number. In equation 5, 𝜎𝑡 is the total photon interaction cross-section [1]. For the purpose of dosimetry and shielding, three interaction modes are of major importance for photon energy E (0 < 𝐸 ≤ 20 𝑀𝑒𝑉). These interaction modes are the photoelectric effect (pe), Compton Scattering (CS) and pair production with interaction cross-section 𝜎𝑝𝑒 , 𝜎𝑐𝑠 , and 𝜎𝑝𝑝 respectively. It is thus convenient to write: 𝜎𝑡 ≈ 𝜎𝑝𝑒 + 𝜎𝑐𝑠 + 𝜎𝑝𝑝 (for 𝐸 ≤ 20 𝑀𝑒𝑉) 𝜇𝑚 =

𝑁𝐴 𝜎 𝐴 𝑡

≈

𝑁𝐴 (𝜎𝑝𝑒 𝐴

+ 𝜎𝑐𝑠 + 𝜎𝑝𝑝 ) = 𝜇𝑝𝑒 + 𝜇𝑐𝑠 + 𝜇𝑝𝑝 = ∑𝑛𝑖

(6) 𝜇𝑖 (7)

where 𝜇𝑖 is the mass attenuation due to each of the three interaction modes. It must be noted that each of the interaction coefficients have threshold energy and energy region where they dominate i.e., have high interaction cross-section. To illustrate this, the mass attenuation coefficient as a function of photon energy for Pb obtained via WinXcom computer code [3] is plotted together with the three partial attenuation coefficients due to the three interaction modes in Figure 3. The mass attenuation coefficient is high at the low energy region and rapidly decreases with energy as indicated in the figure. The pair production interaction dominates at the low energy region while the Compton scattering and pair production interaction dominates at the intermediate and high energy regions respectively.

Mean Free Path The reciprocal of 𝜇 is called the mean free path (λ) of the photon with a specific energy in the absorber i.e.:

Ambient Dose Buildup Factors 1

𝜆=𝜇

93 (8)

The mean free path (also called the relaxation length) of a photon with specific energy in an absorber, is the mean distance between two successive interactions experienced by the photon within the absorber that removes it from the incident beam. If 𝜇 is measured in cm-1, then 𝜆 will be in cm. for a given thickness 𝑡 of an absorber, the number of mean free path in it is specified by the dimensionless quantity 𝜇𝑡. As expected 𝜇𝑡 is also a function of the material, thickness, and photon energy.

Effect of Scattered Photons on Dose Calculations: Concept of Buildup Factor The setup shown in Figure 2 is not achievable in many photon applications where absorbed dose measurement and shielding calculations are required. There is always a departure from this setup and thus the detector in addition captures scattered photons as shown in Figure 4. This implies that the evaluation of dose via equation 5 and those derived from it will be inaccurate. In such situation the dose measured by the detector will be: 𝐷𝑇 (𝑥) = 𝐷 ′ (𝑥) + 𝐷 ′′ (𝑥)

(9)

𝐷 ′ (𝑥) is the same as in equation 5 and 𝐷 ′′ (𝑥) is the dose due to the detector response to secondary photon beams. The secondary beam comprises photons scattered one or many times within M before emerging into D, characteristic X-rays, Bremsstrahlung, fluorescence, and annihilation photons all of which results from the interaction of primary photons with M particles [4]. The ratio of the total dose to that of the dose due to collided photons is referred to as the buildup factor B i.e.: 𝐵=

𝐷𝑇 (𝑥) 𝐷 ′ (𝑥)

=

𝐷 ′ (𝑥)+𝐷 ′′ (𝑥) 𝐷 ′ (𝑥)

=1+

𝐷 ′′ (𝑥) 𝐷 ′ (𝑥)

The total dose could now be written as:

(10)

94

Oyeleke Olarinoye 𝐷𝑇 (𝑥) = 𝐵𝐷 ′ (𝑥)

(11)

The buildup factor is a dimensionless multiplier which is used to correct the dose measured in good geometry procedure for broad beam geometry. Generally, B is a function (i) photon energy (E), (ii) material thickness or depth of interest (in mfp) in the absorber, (iii) geometry of the source i.e., isotropic point source or parallel beam, (iv) the chemical nature of the attenuator mostly described in terms of its atomic number for pure element and effective atomic number for chemical compound or mixture and (v) the geometry of the absorber (finite, infinite, stacked, layers etc. [2]. Consequently, for bad geometry and anisotropic sources: 𝐷𝑇 (𝑥) = 𝐵(𝜇𝑡, 𝐸, 𝑍)𝐷 ′ (𝑥)

(12)

The value of 𝐵(𝜇𝑡, 𝐸, 𝑍) is always greater than unity except for isotropic sources with good geometry where 𝐵(𝜇𝑡, 𝐸, 𝑍). = 1 as can be seen in equation 11. The buildup factor helps according to equation 12 in the accurate determination of absorbed doses and material thickness required for shielding function. The buildup factor comes in different flavours depending on the detector’s response or radiation quantity of interest of interest. We can thus have energy absorption, exposure, flux and dose buildup factors where the quantity of interest is energy deposited, exposure (air kerma), and absorbed dose in an absorbing medium respectively.

Figure 3. Attenuation coefficients of Pb as a function of energy.

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95

Figure 4. Broad beam (bad) geometry photon transmission.

Effect of B on Shielding Requirement: A Practical Approach Assuming a good geometry approximation, the photon transmission factor (TF) outside a shield of a specific material according to equations 4 and 5 is: 𝐷′

𝑇𝐹 = 𝐷′ = 𝑒 −𝜇𝑡 𝑜

(13)

This is equivalent to the attenuating factor of the absorber. Now, if we consider scattered beam as we have in broad beam geometry (Figure 4), for the same TF factor as required, then: 𝑇𝐹 = 𝐵𝑒 −𝜇

′𝑡

(14)

where, 𝜇′ is the correction to the attenuation coefficient for the broad beam consideration. Equating equations 13 and 14: 𝜇′ = 𝜇 −

𝑙𝑛𝐵 𝑡

(15)

The above equation shows that the narrow beam over-estimate the attenuation coefficient and thus the thickness of the shield required to get a particular TF is underestimated. The corrected attenuation coefficient can then be used in equation 13 to evaluate the shielding thickness required.

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Suppose one wishes to calculate the thickness of lead (Pb) required to reduce photon transmitted dose by 90%. If the energy of the photon is 1.5 MeV, taking the mass attenuation coefficient of Pb for narrow beam as 0.052 cm2/g at 1.5 MeV, if the density of Pb is 11.35 g/cm3, its µ will be 0.5925 cm-1. The required thickness required for narrow beam consideration is: 𝑡=

𝑙𝑛 𝑙𝑛 0.1 = 3.89 𝑐𝑚 0.5925

This is equivalent to a depth of 2.30 mfp. At this depth, the buildup factor of Pb at 1.5 MeV is 1.81. the adjusted µ due to B is now according to equation 15 is 0.44 cm-1. This shows that the narrow beam geometry overestimates the linear attenuation coefficient by at least 34%. Thus the required thickness for the TF will be underestimated if the narrow beam is used. To get the actual thickness required, the corrected µ is used in the narrow beam equation, thus: 𝑇𝐹 = 𝑒 −𝜇

′𝑡′

⟹ 𝑡′ =

𝑙𝑛 𝑙𝑛 0.1 = 5.23 𝑐𝑚 0.44

The above showed that the thickness should be at least 5.23 cm if the desired shielding is to be achieved. This procedure gives an approximate result as the new thickness will require a new buildup factor at 𝜇′ 𝑡 ′ mfp. This is difficult to get as we will need to get 𝑡 ′ first. The most practical approach is to iterate. Once the new thickness (5.23 cm) is obtained one estimate B for this thickness. The thickness is adjusted iteratively until one gets the desired TF i.e: 𝑇𝐹 = 𝐵(𝜇′ 𝑡 ′ )𝑒 −𝜇

′𝑡′

(16)

Methods of Evaluating Photon Buildup Factor The first set of buildup factor (B) data was provided for mono-energetic point isotropic sources of gamma rays traversing through infinite

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97

homogeneous medium by Goldstein and Wilkins [5, 6]. This was a sequel to the development of the concept of buildup for the first time by Gladys White in 1950 [7]. The data considered only the incoherent interaction of photons using the moment method which affected the accuracy of the data [8]. Recently, many data sets for buildup factor have been published using an array of different methods by different research groups. These groups have published the values of B for different photon absorbing materials, energy and depth. Amongst all the available methods only few are widely accepted based on issues that border on accuracy and ease of procedure. Generally, these methods can be classified into four broad categories: 1. 2. 3. 4.

Experimental procedure Photon transport simulation software Analytic expressions Computer codes based on analytic expressions

Experimental Method The experimental determination of B follows similarly to the setup used for the determination of linear attenuation coefficient. Considering Figure 2, the photon transmission equation is then given as: 𝑅 = 𝑅𝑜 𝑒 −𝜇𝑡

(17)

where 𝑅 and 𝑅𝑜 are the detector response with and without the absorber in place. If the collimators are removed (bad geometry) such that secondary photons due to scattering and other interactions reaches the detector (Figure 4.), the transmitted photons response would be: 𝑅 ′ = 𝑅𝑜 𝑒 −𝜇𝑡

(18)

According, to the definition of B based on the detector response of interest becomes:

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Oyeleke Olarinoye

𝐵(𝐸, 𝜇𝑡) =

𝑅′ ) 𝑅𝑜 𝑅 ( ) 𝑅𝑜

(

(19)

𝑅′

𝑅

𝑙𝑛 𝑙𝑛 𝐵(𝐸, 𝜇𝑡) =𝑙𝑛 𝑙𝑛 (𝑅 ) −𝑙𝑛 𝑙𝑛 (𝑅 ) 𝑜

𝐵(𝐸, 𝜇𝑡) = 𝑒

𝑜

𝑅′ 𝑅 ) −𝑙𝑛𝑙𝑛 ( ) ] 𝑅𝑜 𝑅𝑜

[𝑙𝑛𝑙𝑛 (

(20)

(21)

The B in the above equation is to be determined for specific depth in mfp. The error associated with the estimated B (∆𝐵) as above can be obtained from the equation: ∆𝑅′ 2 ) 𝑅′

∆𝐵 = 𝐵√[(

∆𝑅 2

+( ) ] 𝑅

(22)

where ∆𝑅 ′ and ∆𝑅 is the error associated with the parameter𝑅 ′ and 𝑅 respectively. The buildup factor estimated this way would be for the detector response used accordingly, furthermore, it will be for the energy of the source used in the experiment. For other photon energies, the source would have to be changed accordingly to one with energy of interest and the procedure repeated accordingly.

Photon Transport Simulation Software The photon transmission experiment can be simulated via the use of computer codes. With such codes, one can obtain the photon flux or dose transmitted through an absorber in narrow and broad beam geometries. This enables the easy calculation of B without going through the rigour of laboratory settings. The transport simulation codes have been proven to be very accurate compared to analytic or deterministic methods of evaluating B in different media, energies, and geometries. These codes are mostly based

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on Monte Carlo methods. Examples of such codes include: ASFIT, PALLAS, and MCNP [9-14]. In recent times, the MNCP simulation code developed by Los Alamos National Laboratory [15] has been used extensively by different research groups and for different materials. The MCNPs are a group of multipurpose codes capable of simulating the transport of photons (gamma and X-rays), neutrons, electrons and heavy ions through matter. Detailed discussion on the use of MCNP can be found in the literature [16].

Analytic Expressions for Evaluating B A lot or research geared towards obtaining buildup factor by the use of analytic expression has been concluded. Consequently, some approximate expressions have been proposed and adopted for calculating B for point isotropic and mono-energetic sources. Notable amongst these expressions are the Taylor, Berger and G.P fitting approximation expressions. Among these three, the G.P fitting method has been proven to be more accurate and thus used extensively by many. However, the G.P fitting approach requires much calculations. A brief discussion of each of the three methods is given below.

Taylor Approximation of B The Taylor function provides a simple fit expression for the evaluation of B in terms of three fitting coefficients. The expression for the formulation is given as [2]: 𝐵(𝐸, 𝜇𝑡) = 𝐴𝑒 −𝑎𝜇𝑡 + (1 − 𝐴)𝑒 −𝑏𝜇𝑡

(23)

The coefficients, A, a, and b are parameters that depend on energy, attenuating material and detector response. The parameters have been compiled for some materials and energy by [17]. The expression is easy to

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Oyeleke Olarinoye

use but its accuracy is an issue when B is required for low atomic number material and low energy [18].

Berger Formulation for B The Berger formulation just like the Taylor formula, provides a simple fitting expression for the evaluation of B. The Berger formula is of the form: 𝐵(𝐸, 𝜇𝑡) = 1 + 𝐴𝜇𝑡𝑒 −𝑏𝜇𝑡

(24)

Also the coefficients A and b are energy, material and detector response dependent. Similar to the Taylor formula, the Berger formula is less accurate in the low energy regions and for low atomic number materials [17].

Geometric Progression (G.P.) Fitting Formulation of B The geometric progression (G.P.) fitting method of evaluating photon buildup factors is by far the most used analytic expression. It was developed by Harima (1991). The method has been found to be very accurate compared to other analytic expressions. Its accuracy is with 5% using data from photon transport computer codes such as PALLAS, ASFIT, EGS4 and MCNPs [914, 19]. This accuracy spans through a large spectrum of photon energy and materials. Consequently, the method has been used by the ANS- ANSI/ANS 6.4.3-1991) [20] to evaluate and compile exposure and energy absorption buildup factor for 23 elements, water air and concrete for photon energies within 15 keV and 15 MeV and for depth up to 40 mfp. The method has been improved upon to include depth up to 100 mfp. The ANS data forms the basis for the use of the method for other materials and depth not included in the report. According to G.P method, the evaluation of B follows three distinct procedure viz:

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1. calculation of equivalent atomic number, Zeq 2. Evaluation of G.P. fitting parameters 3. Estimation of buildup factor from the fitting parameters

Calculation of Effective Atomic Number (Zeq) To evaluate Zeq of materials, their Compton partial interaction coefficient (µc) and mass attenuation coefficients (µT) (both in cm2/g) must be obtained first for the photon energy of interest (say, 0.015 MeV– 15 MeV). The ratio, R=c/T , of each material is subsequently calculated and matched at same energies to the corresponding ratio of elements up to the heaviest element in composite materials in the ANS data. If there is a match, then the atomic number of the element it matches with at a specific energy becomes the Zeq of the material. Otherwise, if the value of R of the material fall between ratios of two successive elements, the Zeq is obtained by interpolation using the expression:

(25) R1 and R2 are the Rs of two successive elements of atomic numbers Z1 and Z2 respectively within which R falls at a particular energy.

Evaluation of G.P. Fitting Parameters Calculation of photon buildup factor by the G.P., the fitting procedure requires five fitting parameters. These parameters (a, b, c, d, and Xk) depend on Zeq and photon energy. The ANS has tabulated these parameters for 23 elements and for 25 standard photon energies. For cases where the ratio R of the material fits that of any of the elements, the parameters of the element is adopted for that material. However, if the R of the material does not match

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any of the 23 elements, its G.P. fitting coefficients is also interpolated using the logarithmic interpolation formula: 𝐹=

𝐹1 (𝑙𝑜𝑔𝑙𝑜𝑔 𝑍2 −𝑙𝑜𝑔𝑙𝑜𝑔 𝑍𝑒𝑞 )+𝐹2 (𝑙𝑜𝑔𝑙𝑜𝑔 𝑅𝑍𝑒𝑞 −𝑙𝑜𝑔𝑙𝑜𝑔 𝑍1 ) 𝑙𝑜𝑔𝑙𝑜𝑔 𝑍2 −𝑙𝑜𝑔𝑙𝑜𝑔 𝑍1

(26)

where F1 and F2 are the values of the G-P fitting parameters obtained from ANS database for Z1 and Z2 respectively.

Evaluation of Buildup Factors The buildup factor (B(E,x)) is estimated for the considered material, energy, and depth up to 100 mfp by the using the analytical expressions: 𝐵(𝐸, 𝑥) = 1 +

(𝑏−1)(𝐾𝑥 −1) 𝐾−1

for 𝐾 ≠ 1

(27)

𝐵(𝐸, 𝑥) = 1 + (𝑏 − 1)𝑥 for 𝐾 = 1

(28)

where, 𝑥 −2) −𝑡𝑎𝑛ℎ(−2) 𝑋𝑘

𝑡𝑎𝑛ℎ𝑡𝑎𝑛ℎ (

𝑎

𝐾(𝐸, 𝑥) = 𝑐𝑥 + 𝑑

1−𝑡𝑎𝑛ℎ(−2)

for 𝑥 ≤ 40 𝑚𝑓𝑝

(29)

For 𝑥 > 40 𝑚𝑓𝑝, 𝐾(𝐸, 𝑥) = 1 + (𝐾35 − 1)∅ for, 0 ≤ ∅ ≤ 1 𝐾

𝜖(𝑥)𝑓

𝐾(𝐸, 𝑥) = 𝐾35 (𝐾40 ) 35

𝜖(𝑥) =

𝑥 0.1 −1 35 40 0.1 ( ) −1 35

( )

,

for, ∅ < 0, ∅ > 1

(30)

(31)

(32)

Ambient Dose Buildup Factors 𝐾 −1

where 𝑓 = 0.8 and ∅ = 𝐾40 −1 35

𝐾35 = 𝐾(𝐸, 35), and 𝐾40 = 𝐾(𝐸, 40),

103 (33) (34)

The factor K (E, x) is the photon dose multiplier factor at energy E, and depth 𝑥 = 𝜇𝑡 (mfp). Although, the standard ANS data (ANSI/ANS 6.4.3-1991) presented data for only 25 standard energies, however, B can be evaluated for energies of laboratory sources by using logarithm interpolation. The interpolation of the fitting parameters is done for the energy of interest and used subsequently for evaluating B using equations 27 to 34. The accuracy of the G.P. fitting formulation has been found to be within 3% for water up to a depth of 40 mfp, this is in contrast to the Taylor and Berger expressions with deviations as high as 53.2% and 42.7% respectively [4, 21]. This explains the reason for the wide application of the G.P fitting method compared to the latter two.

Computer Codes Based on Analytic Expressions Based on the enormous calculations and steps involved in the use of the G.P. procedure, coupled with its accuracy, some computer codes have been written for the purpose of evaluating B based on the method. Two recent codes written for this purpose are EXABCal and Phy-x-psd codes [22, 23]. EXABCal code is a free, fast and easy to use programme written in Python programming language. The code was constructed to calculate B for compound, mixture and elements for energies between 15 keV and 15 MeV and for depth up to 40 mfp. The code was written following the sequence of the G.P. fitting method. The accuracy of the programme is very good and comparable to manual calculations using the G.P. method and the Monte Carlo methods (Olarinoye et al. 2019). However, the program does not calculate for depth greater than 40 mfp and for energy not included in the original ANS data [20]. The code has been made available free of cost by

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the authors upon request via the email address: (leke.olarinoye@ futminna.edu.ng). Another free software based on the G.P fitting method is the online user friendly software-Phy-X/PSD. The software is also capable of evaluating B to good accuracy compared to result from the Monte Carlo methods. However, the software is not available for use offline, consequently, a lot of internet data is expended when using it for calculation. The code can be assessed online via: http://www.phy-x.net/psd.

Buildup Factor for Multi-Layered Shields Sometimes due to cost, space and geometry constraints, shielding material in layers are used instead of a single homogeneous material. In fact, multi-layer shielding has been adjudged to be more practical than homogenous single-layer for gamma-ray shielding [2]. Treating such material as material using the additive rule of the attenuation coefficients of the different layers and its subsequent use in evaluation of B may introduce some errors. To address this issue, an improved set empirical equations for obtaining buildup factors of n-multi-layer barriers originally developed by Kalos [24] was presented by Linn and Jiang in 1996 [25]. Accordingly, the B for n-layered absorber for a plane-normal source is given as: 𝐵(∑𝑛−1 𝑥𝑖 , 𝑥𝑛 ) = 𝐵𝑛 (𝑥𝑛 ) + [𝐵𝑛 (∑𝑛−1 𝑖 𝑖=1 𝑥𝑖 ) − 𝐵𝑛 (𝑥𝑛 )] × [𝐾(∑𝑛−1 𝑖=1 𝑥𝑖 )𝐶(𝑥𝑛 )]

(35)

where, 𝐵𝑛 (𝑥𝑛 ) is the B of the nth-layer at depth x, 𝐾(∑𝑛−1 𝑖=1 𝑥𝑖 ) =

𝐵(∑𝑛−2 𝑖=1 𝑥𝑖 ,𝑥𝑛−1 )−1 𝐵𝑛 (∑𝑛−1 𝑖=1 𝑋𝑖 )−1

𝐶(𝑥𝑛 ) =𝑒𝑥𝑝 𝑒𝑥𝑝 (−1.08𝛽𝑥𝑛 ) + 1.13𝛽𝑙(𝑥𝑛 ) (for high-Z material on the incidence side)

(36) (37)

Ambient Dose Buildup Factors 𝛾

𝐶(𝑥𝑛 ) = 0.8𝑙(𝑥𝑛 ) + (𝐾) 𝑒𝑥𝑝(−𝑥𝑛 )

105 (38)

(for low-Z-material on the incident side) (𝜇𝑚 )𝑛 𝑚 )𝑛−1

𝛽 = (𝜇 𝛾=

(39)

(𝜇𝑐 )𝑛−1 (𝜇𝑐 )𝑛

𝑙(𝑥𝑛 ) =

𝐵𝑛 (𝑥𝑛 )+1 [1 − 𝐵𝑛−1 (𝑥𝑛 )+1

(40)

𝑒𝑥𝑝(−𝑥𝑛 )]

(41)

The above expressions can be used for any n-layers of shields taking two at a time for each computation, then adding a layer subsequently until all the layers have been accommodated. The equivalent thickness (𝑥𝑒𝑞,12 ) and equivalent atomic numbers (𝑍𝑒𝑞,12) of one layer obtained from two layers taken at a time is given as: 𝑥𝑒𝑞,12 = 𝑥1 + 𝑥2 𝑍𝑒𝑞,12 =

𝑍1 𝑥1 +𝑍2 𝑥2 𝑥1 +𝑥2

(42) (43)

The above equations/procedure give good results for multi-layered shields [26].

Effect of Photon Energy, Material Depth on B Generally, at energies above the K-absorption edge of a material B vary smoothly with respect to energy, depth and atomic number of the absorbing material. The behaviour of buildup factor with energy for water is shown in Figure 5. The energy range can be divided into: low (0.015 – 0.03 MeV); intermediate (0.03- 1MeV); and high (1-15 MeV) energy regions. In the low

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energy spectrum, the photoelectric effect is the major mode of interaction. Here, buildup factors are generally low and vary inversely as the atomic number. This is due to the fact that the photoelectric process removes the photon completely from the beam thus preventing photon buildup. As the photon energy increases, the influence of the photoelectric effect diminishes. The Compton interaction mode dominates. The buildup factors are very high in this region due to the fact that Compton scattering does not remove photons completely from the beam but rather scatters them. Beyond 1.02 MeV (high energy) region, pair production is the main interaction mode of photon interaction. The pair production interaction removes photons completely from the beam after interaction thus preventing buildup. Consequently, the buildup factors in the high energy region are also very low. As the thickness of the absorber increases, multiple scattering takes place thus the B increases with depth. This behaviour is similar for many materials if the photon energy does not include the absorption edge of the elements constituting the absorber.

Figure 5. Energy absorption buildup factors as a function of energy and depth.

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NEUTRON DOSE BUILDUP FACTOR Similar to photons, the total dose rate due to uncollided neutrons after passing through a shield material of thickness t is [1, 27]: 𝐷 = 𝐵𝐷𝑜 = 𝐵

𝑓(𝐸)𝑒𝑥𝑝(−𝛴𝑟 𝑡) 4𝜋𝑑 2

(44)

here, B, f(E), 𝛴𝑟 and d, are the neutron buildup factor, flux to dose conversion coefficient, total removal cross-section and detector source distance respectively. D and 𝐷𝑜 are average doses measured at the detector with and without buildup respectively. The shielding of neutrons involves three distinct steps [6, 27, 28] which are: slowing down of fast neutrons via scattering, absorption of slowed down neutrons, and the absorption of secondary radiations such as photons that are produced from other processes involved in the slowing down and absorption processes such as radiative capture. All these neutron interactions have different interaction crosssections, thus making interaction of neutrons with a shield very complex. It is this complexity that makes the use of B in neutron transport and dose estimation very scarce in the literature. Furthermore, B for neutrons dose is not unique with material unlike the photon B. Rather, it is sensitive to source geometry, neutron fluence, thickness of barrier, and energy spectrum. Consequently, a B value of 5 has been suggested for use for neutron when equivalent water thickness of 20 cm or more is used as a rule of thumb [2]. The neutron buildup can be obtained through experiment similar in procedure to that of photons. However, since neutron reaction cross-sections of materials are known with good accuracy, neutron B are mostly obtained by analytic solutions to neutron transport equations and by Monte Carlo simulations. Analytic solution of the neutron transport equation is a fast way of obtaining B, though it may not be very accurate [29], however, the analytic solution method may be used as an initial shielding analysis procedure, since they are fast. The most reliable and accurate way of obtaining neutron dose buildup factor is via the simulation of neutron transport in material using Monte Carlo based computer codes such MCNPs

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[30]. Another way of obtaining B is through the use of empirical expressions. Salehi et al. [27] and Shin et al. [31] have given fitting expression for the evaluation of B for iron and concrete as a function of mass thickness (x): 𝐵(𝑥) = 1 + 𝑎(1 − 𝑒𝑥𝑝(𝑏𝑥))𝑒𝑥𝑝(𝑐𝑥)

(45)

In equation 45, a, b, and c are fitting parameters with values equal to 6.19, 0.02 and 0 for neutron energies between 80 to 120 MeV. The equation has yielded good results when compared with MCNP simulations [27, 30].

CONCLUSION For practical estimation of ambient dose in a medium due to absorption of gamma rays and fast neutrons, both primary and scattered radiations must be considered when the absorber thickness is greater than 1 mfp. Consequently, the use of radiation buildup factors is very important for dose and shielding requirement calculations. There are many methods of estimating dose buildup factors. The choice of method is mostly dictated by dose quantity of interest, geometry of absorbing medium, radiation parameters (type and energy), and accuracy required. However, the use of Monte Carlo based methods can be used for nearly all cases.

REFERENCES [1]

[2]

Tsoulfanidis N., Landsberger S. 2014. Measurement and detection of radiation, 4th Edition. 146, 150 & 157. CRC Press, Taylor and Francis Group, London. Martin, J. E. 2006. Physics for Radiation Protection: A Handbook. 2nd edition. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Pp. 384, 389, 393; 399.

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[4]

[5]

[6] [7]

[8]

[9]

[10]

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[13]

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Gerward, L., Guilbert, N., Jensen, K. B. 2004. “WinXcom: A programme for calculating X-ray attenuation coefficients.” Radiation Physics and Chemistry 71, p. 653-654. Durani, L. 2009. “Update to ANSI/ANS-6.4.3-1991 for low-Z and compound materials and review of particle transport theory.” UNLV Theses/Dissertations/Professional Papers/Capstones. Paper 43. Goldstein, H. Wilkins, Jr., J. E. 1954. “Calculations of the Penetrations of Gamma Rays.” NDA/AEC Report NYO-3075, US Government Printing Office, Washington, DC. Shultis J. K., Faw R. E. 2005. “Radiation shielding technology.” Health Physics 88(4):587–612. White, G. R. 1950. “The penetration and diffusion of Co-60 gamma rays in water using spherical geometry.” Physical Review, 80: 154156. Mann, K. S. 2019. “Investigation of Gamma-Ray Shielding by Double-Layered Enclosures.” Radiation Physics and Chemistry, 159: 207-221. https://doi.org/10.1016/j.radphyschem.2019.03.007. Gopinath, D. V., Samthanan, K. 1971. “Radiation in OneDimensional Finite System- Part I: Development in Anisotropic Source-Flux Iteration Technique ASFIT.” Nuclear Science Engineering 43(2): 186-196. Takeuchi, K., Tanaka, S. 1984. “PALLAS-ID (VII): A code for direct integration of transport equation in one dimension plane and sphere geometrics.” Report JAERI-M 84-214, Japan Atomic Energy Research Institute, Japan. Nelson, W. R., Hirayama, H., Rogers, D. W. 1985. “EGS4 code system”, Report SLAC-265, SCAL Stanford Nat. Lab, USA. Sardari, D., Abbaspour, A., Baradaran, S., Babapour, F. 2009. “Estimation of gamma- and X-ray photons buildup factor in soft tissue with Monte Carlo method,” Applied Radiation and Isotopes 67: 14381440. Hirayama, H. 2002. “Double Differential Bremsstrahlung Yields for a Discrete Ordinate Code by EGS4.” report KEK Internal 200-5.

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[14] Singh, V. P., Medhat, M. E., Badiger, N. M. 2014 “Assessment of exposure buildup factors of some oxide dispersion strengthened steels applied in modern nuclear engineering and designs.” Nuclear Engineering Design 270: 90-100. [15] MCNP 2003. X-5 Monte Carlo Team. A general Monte Carlo Nparticle transport code, version 5, volume 1. Overview and theory, LA-UR-03-1987, Los Alamos National Laboratory. [16] Radaidel M. I. Ibrahim J. 2020. “Avanced gamma-ray transport by Monte Carlo simulation” In A closer look at gamma rays, Edited by Singh V. P. Mann K. S. 51-80. Nova Science Publishers, Inc. New York. [17] Harima, Y., Tanaka, S., Sakamoto, Y., Hirayama, H. J. 1991 “Development of new gamma- ray buildup factor and application of shielding calculations,” Nuclear. Science Engineering 94: 24-35. [18] Harima, Y., Sakamoto, Y., Tanaka, S., Kawai, M. 1986. “Validity of the geometric progression formula in approximating gamma-ray buildup factors”, Nuclear Science Engineering 94: 24-35. [19] Sakamoto, Y., Trubey, D. K. 1991. “Geometric Progression GammaRay Buildup Factor Coefficients.” Radiation Safety Information Computation Centre Data Package DLC- 129/ANS643, Oak Ridge Nat. Lab, USA. [20] ANSI/ANS-6.4.3. 1991. “Gamma-ray attenuation coefficients and buildup factors for engineering materials.” American Nuclear Society. La. Grange Park., IL. [21] Hirayama, H. J. 1993. “Calculation of gamma-ray exposure buildup factors up to 40 mfp using the EGS Monte Carlo code with a particle splitting.” Journal of Nuclear Science and Technology 32 (12): 12011207. [22] Olarinoye, I. O., Odiaga, R., Paul, S. 2019. “EXABCal: A programme for calculating photon exposure and energy absorption buildup factors.” Heliyon, 5, eo2017. [23] Şakar E. Özpolat O. F. Alim B. Sayyed M. I. Kurudirek M. 2019. “Phy-X/PSD: Development of a user friendly online software for

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[24] [25]

[26] [27]

[28]

[29]

[30]

[31]

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calculation of parameters relevant to radiation shielding and dosimetry.” Radiation Physics and Chemistry, 166: 108496. Kalos, M. H. 1956. “A Monte Carlo calculation of the transport of gamma rays.” NDA, 56-57. Lin, U. Jiang, S. 1996. “A dedicated empirical formula for gamma-ray buildup factors for a point isotropic source in stratified shields.” Radiation Physics and Chemistry 48 (4): 389- 401. Mann, K. S. 2019. “Investigation of gamma-ray shielding by doublelayered enclosures.” Radiation Physics and Chemistry 159: 207-221. Salehi D. Danish S. Jozani M. S. 2018. “Computation of neutron dose buildup factors for ordinary concrete in the fast neutron range of energy: A comparative study.” Iran Journal of Science and Technology. Accessed January 28, 2020 https://doi.org/10.1007/ s40995-018-0492-1. Shin K, Kotegawa H, Sakamoto Y, Nakane Y, Nakashima H, Tanaka S. 1997. “Point isotropic buildup factors of medium energy neutrons for concrete, iron and a double layer of iron followed by concrete.” Radiation Protection Dosimetry 71:269–278. Fernandes J. C. L, Vilhena MT, Bodmann BE, Borges V. 2013. “On the buildup factor from the multi-group neutron diffusion equation with cylindrical symmetry.” World. Journal of Nuclear Science and Technology 3:1–5. Shirani A, Shahriari E. 2007. “Determination of neutron dose equivalent buildup factors for infinite slabs irradiated by point isotropic neutron sources using the MCNP code.” Journal of Science Islamic Republic of Iran 18:177–180. Shin K., Ishii Y. 1992. “Buildup factors for medium energy neutrons up to 400 MeV.” Radiation Protection Dosimetry 40(3):185–199.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 5

CALCULATION OF BUILDUP FACTORS USING TAYLOR’S APPROXIMATION FOR MULTI-LAYERED SHIELDS Nisha Raj* Department of Physics, Government College, Barwala, Panchkula, India

ABSTRACT The buildup factors play a vital role in radiation shielding analyses for designing and development of a shield to reduce the intensity of radiations reaching out to any object or at point of observation. In particular, the investigations of buildup factors for multi-layer shields are more crucial to meet practical shielding requirements. The Taylor’s approximation has been widely exercised through a number of studies for radiation shielding calculations and it is observed that this approximation is accurate enough to evaluate buildup factor data for elements and compounds composing single-layered shields. In this chapter, Taylor’s formula is attempted for estimation of buildup factors for multi-layered shields. Numerical *

Corresponding Author’s Email: [email protected].

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Nisha Raj calculations have been performed by developing a program source code employing this fitting approximation and the computation is able to reproduce buildup factors data for single-layer shields. Moreover, results for two-layered, three-layered, four-layered and five-layered have also been produced numerically. The program calculates buildup factors in the energy range of 0.5 MeV-10 MeV for shields having effective atomic number lying between 10 and 92. Wherever possible, the validity of the developed source code is tested by comparing outputs with available results in literature.

Keywords: gamma radiation, buildup factor, Taylor approximation, multilayer shields, program BUF

INTRODUCTION The concern of protection against radiation grows with the advancements of nuclear technologies in view of its extensive use in industries posing increased risk of radiation exposure to mankind. For this reason, the understanding of interaction mechanisms of radiations with matter for shielding purposes has been an area of interest for radiation physicists and researchers since past many decades. In the shielding applications, the calculations of buildup factor data are always central for any shield to be designed whether being a composite of mixed materials or having the component materials stacked together. A composite shield is generally built from a base material mixed with additive elements or compounds. By doing so, the shielding capability of the material can be enhanced. For instance, the material density can be increased by varying the quantity of additives in a concrete which consequently act as a better shield [1]. However, the homogeneous mixing of materials in a composite shield is also difficult to obtain which can further lead to inconsistent shielding of radiations [2, 3]. This non-homogeneous mixture of the composite can also cause pure region gaps for the radiation to penetrate through [4]. Such defects of the composite shield can be prevented by using a multi-layered shielding design approach [5]. Moreover, in real applications, the radiations interactions occur with more than one attenuation media. For this reason, the

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studies and investigations should be more targeted for calculation of buildup factor (B) data for multi-layer shields. This problem needs to be tackled carefully since the calculation of buildup factors are more complex resulting from different effects produced in each shielding layer. Considerable methods have been developed over years to calculate buildup factors with good accuracy for many elements, compounds and mixtures that include invariant-embedding method [6, 7], Monte-Carlo simulations [8], and the geometric-progression (G-P) formula [9-11]. For many computational calculations, it is convenient to express the tabulated data of B-values [12] in some mathematical forms and many such functions have been developed. There are a number of empirical formulae proposed well surveyed by Trubey (1966) [13] to calculate B in which few parameters are to be adjusted up to a reasonable fit to basic buildup factor data presented mostly by Goldstein and Wilkins [12]. The different empirical fitting formulae viz. linear approximation [14], Taylor’s approximation [15], Berger’s approximation [16], Capo’s formula [17], Broder’s formula [18], Lin and Jiang formula [19] and the geometric-progression formula [20] have been broadly examined to evaluate the buildup factors [14] mostly for single-layered shields. Harima (1983) [21] proposed an empirical formula for gamma ray buildup factors for two-layered shields. Kuspa [22] has investigated the buildup factors in single- and double-layered shields using Monte-Carlo method. Hirayama et al. [23] and Shin et al. [24] determined the buildup factors in two-layered and three-layered shields with different combinations of component materials using EGS4 MC codes. The absorbed dose buildup factors in two-layer shields were developed by Guvendik et al. (2000) using formulae based on MCNP codes within the thickness of 1 to 10 mfp [25]. Sharaf et al. (2015) [26] and Mann et al. (2016) [27] used the G-P formula to evaluate energy buildup factors in multi-layer style structures. Very recently, Sajali et al. (2019) [28] have presented a good review on multi-layer radiation shielding and highlighted the major findings on material arrangements and the buildup factors. The simplest linear approximation was employed earlier by Wood [14] to calculate the buildup factors for multi-layer shields through numerical computations by developing a program code BMIX. The program BMIX

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assumes linear dependence of B on the attenuation thickness and is cumbersome to use in general. To this endeavor, using a better fitting approximation as Taylor’s form, the program code BUF has been developed and described in this chapter to calculate buildup factors in multi-layered shields. The program code BUF may be looked as an extended version of BMIX. Notably, the program BUF generates the buildup data for intermediate and high incident gamma photon energies ranging from 0.5 MeV to 10 MeV in shields with multiple layers having effective atomic number between 10 and 92.

THE PROBLEM OF SHIELDING The last century has seen radiations and radioactivity evolution from laboratory interests to essential features of a modern technological age. The introduction of radiations through different capacities nuclear power plants, nuclear armaments facilities, medical diagnostics like X-ray imaging, CT scanning, radiotherapy machines etc., and other intense sources of radiations like solar rays, cosmic rays and radioactive materials do require shields that are thick enough compared to the average distance between the photon collisions. Most of the radiations are released during the nuclear fission process itself inside a nuclear reactor core. Besides the energetic neutrons and gamma rays that emit during the fission event, other highly radioactive nuclides that emit alpha, beta and gamma radiations are also generated through fission fragments. Along with the grave understanding of the different types of radiations, their potential benefits and harms that could arise from radiation exposure, one must possess a comprehensive knowledge of technical subjects’ viz. radiation source characteristics, radiation protection criteria, the dosimetry involved and the basic physics describing the interaction mechanisms of such radiations with matter. This study is quite more complex than it appears in first instance for many reasons like

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1. an exposure may involve dissimilar radiations including charged particles or neutral rays at one time which are understood by relatively different radiation physics principles, 2. the human body consists of various inhomogeneous geometry and density tissues leading to severely complex interaction mechanisms. Radiation dosimetry studies describe the regulatory limits set for radiation dose associated with radiosensitive body organs [29]. In a more general sense, shielding analysis is the study of how radiation is generated, how it got transported from its origin, how it interacted with matter, how it created changes microscopically in the medium through it traversed and how the medium was affected by those changes. In order to protect surrounding man-power working in the vicinity of radiation applications against radiation exposures, it becomes necessary to absorb the nuclear radiations by some thick shield to reduce the exposure/dose level to an optimum level. The attenuation of radiations to tolerable dose level is normally done by covering the reactor core by sufficiently huge mass of suitable materials. Such shields made for this purpose are broadly labeled as biological shields. The problem of shielding is concerned with the type of radiation that causes ionization of the medium with which it interacts. The radiation consists of energetic particles carrying electric charge like β-particles, α-particles, or protons and some recoil nuclei. Such radiations are termed as directly ionizing radiations. Other types of radiations such as X-rays, neutrons or gamma rays are not charged and therefore involve a more complex mechanism of interaction with the emission of further secondary charged particles that cause most ionization in the interacting medium. Consequently, the X-rays, γ-rays and neutrons are called indirectly ionizing radiations. This classification of radiations after ionization capabilities has significant implications in the analysis of shielding methods. Directly ionizing radiations can be comparatively easily stopped as these interact very strongly with atoms in the shielding media. In contrast, indirectly ionizing radiations may be rather penetrating following with massive and expensive shielding techniques. This chapter has for this reason been diverted more towards shielding of indirectly ionizing radiations, and in particular γ-rays.

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Evidently, the best shielding results from any radiation can only be produced once sufficient understanding of all its possible interaction mechanisms with matter is made. Few important interaction mechanisms of γ-rays with matter are briefed in the next subsection.

Processes of Interactions of Gamma Rays with Matter Since adequate narrations have been given by many authors in literature [30-32] concerning the various processes through which gamma photons interact with matter, it would be out of place to present here the extended details for those. However, in order to describe properly the choice of data to be useful for the calculations, an attempt has been made to concisely summarize the main interaction processes here. Before beginning, a clear distinction must be made between primary interactions of gamma photons with matter and secondary interactions that generate out of primary ones, which further produce gamma rays. Fig. 1 depicts most of the interactions [12] which are all measurable in the energy region of interest. Only the first three processes are taken into account in this chapter for discussion neglecting all other justifying by a remark that below energy 10 MeV, other processes contribute very small in comparison to the first three [12].

Photoelectric Effect This process refers to interaction of the incident photon with a bound electron of the target medium resulting into absorption of entire incident energy and ejection of a bound electron usually from K- or L-shell. The vacancy thus created is immediately filled by electron transition within shells and as a result, the characteristic X-rays of the atoms of the target appear. Therefore, this process is effectively predominant interaction mode when incident photon energy (usually < 0.5 MeV) enters into the target

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medium with high atomic number materials such as lead, uranium or tungsten.

Compton Scattering This is the case when the incident photon gets scattered by an electron of the target medium, resulting in the transfer of only a fraction of its energy and momentum to the electron. As scattering is possible in all directions, the energy transferred varies from zero to large values of incident energy. This mode of interaction becomes significant in the incident energy range 0.5 MeV to 1.5 MeV for targets having low or intermediate atomic numbers like aluminum, iron or water. The major difficulty in gamma attenuation arises from implications of multiple Compton scattering processes.

Figure 1. Schematic classification of various interaction mechanisms of gamma photons with matter.

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Pair-Production In this interaction mode, which becomes effective in high incident photon energies i.e., greater than 1.5MeV, the incident photon is entirely absorbed, and in its place an electron-positron pair appears in the vicinity of an atomic electron or nucleus. In the first instance, the interaction seems to be completely absorptive but a closer inspection exposes that “annihilation gamma rays” of comparatively low energy are produced during this process. The studies of attenuation of gamma rays must include explicitly these annihilation gamma rays. Table 1 summarizes the photon atomic cross-sections for above three interaction modes [30]. Table 1. Dependence of interaction modes on atomic number Z and incident gamma photon energy 𝑬𝜸 Interaction mode

Z-dependence 4−5

𝐸𝛾 -dependence

Photoelectric effect

𝑍

Compton scattering

𝑍

1/𝐸𝛾3.5 1 𝐸𝛾

Pair-production

𝑍2

𝐸𝛾

Linear and Mass Attenuation Coefficients It is often convenient to use the linear attenuation coefficients in the studies of photon transmission in target absorbers. This term, symbolized by µ, and depending on incident photon energy and atomic number Z of target, uniquely characterizes the diffusion mechanisms of gamma rays in the target. The linear attenuation coefficient µ has dimensions of inverse length (𝑐𝑚−1), which is interpreted as the probability that a photon will interact with the target per unit path length. Further, the mean free path of a photon λ in the target medium is given by

Calculation of Buildup Factors … 1

𝜆=𝜇

121 (1)

This is also clear from above equation 1 that if the thickness of the target material or shield is x in centimeters, then μx will be the shield thickness in units of mean free path (or mfp’s). In all kinds of shielding calculations, we are generally interested in total radiation count, collided component as well as uncollided one. Here, the collided component is that which has undergone interaction with the shield atoms through some mechanism and an uncollided component passes through the shield without occurrence of any type of interaction modes. Next, the mass attenuation coefficient (µ/ρ) is the probability of an interaction mode (PE, CS, PP) per unit density thickness. Its units are cm2/g. In other words, µ/ρ is the probability of interactions per g/cm2 travelled by the photon. The attenuation coefficient and the target density can be employed to estimate the transmission of gamma rays through a chosen thickness of target or shielding material or the thickness of a shielding material necessary to attain a desired stage of attenuation. The linear and mass attenuation coefficients have inverse dependence on incident gamma energy E and are directly proportional to the atomic number Z of the elements from which the shielding material has been built [31]. Now, since the density of shielding material may vary in various applications and procedures, it becomes somewhat important to eliminate the dependence of µ on density and therefore, a mass attenuation coefficient, μ/ρ, where ρ denotes the density of the shielding material becomes the quantity of main interest having units of cm2/g. The comprehensive data tables of the linear and mass attenuation coefficients for various materials are available in various shielding manuals and reports [12, 13]. Moreover, the values of linear attenuation coefficients 𝜇𝑖 (𝑐𝑚−1 ) for the few very commonly used materials in radiation shielding are listed in Table 2. These coefficients account for all kinds of interaction modes that may remove the photons from the primary beam and play a central role in the calculation for buildup factors. As mentioned earlier, 𝜇𝑖 ’s are target-specific and dependent on the incident photon energy.

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Table 2. Linear attenuation coefficients in units of 𝒄𝒎−𝟏 for water, aluminum, iron, lead and ordinary concrete E (MeV)

Water ρ=1.0 g/cm3

Aluminum ρ=2.67 g/cm3

Iron ρ=7.87 g/cm3

Lead ρ=11.35 g/cm3

Concrete ρ=23 g/cm3

0.500 1.000 2.000 3.000 4.000 5.000 6.000 6.129 7.000 7.115 10.000

0.0969 0.0707 0.0494 0.0397 0.0340 0.0303 0.0277 0.0274 0.0258 0.0256 0.0222

0.2279 0.1659 0.1167 0.0956 0.0838 0.0765 0.0717 0.0713 0.0683 0.0680 0.0626

0.6625 0.4270 0.3358 0.2851 0.2608 0.2477 0.2407 0.2403 0.2370 0.2368 0.2357

1.8319 0.8061 0.5228 0.4806 0.4764 0.4849 0.4984 0.5002 0.5141 0.5161 0.5643

0.2050 0.1494 0.1048 0.0851 0.0740 0.0669 0.0620 0.0616 0.0585 0.0582 0.0524

Source: James E. Martin, Physics for Radiation Protection, 2006 [32].

THE IDEA OF BUILDUP FACTOR As has mentioned in the previous section, the practical shielding calculations include total impact of radiations reaching the point of observation (may be a detector or human body). In order to determine the complete aftermath after transmission or to exclusively ensure the shielding from gamma radiations, the idea of buildup factor denoted by B, has today become universally functional. The contributions to the buildup factor B originates from those photons that have undergone scattering interactions in the shielding medium and those low-intensity secondary radiations generated in the medium itself. To understand it, consider Compton scattering interaction mode which leaves the incident gamma photon scattered with degraded energy in comparison with complete removal of gamma photons by photoelectric effect and pair-production modes although the latter processes also cause generation of secondary radiations like characteristic X-rays and annihilation gamma rays respectively. For all such radiations to account for, this simple correction amends the end result to include the contributions from these scattering and secondary rays. Since,

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the interaction of gamma rays follows from Lambert-Beer law 𝛷 = 𝛷0 𝑒 −𝜇𝑥 with the preset conditions of monochromatic beam, narrow beam geometry and thin absorbing target. If any of these conditions gets violated, the buildup factor B as a correction factor should be added to the Lambert-Beer law making it 𝛷 = 𝛷0 𝐵𝑒 −𝜇𝑥 . The factor B can have values higher than or equal to unity. Clearly, when B equals one, Lambert-Beer law is fully valid. Accordingly, higher values of B imply deviations from Lambert-Beer law [33]. Therefore, the buildup factor is a correction part used to deal with the rise of observed radiation transmission through shielding material due to scattered radiations. Generally, it is a good approach to describe it as the ratio of total dose flux to the uncollided flux. A buildup factor depends on the following parameters:    

the energy of the source radiation, the composition or nature of the shielding material, the thickness of shielding material, the source geometry.

Here, the source geometries are referred to (a) point isotropic, (b) plane isotropic and, (c) plane parallel. In accordance of above-mentioned factors, the functional dependence of buildup factor B may be stated as𝐵(𝑍, 𝐸𝛾 , 𝜇𝑥). For instance, consider gamma rays exposure from a monochromatic point isotropic source of intensity (or flux) 𝛷0 and energy 𝐸𝛾 which has been made incident on an absorber shield of thickness x. In the absence of any shield, the total exposure rate at point of observation [31] is 𝑋0̇ = 𝐾𝛷0

(2)

with 𝐾 being a constant depending upon geometry of the source and the incident energy. And when the shield is in position, the gamma intensity 𝛷 out from the shield is different from 𝛷0 and the determination of exposure rate 𝑋0̇ is now left with computation of 𝛷.

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Further, the computation of Φ would be easier if each and every photon after interaction with the target medium got absorbed or removed from the flux. As then, the flux would simply be equal to the flux of uncollided gamma rays i.e.𝛷 = 𝛷0 𝑒 −𝜇𝑥 , where µ is the total attenuation coefficient. But actually, this doesn’t happen now. During photoelectric effect, the incident gamma flux may lead to emergence of characteristic X-rays whereas in the pair-production, the generation of annihilation radiation is another example of secondary flux. The Compton effect itself doesn’t result in absorption of photons rather just scattering them with mere loss of energy. Therefore, we need to first compute𝛷, then its value should be used to calculate total exposure rate 𝑋0̇ using equation 2 over the complete incident energy range as below 𝐸 𝑋̇ = ∫0

𝐾𝛷(𝐸)𝑑𝐸

(3)

The computation of above equation results into the following form 𝑋̇ = 𝑋0̇ 𝐵(𝜇𝑥) 𝑒 −𝜇𝑥

(4)

Where 𝑋0̇ is the exposure rate in the absence of shield as given by equation 2 B(μx) is called the exposure buildup factor for the point isotropic source geometry. The calculated buildup factors for many shielding materials are available in tabular form at many places in literature [12, 34, 35]. From the original data of Goldstein and Wilkins [12] in which extensive data of buildup factors for most materials of interest in shielding applications are reported, the exposure buildup factor for point isotropic source in an infinite medium is given in Table 3.

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Table 3. Exposure Buildup Factor for point isotropic source in infinite media E (MeV) 0.255 0.5 1.0 2.0 Water 3.0 4.0 6.0 8.0 10.0 0.5 1.0 2.0 Aluminum 3.0 4.0 6.0 8.0 10.0 0.5 1.0 2.0 3.0 Iron 4.0 6.0 8.0 10.0 0.5 1.0 2.0 3.0 Tin 4.0 6.0 8.0 10.0 0.5 1.0 2.0 Tungsten 3.0 4.0 6.0 8.0 10.0 0.5 1.0 2.0 3.0 Lead 4.0 6.0 8.0 10.0 0.5 1.0 2.0 Uranium 3.0 4.0 6.0 8.0 10.0

x

Material

1 3.09 2.52 2.13 1.83 1.69 1.58 1.46 1.38 1.33 2.37 2.02 1.75 1.64 1.53 1.42 1.34 1.28 1.98 1.87 1.76 1.55 1.45 1.34 1.27 1.20 1.56 1.64 1.57 1.46 1.38 1.26 1.19 1.14 1.28 1.44 1.42 1.36 1.29 1.20 1.14 1.11 1.24 1.37 1.39 1.34 1.27 1.18 1.14 1.11 1.17 1.31 1.33 1.29 1.24 1.16 1.12 1.09

2 7.14 5.14 3.71 2.77 2.42 2.17 1.91 1.74 1.63 4.24 3.31 2.61 2.32 2.08 1.85 1.68 1.55 3.09 2.89 2.43 2.15 1.94 1.72 1.56 1.42 2.08 2.30 2.17 1.96 1.81 1.57 1.42 1.31 1.50 1.83 1.85 1.74 1.62 1.43 1.32 1.25 1.42 1.69 1.76 1.68 1.56 1.40 1.30 1.23 1.20 1.56 1.64 1.58 1.50 1.36 1.27 1.20

4 23.00 14.30 7.68 4.88 3.91 3.34 2.76 2.40 2.19 9.47 6.57 4.62 3.78 3.22 2.70 2.37 2.12 5.98 5.39 4.13 3.51 3.03 2.58 2.23 1.95 3.09 3.74 3.53 3.13 2.82 2.37 2.05 1.79 1.84 2.57 2.72 2.59 2.41 2.07 1.81 1.64 1.69 2.26 2.51 2.43 2.25 1.97 1.74 1.58 1.48 1.98 2.23 2.21 2.09 1.85 1.66 1.51

Source: Goldstein and Wilkins, USAEC, 1954 [12].

7 72.90 38.80 16.20 8.46 6.23 5.13 3.99 3.34 2.97 21.50 13.10 8.05 6.14 5.01 4.06 3.45 3.01 11.70 10.20 7.25 5.85 4.91 4.14 3.49 2.99 4.57 6.17 5.87 5.28 4.82 4.17 3.57 2.99 2.24 3.62 4.09 4.00 4.03 3.60 3.05 2.62 2.00 3.02 3.66 3.75 3.61 3.34 2.87 2.52 1.67 2.50 3.09 3.27 3.21 2.96 2.61 2.26

10 166.00 77.60 27.10 12.40 8.63 6.94 5.18 4.25 3.72 38.90 21.20 11.90 8.65 6.88 5.49 4.58 3.96 19.20 16.20 10.90 8.51 7.11 6.02 5.07 4.35 6.04 8.85 8.53 7.91 7.41 6.94 6.19 5.21 2.61 4.64 5.27 5.92 6.27 6.29 5.40 4.65 2.27 3.74 4.84 5.30 5.44 5.69 5.07 4.34 1.85 2.97 3.95 4.51 4.66 4.80 4.36 3.78

15 456.00 178.00 50.40 19.50 12.80 9.97 7.09 5.66 4.90 80.80 37.90 18.70 13.00 10.10 7.97 6.56 5.63 35.40 28.30 17.60 13.50 11.20 9.89 8.50 7.54 8.64 13.70 13.60 13.30 13.20 14.80 15.10 12.50 3.12 6.25 8.07 9.66 12.00 1.57 15.20 14.00 2.65 4.81 6.87 8.44 9.80 13.80 14.10 12.50 2.08 3.67 5.36 6.97 8.01 10.80 11.20 10.50

20 982.00 334.00 82.20 27.70 17.00 12.90 8.85 6.95 5.98 141.00 58.50 26.30 17.70 13.40 10.40 8.52 7.32 55.60 42.70 25.10 19.10 16.00 14.70 13.00 12.40 18.80 19.30 20.10 21.20 29.10 34.00 33.40 -7.35 -10.60 14.10 20.90 3.63 41.90 39.30 -2.73 5.86 9.00 12.30 16.30 32.70 44.60 39.20 -6.48 9.88 12.70 23.00 28.00 28.50

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THE TAYLOR’S APPROXIMATION One of the most useful forms out of the available fitting formulae is sum of exponentials sufficiently accurate to be used for many shielding applications commonly known as Taylor’s approximation [15] 𝐵(𝜇𝑥) = 𝐴 𝐸𝑥𝑝(−𝛼1 𝜇𝑥) + (1 − 𝐴)𝐸𝑥𝑝(−𝛼2 𝜇𝑥)

(5)

Here, A, 𝛼1 , and 𝛼2 are functions of energy. Clearly, when𝑥 = 0, the value of buildup factor B approaches unity, since there would be no buildup of secondary rays in the absence of any shield. Berger’s form is also similar and more accurate approximation developed in the form of exponents; 𝐵 = 1 + 𝐶𝜇𝑟 𝑒 −𝛽𝜇𝑟 , in which C and β depend on energy. More complex mathematical form of B leads to a better fit obtained over a wider range of μr to the original data. But unfortunately, this form involves more complexity in analytical calculations than the Taylor’s approximation making the latter of extensive use. In this chapter, this approximation has been employed to illustrate the calculation of buildup factor B using equation 5 for multi-layered shielding applications. As has been pointed above, the magnitude of buildup factor B depends upon the nature of intervening shielding material and the geometry of the source. That means while calculating the buildup factor data, one is to begin with what available data is to use in the dealing application. One has to carefully judge for the theoretical arrangements of source geometry as to which out of plane isotropic, point isotropic and plane parallel would be appropriate for his particular application. In general, it is quite reasonable to use buildup data for point isotropic source geometry in infinite media for a simpler demonstration of calculation of exposure buildup factor B. The coefficients A, 𝛼1 , and 𝛼2 in equation (5) are readily available in lots of manuals for shielding purposes (Goldstein, 1954 [12], Schaeffer, 1973 [35]). The fitted values of these coefficients although based on older data from H. Goldstein, Fundamental Aspects of Reactor Shielding are given in Table 4.

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Table 4. Fitting Parameters for the Taylor’s formula of the exposure buildup factor for a point isotropic source geometry Material Water

Concrete

Aluminum

Iron

Tin

Lead

E (MeV)

A

a1

0.5 1 2 3 4 6 8 10 0.5 1 2 3 4 6 8 10 0.5 1 2 3 4 6 8 10 0.5 1 2 3 4 6 8 10 0.5 1 2 3 4 6 8 10 0.5 1 2 3 4 6 8 10

100.84500 19.60100 12.61200 11.11000 11.16300 8.38500 4.63500 3.54500 38.22500 25.50700 18.08900 13.64000 11.46000 10.78100 8.97200 4.01500 38.91100 28.78200 16.98100 10.58300 7.52600 5.71300 4.71600 3.99900 31.37900 24.95700 17.62200 13.21800 9.62400 5.86700 3.24300 1.74700 11.44000 11.42600 8.78300 5.40000 3.49600 2.00500 1.10100 0.70800 1.67700 2.98400 5.42100 5.58000 3.89700 0.92600 0.36800 0.31100

0.12687 0.09370 0.05320 0.03550 0.02543 0.01820 0.02633 0.02991 0.14824 0.07230 0.04250 0.03200 0.02600 0.01520 0.01300 0.02880 0.10015 0.06820 0.04588 0.04066 0.03973 0.03934 0.03837 0.03900 0.06842 0.06086 0.04627 0.04431 0.04698 0.06150 0.07500 0.09900 0.01800 0.04266 0.05349 0.07440 0.09517 0.13733 0.17288 0.19200 0.03084 0.03503 0.03482 0.05422 0.08468 0.17860 0.23691 0.24024

a2 -0.10925 -0.02522 0.01932 0.03206 0.03025 0.04164 0.07097 0.08717 -0.10579 -0.01843 0.00849 0.02022 0.02450 0.02925 0.02979 0.06844 -0.06312 -0.02973 0.00271 0.02514 0.03860 0.04347 0.04431 0.04130 -0.03742 -0.02463 -0.00526 -0.00087 0.00175 -0.00186 0.02123 0.06627 0.03187 0.01606 0.01505 0.02080 0.02598 -0.01501 -0.01787 0.01552 0.30941 0.13486 0.04379 0.00611 -0.02383 -0.04635 -0.05864 -0.02783

Source: J. R. Lamarsh, and A. J. Baratta, Introduction of Nuclear Engineering, 3rd edition, 2001 [31].

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This should be clear at this point that the above tabulated values are for particular shielding material and for various incident photon energies. Although Taylor’s form is very precise, this method still needs to be used carefully for low energy photons in the low atomic number materials [31].

GOLDSTEIN’S APPROACH FOR MULTI-LAYER SHIELDS The calculation makes use of Goldstein’s approach of effective atomic number 𝑍 in multi-layer shields [14]. This approach allows us homogenization of different layers of the shield thereby specifying an effective atomic number 𝑍 for the composite shield. Evidently, the tabulated values of exposure buildup factor B in Table 2 are for infinite homogeneous media. So, practically, this approach eases to an extent to tolerate the error introduced from finite mediums. In this situation, B depends on actually penetrated number of mean free paths (mfp’s) by the photons and on effective atomic number 𝑍.

Figure 2. Schematic diagram of a three-layered reactor shield.

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Referring to Fig. 2 for a multi-layer shield, the effective Z may be calculated from the expression 𝑍=

∑3𝑖=1

∑3𝑖=1

𝑍𝑖 𝜇𝑖 𝑥𝑖 𝜇𝑖 𝑥𝑖

(6)

Of course, the denominator represents the actual shield thickness in units of mfp’s and B now, be determined by interpolating in the available B-data for a single shielding material of atomic number 𝑍 and attenuation thickness say 𝑋 = ∑3𝑖=1

𝜇𝑖 𝑥𝑖 .

THE COMPUTER PROGRAM BUF The FORTRAN program written for numerical computation of exposure buildup factor B is quite straightforward and is easily understandable. The program code BUF is appended in the end of the chapter as appendix A. The glossary of variables used in the program has been briefed in the beginning. The addition of comments at appropriate places makes the program userfriendly. The subroutine used here, INTPOL, for double interpolation procedure is based on the one mentioned on pages I-268 to I-271 of the article by Spencer [36]. Notably, the buildup factor determined here is for exposure after passing through the shield. Other buildup factors have also been developed like dose-equivalent buildup factors and energy deposition buildup factors for deposition of energy in the medium. But here chapter is focused to calculate only the exposure buildup factor keeping in mind that during radiation protection, the major considerations are regarding exposure of radiation before and after placing a shield. Hence, an exposure buildup factor is of more common use for further calculations. It is important to mention here that the program will only work properly when the particular values of 𝑍 and 𝐸𝛾 input in the program lie within the mesh data of fitted parameters of A, 𝛼1 , and 𝛼2 . For illustration, just check that the effective atomic number 𝑍 range is 10(𝑊𝑎𝑡𝑒𝑟) < 𝑍 < 92(𝑈𝑟𝑎𝑛𝑖𝑢𝑚) and the incident photon energy lie within 0.5 𝑀𝑒𝑉 < 𝐸𝛾
10 MeV, necessary to expel particles from the atomic nucleus. The incident photon interacts with the nucleus of the atom leaving it excited, subsequently, it disintegrates into two or more products; emitting a neutron or a proton [16].

Meson Production Process in which the γ rays require an energy higher than 150 MeV, therefore when interacting with the atomic nucleus they are absorbed by the nucleons and leads to the production of processes such as: intranuclear cascades, spallation and high energy fission, from where Mesons originate. In this mechanism the cross-section is negligible, otherwise, in some other interaction mechanisms [13].

Delbrück Scattering It is understood as the creation of virtual pairs in the nuclear field, continuing with the annihilation and emission of a single photon.

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Comparisons have been made between experimental and theoretical data, however, in order to have an agreement between them, it was proposed to make Coulomb corrections; which depend on the energy of the photon and the angle of dispersion. Despite the above, the corrections show to have a different effect on the cross-sections, according to energy, and therefore are difficult to distinguish [17].

Rayleigh Scattering Another of the Coherent dispersion mechanisms better known as Rayleigh dispersion. The photon is scattered by strongly bonded atomic electrons, excitation and ionisation do not occur in the atom, because there is practically no energy transfer. The probability of Rayleigh scattering is eloquent for low energy photons and predominates in absorbent materials with a high Z atomic number [18].

Nuclear Resonance Scattering This process requires special conditions (variation of energy and bandwidth at the nuclear level) to be carried out. Therefore, the photon when interacting with the nucleons of the material is scattered (inelastic / incoherent) and an excitation of the nuclear level originates, when deexcitation occurs, a re-emission of the photon beam with resonant condition will be obtained [13, 19]. Once the interaction mechanisms of the photons have been mentioned, it is worth mentioning that there are only three the most probable events by which they interact with matter: photoelectric effect, Compton scattering and pair production.

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NEUTRONS Neutron sources include nuclear reactors, accelerators and isotopic sources, although there are also spontaneous sources for their generation, such as cosmic rays. Its utility is based on the production of energy and radionuclides required for medical diagnosis and treatment of cancer, as well as having numerous applications in the industry, including non-destructive tests and analyses [20]. The reactors generate significant neutron fluxes and represent a significant contribution to the ambient radiation around the reactor; particle accelerators create neutrons either through capture reactions or for the production of isotopes. In this type of installations (reactors and accelerators) due to the aforementioned reactions, the materials become radioactive, that is, they become activated and can produce new unwanted radiation sources that contribute to radiation in the environment that are added to the field of already existing radiation. However, these ′′new radiations′′ serve to identify elemental species in a sample, activating it and subsequently detecting the radiation emissions it produces, this analysis is a nuclear technique called neutron activation analysis.

Neutrons Sources To carry out radiation detection, it is necessary to have calibration sources, which are generally based on capture reactions (of different types of radiation) and in particular reactions of the type (α, n), these reactions do not modify the atomic number Z, which is what identifies each element. The release of a neutron with certain energy is evident, which when interacting with matter will be decreased in speed, that is, it will become a thermal neutron and therefore, capture reactions are carried out in this type of neutron and even at low energies, because the neutron is an uncharged particle and does not have to overcome the Coulomb barrier [11, 21].

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In contrast, unlike the previous ones, some advantages of isotopic neutron sources are: they do not require power, are compact, small and are easy to handle. One type of radioisotopic neutron has a mixture of α-decaying radionuclide like 241Am, 210Po or 226Ra, and a target material like beryllium. Its application is varied and according to the source, the production of neutrons with a certain energy distribution is generated. In Table 1 are some (α, n) isotopic neutron sources [22], the energy of α-particles and the neutron yield, Yn. Table 1. (α, n) isotopic neutron sources Source 239Pu-Be 210Po-Be 241Am-Be 244Cm-Be 242CmBe 226Ra-Be 227Ac-Be

α-particle energy [MeV] 5.14 5.30 5.48 5.79 6.10 7.69, 6.00, 5.49, 5.30, 4.77 7.365, 6.71, 6.56, 5.90, 5.65

Yn [s-1 per 106 alphas] 65±9.2 % 73±9.6 % 82±9.8 % 100±9.0 % 118±8.5 % 502±10 % 702±8.5 %

INTERACTION OF NEUTRONS WITH MATTER When neutrons interact with matter, they undergo absorption or dispersion mechanisms, which depend on the cross-section, whose unit is the barn (b = 10-24 cm2). These interactions will be listed below.

Absorption This mechanism is carried out between thermal neutrons and nuclei with fairly high cross-sections. When the nuclei in the medium capture the neutrons, different nuclear reactions (n, γ), (n, α) or (n, p) are activated and

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originated. They allow the elemental composition of a sample to be identified or different radioisotopes to be produced with different uses.

SCATTERING Elastic Scattering Elastic scattering is a common mechanism by which fast neutrons lose their energy when they interact with low atomic number atomic nuclei. In this process, the total kinetic energy of the two colliding particles is preserved, that is, only a redistribution of kinetic energy occurs, according to the laws of conservation of energy and linear momentum.

Figure 5. Elastic scattering.

Because part of the kinetic energy of the neutron is deposited in the nucleus and there is conservation of energy in the process, the original kinetic energy of the incident neutron is simply distributed in the scattered neutron and the retreating nucleus. This mechanism is common in fast neutrons, whereby they lose energy when they interact with nuclei with low atomic numbers, which are usually used as moderators in nuclear reactors. Next, the elastic dispersion is shown, said mechanism resembles the meeting between two billiard balls.

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The loss of kinetic energy of the neutron during the collision, is expressed as follows: 4𝑀𝑚

𝐸𝑘 = (𝑀+𝑚 𝑛)2 𝛽 𝑛

(5)

where, EK Kinetic energy lost during the collision. M Recoil nucleus mass. mn Neutron mass. β Recoil nucleus angle. If β = 90°, we have that EK = 0; therefore, there is no loss of kinetic energy from the neutron during the collision, in this way it is not deflected and continues on its path until it meets another nucleus again. If β = 0°, there is a frontal collision of the neutron with the nucleus of an atom, in this case the neutron can transfer the maximum kinetic energy to the nuclei of the atoms according to the mass of the nucleus with which it is interacting. That is, the lower the mass of the nucleus; the greater the kinetic energy transfer and the greater the mass of the nucleus, the less energy transfer. Therefore, the loss of kinetic energy of the neutron largely depends on the mass of the nucleus with which the neutron is impacted. Thus, low mass number compounds are good moderators for deceleration of fast neutrons. An example of frequently used substances is light water (H2O), heavy water (D2O), paraffin (CnH2n + 2), graphite (C) or materials rich in hydrogen.

Inelastic Scattering It can occur when fast and intermediate neutrons collide with nuclei of high atomic number. During this mechanism, the neutron deposits part of its kinetic energy to the nucleus, which remains in an excited state due to the excess of absorbed energy originating a composite nucleus; which subsequently loses the excitation energy immediately as characteristic post-

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collision gamma radiation. In this process there is no conservation of energy, but of the moment [23].

Figure 6. Inelastic scattering.

DETECTION OF GAMMA RAYS The detection of the photons is carried out through the production of electrons or positrons that are generated when they interact with the detector material; depositing its energy and generating a voltage pulse as a result, which translates as the interaction of the photon. The height of the pulse originated is proportional to the energy deposited on the detector, this will allow different important points to be evaluated for health physics such as: dosimetry, shielding, risks, etc. Detectors are devices that produce flashes of light when ionising radiation passes through them, there are a variety of them in different states: solid, liquid and gaseous. Next, a brief description of the most used ones will be provided, as well as some other used materials different from the classic ones for this process.

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Scintillation Detectors These counters must be coupled to a system which is made up of: the scintillator, a photomultiplier (it amplifies the light pulses and converts them into electricity) and an electronic amplifier that intensifies the electrical signal. These detectors are divided into two main groups: organic and inorganic. However, the former are not usually used for gamma spectroscopy due to their low efficiency, the other group presents: greater light production and a linear response in gamma rays, however, the response is slow. Features of some scintillators are shown in Table 2 and 3 [14, 18, 24, 25]. Table 2. Properties of organic scintillators Scintillator

Density [g/cm3]

NE102A(P) 1.032 NE110(P) 1.032 NE221(L) 1.080 NE224(L) 0.887 NE105(P) 1.032 NE213(L) 0.874 NE224(L) 0.887 NE226(L) 1.610 NE226(L) 0.860 NE226(L) 0.850 NE235(L) 0.875 NE321A(L) 0.800 NE314A(L) 0.902 NE314A(L) 0.951 P-plastic, L-liquid.

Light output (% anthracene) 65 60 55 80 65 78 80 20 52 28 60 51 40 34

Decay constant [ns] 2.400 3.300 4.000 2.600 2.400 3.200 2.500 3.100 2.000 2.200 4.000 3.000 2.200 3.800

Wavelength of Max. emission [nm] 423 434 425 425 423 425 425 425 425 425 425 425 425 425

H/C ratio 1.104 1.104 1.669 1.330 1.103 1.212 1.331 0.004 1.890 2.050 1.730 1.960 1.310 1.470

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Scintillator

Density [g/cm3]

NaI(Tl) CsI(Na) CsI(Tl) LiI(Eu) CaF2(Eu) CdWO4 Bi4Ge3O12

3.67 4.51 4.51 3.49 3.18 7.90 7.13

Decay time [μs] 0.23 0.63 1.00 0.94 0.94 0.90 0.30

Scintillation relative efficiency [%] 100 80 45 30 50 20 8

Wavelength of maximum emission [nm] 410 420 565 470 435 530 480

Zeff

50.8 54 54 40.8 16.4 64.2 75.2

ACTIVATION ANALYSIS Neutron Activation Analysis (NAA) is a non-destructive nuclear technique, discovered in 1936 by Hevesy and Levi. It consists in irradiating a sample with neutrons from a reactor, accelerator or other sources. Neutron capture follows from this process, when a stable nucleus absorbs a neutron it becomes radioactive. These nuclei emit characteristic γ rays (fast or delayed) which, when detected, indicate the presence of a certain element in the sample. Irradiation and reading can take time, however, its detection limit is 1:1015, this makes it a technique with a wide variety of applications in safety, medicine, the environment, biology, etc. [26, 27]. This method, whose measurement is based on the detection of the characteristic gamma radiation emitted by the irradiated sample. If γ-rays are measured simultaneously with irradiation, the method is called early gamma-ray neutron activation analysis (PGNAA) and delayed γ-ray neutron activation analysis (DGNAA) in which γ-ray measurement is performed after a specific time of decay [28]. In particular, PGNAA is implemented in bulk samples and is widely applied in fields such as: industry, geology, the environment, etc. This method analyses the emitted prompt γ rays produced by the reactions (n, γ),

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extracting information such as the energy and the number of emitted prompt γ rays, the elemental concentration of a sample can be determined [29, 30].

MONTE CARLO As previously mentioned, the PGNAA has various applications, however, it is necessary to study its performance to optimise them. For this, Monte Carlo Codes (MC) are usually implemented to model the transport of particles, in particular neutrons and γ rays [31]. On the other hand, in treatment rooms where linear accelerators operate, high energy beams are involved, it is prudent to perform radiation dosimetry for the risks involved. To guarantee that the present dose does not exceed the acceptable limits for occupational health. An important factor involved in these facilities is scattered radiation and contributes to existing radiation. For this, the environmental equivalent dose H*(10), allows us to estimate its effects. MCs are also employed to estimate H*(10) around the treatment room and even in the design of radiation shields, to ensure that occupational personnel, the patient, and the general public are not vulnerable to it. Shields are required in nuclear facilities, where neutrons and γ-rays are often involved. Particle transport can also be simulated to compare shielding performance [32-34]. It is evident that the use of MC is very useful, these codes allow simulating experiments whose conditions are complex, expensive, require a large investment of time and are even impossible to carry out. The simulations performed using these codes have a high level of confidence, as long as the nuclear database is complete and the system is completely determined [31]. Currently, it is proposed to model with MC and the MCNP5 code to model a spherical moderator, using water and polyethylene as moderators; their task will be to terminate neutrons emitted by a 241AmBe source, so that capture reactions (n, γ) are carried out. A γ-ray spectrometer and a NaI (Tl) scintillator were used and the spectra of the γ-rays induced in the moderators were obtained by calculations.

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Using the MCNP5 code [35], the moderator was modelled with a spherical geometry of 3, 5, 8 and 10 inches in diameter, using water and polyethylene as materials; whose densities are 1.00 and 0.93 g/cm3 respectively, these materials have been studied and have moderating characteristics [36, 37]. To estimate the pulse height spectrum of early γ rays emitted during neutron capture in the moderator nuclei. A 3′′3′′ NaI (Tl) scintillation detector was modelled at the bottom of the moderator. The model included the aluminium cover, the I and Na detector and the Lucite base. The neutron source was modelled as a point and isotropic source that was placed at 5cm from the moderator surface. The neutron spectrum was from a 241AmBe source obtained from the International Atomic Energy Agency [38]. Figure 7 shows the model used in the Monte Carlo calculations. In the calculations, treatment S (α, β) was included in the cross-sections for thermal neutron transport. In order that the pulse height spectra are similar to those measured with a NaI(Tl) and multichannel spectrometer, in tally f8 the Gaussian energy broadening (GEB) was used, with parameters a = 0.01, b = 0.07 y c = 0.30. In the calculations, 5E+8 stories were used, which allowed obtaining uncertainties of less than 3%. Figure 8 shows the pulse height spectra of the photons induced in the moderators, 5 and 8 inches in diameter, of polyethylene and water during interaction with 241AmBe neutrons. The figure includes the early γ-ray energies corresponding to the capture of thermal neutrons in H (2.22 MeV), Al (1.78 and 0.86 MeV), O (0.86 MeV), I (0.44 and 0.65 MeV) and Na (0.47 MeV) [39, 40]. The 2.22 MeV photon is observed in the water and polyethylene moderators because both moderators have hydrogen, the other photons are due to the capture of neutrons in the NaI and the aluminium shell. In the case of polyethylene moderators, a 4.44 MeV photon is observed, which is produced during the inelastic dispersion of fast neutrons (E > 5 MeV) with 12C i.e., 12C(n, n´γ)12C [41]. Related to these photons, two other peaks of 3.93 and 3.42 MeV appear in the spectra, corresponding to the

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single escapement and double escapement of the 4.44 MeV photons from the scintillator.

Figure 7. Moderator model, detector and neutron source.

Figure 8. Pulse height spectra of γ rays induced during interaction between 241AmBe neutrons and polyethylene and water moderators.

Figure 9 shows the PHS of the γ rays, between 1 to 5 MeV, which are produced when the neutrons of the 241AmBe source are captured by the nuclei of the 3′′ diameter spheres of the water and polyethylene moderators.

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When comparing both spectra, the 2.22 MeV photon in polyethylene and water is incipiently observed, and the 4.44 MeV photon with the exhaust peaks, in the case of polyethylene. Figure 10 shows the PHS of γ rays induced by neutron capture in the 5′′ diameter spheres of water and polyethylene. Unlike the 3′′ spheres, the PHS in the 5′′ spheres the hydrogen capture photon (2.22 MeV) is higher and the presence of the 4.44 MeV photon from the 12C(n, n´γ)12C reaction in the carbon is better defined than in the case of the 3′′ spheres.

Figure 9. Pulse Height Spectra (PHS) of the gamma rays induced in the 3′′ diameter spheres of water and polyethylene.

It can be seen that the 2.22 MeV peak is higher in polyethylene compared to water, despite the fact that the atomic fraction of the hydrogen atoms in both moderators is approximately the same (66.6662% in polyethylene and 66.6657% in water). The probable explanation is due to the fact that the other component of polyethylene is C which is a good moderator, whereas in water it is oxygen that does not have good characteristics as a moderator. Figure 11, shows the gamma-ray PHS induced by neutron capture in the 8′′ diameter spheres of water and polyethylene.

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Figure 10. PHS of the gamma rays induced in the 5′′ diameter spheres of water and polyethylene.

Figure 11. PHS of the gamma rays induced in the 8′′ diameter spheres of water and polyethylene.

With the 8′′ diameter moderator the same trend is observed as in the previous case. In the case of 8′′ moderators, the Compton edge of the 2.22 MeV photopeaks are smaller than those observed in the 5′′ moderators; it is

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attribute this to the fact that, as the volume of the spheres increases, the probability of capturing neutrons in hydrogen increases, so the photopeak has a better definition. Figure 12 shows the gamma-ray PHS induced by neutron capture in the 10′′ diameter spheres of water and polyethylene.

Figure 12. PHS of the gamma rays induced in the 10′′ diameter spheres of water and polyethylene.

In this Figure, the Compton edge of both photopeaks is smaller and despite the fact that for both moderators the height of the photopeaks is less than that observed with the 8′′ moderators, the area under the curve of the photopeaks tends to be greater. Also, it is observed that with the 10′′ sphere of polyethylene the photo peak of 4.44 MeV is smaller compared to the 8′′ sphere of polyethylene, this is attributed to the fact that as the size of the moderator increases, the amount of energy neutrons greater than 5 MeV decreases, and therefore, the 12C(n, n´γ)12C inelastic dispersion also decreases. Figure 12 shows the gamma-ray PHS induced by neutron capture in the 10′′ diameter spheres of water and polyethylene.

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CONCLUSION The simulation was performed using the Monte Carlo method, with which the PHS of the gamma rays were calculated, and which were produced during the interaction between the neutrons of a 241AmBe source with spheres of 3, 5, 8 and 10 inches in diameter, of water and polyethylene. As mentioned, neutrons when reaching thermal energies carry out capture reactions (n, γ) where there is emission of characteristic γ radiation, in this case a 2.22 MeV photon and a 4.44 MeV photon, due to the capture of neutrons from nuclei H and C, respectively. On the other hand, the area under the 2.2 MeV curve is proportional to the photon flux. The larger diameter spheres of water and polyethylene adhere to the model since they represent a larger area under the 2.2 MeV photopeak curve. These results can provide important information to estimate the dose.

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Zerbo, B. (2017). EuroGammaS gamma characterisation system for ELI-NP-GBS: the nuclear resonance scattering technique. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 865: 60-62. L'Annunziata, M. F. (2016). Radioactivity: introduction and history, from the quantum to quarks. Elsevier. Thoennessen, M. (2016). Neutron-Induced Reactions. The Discovery of Isotopes. Springer, Cham. Vega-Carrillo, H. R., and Martinez-Ovalle, S. A. (2016). Few groups neutron spectra, and dosimetric features, of isotopic neutron sources. Applied Radiation and Isotopes, 117: 42-50. L'Annunziata, M. F. (2007). Radioactivity: Introduction and history (1st ed.). NL: Elsevier Science. Boyes, W. (Ed.). (2009). Instrumentation reference book. Butterworth-Heinemann. Lecoq, P., Gektin, A., & Korzhik, M. (2017). Scintillation and inorganic scintillators. Inorganic Scintillators for Detector Systems. Springer, Cham: 1-41. Marchese, N., Cannuli, A., Caccamo, M. T., and Pace, C. (2017). New generation non-stationary portable neutron generators for biophysical applications of Neutron Activation Analysis. Biochimica et Biophysica Acta (BBA)-General Subjects, 1861: 3661-3670. Grdeń, M. (2020). Non-classical applications of chemical analysis based on nuclear activation. Journal of Radioanalytical and Nuclear Chemistry, 323: 677-714. Ghal-Eh, N., Ahmadi, P. and Doost-Mohammadi, V. (2016). A quantitative PGNAA study for use in aqueous solution measurements using Am–Be neutron source and BGO scintillation detector. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 808: 123-127. Hei, D., Jiang, Z., Jia, W., Cheng, C., Wang, H., Li, J., and Chen, D. (2016). The background influence of cadmium detection in saline

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elemental analysis. STI/pub/1263, International Atomic Energy Agency. [41] Im, H.-J., and Song, K. (2009). Applications of prompt gamma-ray neutron activation analysis: detection of illicit materials. Applied Spectroscopy Reviews, 44: 317-334.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 7

PHANTOM BASED COMPUTATIONAL MODELS FOR DOSE CALCULATION IN MEDICINE Shashi Bala and Ashwani Koul Department of Biophysics, Panjab University, Chandigarh, India

ABSTRACT A review has been provided on the radiation dosimetry and the development of various phantoms along with computational approaches for radiation dose assessment in this chapter. Although ionising radiations have been utilised in different fields including medical diagnosis, cancer therapy, food preservation, nuclear reactors, etc., its excessive exposure causes toxicity and cancer induction in the human population. Regulatory committees are engaged in different activities to reverse the adverse effects induced by radiation exposure. Nuclear shielding is necessary for the prevention and safety of public health and the environment from exposure to radiation. However, unique dosimetry systems have been used for dose prediction and exposure measurement from internal/ external sources. The 

Corresponding Author’s Email: [email protected].

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Shashi Bala and Ashwani Koul dosimetric analysis helps in designing the shields for radioactive sources, imaging techniques, low energy accelerators, and nuclear reactors. The development of computational phantoms simplifies the complex anatomy of the human body to represent geometrical structures accurately. These phantoms are the best tools available for dosimetric analysis, image interpretation, and treatment dose evaluation. Monte Carlo (MC) programme has also been employed to calculate the absorbed and effective doses due to environmental, occupational, or accidental exposures to radiation. In modern medicine, we have employed computational phantoms with MC simulations and image processing algorithms for dosimetric analysis. These computational phantoms have been extensively combined with radiation transport codes for the calculation of organ doses and quantities for radiation protection. Here we present an overview of the dosimetric analysis by using various phantom based computational models in medicine.

Keywords: radiation, dosimetry, shielding, computational phantoms

INTRODUCTION Over the last few decades, increasing use of radiation in industrial, medical and scientific areas have raised serious health concerns [1-3]. Ionising radiations like X-rays, gamma rays etc., are routinely used for medical imaging, therapeutic procedures and in industrial applications (Radiology and Nuclear Medicine) [3-6]. If a disaster occurs at a nuclear power plant or nuclear weapon detonation, countless life forms are affected by radiation exposure that could have far reaching consequences [7, 8]. Radioactive materials can be trapped into aerosols arising through natural decay processes, nuclear accidents, decommissioning and decontamination operations of nuclear power stations [9]. Nuclear power accidents at Chernobyl and Fukushima Daiichi nuclear power plant disasters discharged highly radioactive aerosols into the surrounding environment [10]. Radiation sickness or toxicity is commonly referred to as Acute Radiation Syndrome (ARS) and is observed only after undue exposure to ionising radiation [11]. Exposure to ionising radiation may lead to cell damage, apoptosis or mutations and the severity of damage caused by radiation

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depends on the radio sensitivity of the tissues [12, 13]. Therefore, it is essential to accurately and quickly estimate radiation exposure so as to avoid exposure and act upon its impending health effects. Radiation dosimeter is a device or instrument which evaluates the quantity and the distribution pattern of ionising energy deposited to the object of interest [14]. It is a widely accepted tool for drug development, assessing clinical results and establishing the safety of a specific radionuclide [15]. Internal dosimetry has been devised to measure the environmental exposure from radiation epidemiological studies and related quantities of occupational exposures and organ doses for radiation protection [16]. Radiation shielding is defined as, including some absorbing material between the individual and radiation sources, to control the adverse effects of nuclear radiation [17]. Various safety regulating organisations like Atomic energy regulatory Board (AERB), International Commission on Radiological Protection (ICRP) etc. provide shielding materials for the safety of nuclear reactors, spent-fuel casks, fuel-cycle, handling and radioactive waste disposal, accelerators and nuclear-fusion test facilities that are used in medicine, industry and research [18, 19]. Although, several biological or physical and computational dosimetric techniques have been adopted to predict the radiation doses [20], however, no single dosimetric method can satisfy all the requirements to meet the challenges of dose estimation for all exposure scenarios [21]. It has been studied that biological or physical dosimetric techniques are cumbersome due to sample collection/analysis and are more time-consuming [22]. Therefore, these dosimetric techniques are impractical for estimating radiation dose in large scale accidentally exposed individuals [23]. However, these parameters are beneficial for estimating the whole body absorbed dose, but it does not provide detailed information about the distribution of dose to various tissues or organs from a particular irradiation [24]. Computational dosimetric modelling is a mathematical process that has been designed to measure absorbed and effective doses [25]. Various algorithms, codes and software have been applied to evaluate the accurate source geometry and duration of radiation exposure, which are usually unclear in accidental scenarios [26]. Medical Internal Radiation Dose

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(MIRD) schema has been introduced by the Society of Nuclear Medicine (SNM) for measuring internal dosimetry of radiopharmaceutical administered to the individual. The MIRDOSE computer software program, along with OLINDA (Organ Level Internal Dose Assessment) code was developed, which is used for internal dose calculations automatically in nuclear medicine procedures [27]. This computational software provides information on the phantoms, organ masses, equations, assumed relationships, and other details [28]. MC simulation technique is the most precise and advanced approach for internal dose calculations exposed from external sources [26, 29]. MC simulations with computational human phantoms are well established parameters to study the physics of nuclear medicine, radiology, radiation therapy and dosimetry [30]. Combined with accurate computational models, MC simulations are considered as reference for the determination of absorbed dose accurately than personalised dosimetry [31]. This has been documented that various human computational phantoms like stylised, voxel-based or boundary representation or hybrid methods (BREP) such as non-uniform rational based spline (NURBS) are widely accepted models for anatomical realism in internal and external radiation dosimetry [32]. Fisher– Snyder phantom with MC techniques was introduced to obtain more accurate anatomical representation of the body [33]. Cristy–Eckerman (CE) stylised phantoms have been adopted to represent comparison in absorbed dose and anatomical geometry of adults and paediatrics body [34]. Computational fluid-particle dynamics (CFPD) along with Monte Carlo NParticle code, version 6 (MCNP6) has proven to be a reliable tool in characterising transport of aerosols in the respiratory tract and allow accurate simulation of radiation transport [35]. Various researchers adopt different codes for calculating internal dosimetry in nuclear medicine procedures, such as MCNP, FLUKA, and Geant4 [36]. These methods are being explored in clinical trials along with the development of different software like Minerva, Cell dose, RADAR, DOSIMG, 3D-RD, OEDIPE and DPM [37]. In this chapter, we intend to discuss these computers based techniques in detail to measure the absorbed and effective dose.

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THEORETICAL PERSPECTIVES Uses of Ionising Radiation in Medicine and Industry In the present era, the utilisation of ionising radiation is pervasive and routine in medicine, research and industry [38]. X-rays and gamma rays are widely adopted in radio therapeutic procedures and medical imaging [39]. X-rays penetrates through different parts of the body to produce medical images, which is helpful to diagnose and treat various ailments. Radioactive isotopes are also utilised in medicine to evaluate the physiological status of organs and metabolic state of the body [40]. Radio therapeutic procedures, by using certain amount of ionising radiation, are utilised to remove the tumour cells [41]. Tele therapy is a well known technique, which produces a beam of gamma rays, for controlling or eliminating cancerous areas [42]. In addition, there are extensive applications of ionising radiation in genetic engineering and environmental protection studies [43]. Ionising radiations such as gamma-ray sources can be used for sterilisation of medical and surgical equipment (e.g., syringes, cotton rolls, wound dressings, surgical gloves, heart valves, bandages and plastics or rubber sheets) [45]. Biological preparations like bone, nerve, and skin, which are utilised in tissue grafts, can be sterilised by using ionising radiations [46]. Certain radioisotopes release energy which is used for the production of electricity in nuclear power plants [47]. Specially designed fuel rods and containments helps to enclose the radioactive materials in nuclear power stations which prevent their release into the environment [48]. Humans are at a much greater risk through natural, occupational and accidental exposures to radiation in nuclear power plants, nuclear laboratories, industries and those employed for transportation of radioactive wastes, etc. Radioactive wastes such as Uranium mill tailings, spent (used) reactor fuel, and other radioactive pollutants can be harmful to various life forms [49].

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Figure 1. Benefits of ionising radiation [44].

Radiation Exposure and Its Detrimental Effects Apart from the beneficial role of ionising radiation, the misuse and improper handling of radioactive sources can cause immense harmful effects [50]. Past use of gamma rays or X-rays in development of nuclear weapons and medical procedures caused acute and chronic effects in the human population [51]. Epidemiological studies on radiation are extensive such as radium dial painters, underground miners, atomic bomb survivors, radiation treated patients [52]. Undesirable effects of radiation were estimated from epidemiological studies conducted on nuclear plant workers in several countries, victims of the atomic bomb explosions in Hiroshima and Nagasaki, Japan (1945), Chernobyl nuclear disaster, Ukraine, Russia (1986) and the Fukushima Dai-ichi nuclear disaster, Japan (2011) [53]. It has been documented that irradiation causes genetic damage, including gene mutations, DNA strand breaks, micronucleus formation, chromosomal aberrant cells and genomic instability [54-56]. Evidence from studies on both human population and experimental animals indicated that cancer incidence expands with the increase in radiation exposure [57, 58]. Due to lack of understanding about the ill effects of radiation, its widespread unrestrained utilisation in early years, inevitably led to serious side effects [2].

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Figure 2. Deleterious impacts of radiation [59].

Safety measures are well designed to ensure the protection of neighbouring communities around nuclear power stations so that there is no adverse effect on their health. Nuclear power plants are also installed in such a way so as to prevent from leakage of radioactive sources and accidental incidents that may cause detrimental effects to the surrounding environment. Special organisations from different countries monitor the radioactive handling, transportation, storage and/ or disposal of radioactive wastes and set the regulations to protect human population and the environment [60]. Moreover, AERB, ICRP, United States Nuclear Regulatory Commission (USNRC) regulates all the activities related to nuclear power stations. These national and international agencies ensure that the use of nuclear radiation energy does not cause undue risk to occupational workers, public and the environment [61]. For the development of nuclear shielding and safety standards, these regulatory committees established several dosimeters to calculate the absorbed and effective doses of radiation [24, 62].

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Nuclear Radiation Shielding and Dosimetry Ionising radiation is highly energetic and transfers its energy to the nearby cells that can damage the living tissues [50]. To safeguard various life forms, shielding materials are introduced for protection from radiation exposure [63]. Shielding materials with characteristics of high atomic number and high density, like lead and concrete, has been utilised for protection from radiation exposure [64]. Several safety agencies provide radiation protection solutions and shielding materials for managing radioactive wastes, nuclear reactors, personal equipment, electric components and prevention of workers exposed to radiation [65, 66]. During radiochemical processing, shielded containers (shipping casks) are employed for transport of radioactive materials from the nuclear reactor site to processing facility, as certified / approved by the Department of Transportation (DOT) and Nuclear Regulatory Commission (NRC) [67]. These regulatory committees also provide personal protective equipment (PPE) for prevention from radioactive contamination [68]. Radiation dosimeters provide the amount of energy deposited in a material or absorbed by the human body from radiation sources [69]. Dosimetric evaluation offers radiation protection, risk assessment, and treatment planning [70]. This technique plays an essential role in measuring the efficacy of treatment by using ionising radiation and the side effects induced by irradiation on healthy tissues. Several radiation dosimetric systems are used in different fields such as medical and research irradiation facilities, which have different requirements for dose determination [14]. Many innovative methods are being developed for processing, slide preparation, scoring and reporting of dose estimations. Radiation exposure can be measured by using both physical and biological dosimetry [73]. Biological dosimetry is an internationally approved reliable method to evaluate the dose of radiation exposure and suspected overexposure [74, 75]. It is a representative method to confirm the doses of radiation received by occupational workers recorded by physical/personal dosimeters such as thermoluminescent dosimeters (TLD) / film badge. It has been

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studied that some of the employees do not carry physical or personal dosimeters in their workplaces [76].

Figure 3. Types of dosimetry [71, 72].

Lack of awareness about the benefits of wearing these dose monitoring devices or careless handling of personal dosimetric techniques or incorrect dosimeter wearing practice, can result in the inappropriate prediction of exposure doses [76, 77]. Therefore, physical dosimeters may provide unreliable assessment of radiation doses in most large scale radiological incidents.

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Figure 4. Personal dosimetry [78, 79].

No single dosimetric method is sufficient to address all the challenges for assessing the doses in many radiation exposure scenarios. Therefore, computational phantoms are introduced for the radiation dose estimations in the fields of medicine and industry.

Computational Phantoms in Medical Dosimetry External and internal dose calculations have been done by dosimetry and computational models in the modern era. Physical phantoms or computational models represent the anatomy of the human body and play an important role in radiation dosimetric assessment [32, 33]. These models are helpful in simulating the transport of ionising radiation through the body along with computer programs and evaluate the energy deposition in various organs, resulting from internal and external radiation exposure [28]. Furthermore, the MIRD committee of the Society of Nuclear Medicine and Molecular Imaging (SNMMI) proposed calculation methods to estimate radiation dose to target organs from radionuclides distributed in source organs [15]. The Oak Ridge National Laboratory (ORNL) mentioned in pamphlet no. 5 of the MIRD committee of the SNM, have introduced various planes, cylindrical, conical, elliptical and spherical surfaced phantoms which can be described by mathematical expressions [80].

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In this chapter, we will discuss different computational models combined with radiation transport codes for calculating doses of radiation exposure which are used for occupational, medical and environmental radiation protection.

Different Phantom Based Computational Approaches and Their Applications in Medicine The computational phantoms are intended to represent anatomical structure of the human body in which radiation risks are concerned [81]. Various standardised computational phantom models have been introduced for occupational health and safety, which include internal and external radiation dose modelling [82-85]. Recently, personal online dosimetry using computational methods (PODIUM) software has allowed fast calculation of radiation doses with different postures and movement of workers in realistic workplace fields [86]. Standardised models, methods, assumptions and mathematical schema have been evolved as MIRD approaches for evaluating the radiation doses after administration of radiopharmaceuticals [87]. Residence time of the radiopharmaceutical and dose factor (S-value) of all organs of interest is required for MIRD schema [88]. By using nuclear imaging modalities, residence time can be obtained. However, MIRDOSE programme and OLINDA/EXM 1.0 software are available commercially, for calculating Svalue [85, 89]. MC simulations deemed to be the most accurate and gold standard technique for fast calculation of internal and external dosimetry [29, 90]. Radiation transport codes have been merged along with MC simulations to calculate the exposure doses [20, 91]. MIRD phantoms along with MC radiation code simulations have been included to predict the rate, distribution and deposition of energy in physical media or in the body [33, 92]. It has been documented that these methods are widely introduced in radiotherapy treatment planning and for proton therapy dose distribution to paediatrics [93]. MC radiation codes such as Electron TRANsport

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(ETRAN), Electron Gamma Shower (EGS), Monte Carlo N-Particle transport (MCNP or MORSE) have been developed at large research centres using computer systems [94]. MC technique together with the computational algorithms or mathematical phantoms (computational approaches) play an invaluable role for the assessment of the location and quantity of maximum dose in the body.

(a)

(b)

(c)

Figure 5. Human Computational Phantoms [95-97].

MIRD committee has developed a series of anthropomorphic (human computational) phantoms which are required for the determination of image quality, to stimulate medical procedure, training and teaching for all imaging

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modalities [32]. It also provides data for new dosimetry and studies based on radiation protection for occupational workers and patients. The development of first stylised phantoms in the 1960s, simplified the complex anatomy of the body by using simplified mathematical and geometrical structures such as spherical, ellipsoidal, conical, cylindrical etc. [98]. These phantoms coupled with MC radiation code simulations provided the shape, location and dimension of specific organs in the body along with the calculation of radiation doses. On the other side, voxel-based or tomographic whole body phantom models were developed in the 1980s along with CT or Magnetic Resonance Imaging (MRI), to produce better anatomic details [99]. Various voxel models like Virtual Human Phantom (VHP), VIP-Man utilised CT or MRI images to produce 3-dimensional models and allow accurate prediction of transport of radiation when combined with MC radiation codes [28, 33]. BREP or NURBS geometries employ surface representation and can be used to stimulate movement of biological tissues [100, 101]. Voxel-based or BREP phantoms cannot be introduced directly with MC radiation transport codes due to complexity of surface representations, requiring highly complex and time-consuming algebraic calculations [28]. Therefore, several other human computational phantoms have been developed by the Radiation Dose Assessment Resource (RADAR) committee of the SNMMI recommended by ICRP, to estimate radiation dose more accurately. The RADAR method was implemented in the personal computer software code OLINDA/ EXM 1.0 which is similar to the MIRD equation (dose absorbed by a target tissue per radionuclide decay in a source tissue) [102, 103]. Fisher–Snyder phantoms combined with MC radiation transport simulation code helps to create an anatomically accurate representation of the body [104]. It has been documented that these types of phantoms play vital roles in calculating the residing activity of radionuclide and radiation exposure in any organ of an adult [33]. All calculations of absorbed and effective doses were done by using C-E phantoms along with the help of tomographic images (CT) [105, 106]. Deposition of highly radioactive micro-particles (aerosols) in the respiratory tract has been calculated by CFPD technique [35]. This technique

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helps to estimate the particle size of the inhaled aerosol, the geometrical pattern of respiratory airways, and breathing condition of an individual. These voxels based models coupled with MC simulations along with radiation transport code allow more accurate assessment of internal dose distribution in the respiratory system [107]. MCNP 6 transport code provides more accurate geometric models in various radiation applications such as medical linear accelerators, radiotherapy treatment planning, verification of plutonium content, nuclear detector designing and its biological effects [108]. Moreover, CFPD-MCNP 6 computational models have been considered as an effective technique to calculate the anatomical structure of the respiratory tract in detail, overall breathing cycle, aerosol distribution and heterogeneous pattern of aerosol deposition [35]. MC computer code using MCNPX, GEANT4, and FLUKA is considered as the most accurate tool for calculating the transport of particle and its interactions with matter, along with a wide range of applications from accelerator shielding to calorimetry, dosimetry, detector design, radiotherapy etc. [109, 110].

CONCLUSION The phenomenal growth of nuclear radiation techniques is beneficial for diagnostic, therapeutic, and industrial purposes. Though it has various applications in different fields, it also causes potential health hazards, if not used cautiously. To protect against the undesirable effects induced by ionising radiation, various organisations regulate important factors like monitoring, protective equipment, nuclear shielding, etc. They develop the safety standards and guidelines to countermeasure the radiation exposure in different fields. Various dosimetric techniques and mathematical expressions have been approved to calculate the absorbed and effective doses from exposure to internal and external sources. Physical or mathematical phantoms are well known entities that represent the anatomical geometry of the human body that has been used for dosimetric analysis. The development of computerised phantom models provides finer anatomical details and includes simplified geometrical models for

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pathology. MC computational dosimetry incorporated with suitable radiation phantoms has been introduced to calculate the internal and external dose exposures accurately. Collectively, human computational phantoms merged with MC radiation transport codes provide accurate anatomical details of the body along with the calculation of radiation doses for radiography, radiotherapy, treatment planning, and also for radiation protection.

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the MIRD Schema and Possible Implications in Radionuclide Therapy Dosimetry.” Medical Physics 35: 1123–1134. Ebrahimnejad Gorji, K., Razzagh A. Firouzjah, F Khanzadeh, Nouraddin A. Goushbolagh, et al. 2019. “Estimating the Absorbed Dose of Organs in Paediatric Imaging of 99mTc-DTPA Radiopharmaceutical using MIRDOSE Software.” Journal of Biomedical Physics and Engineering 9: 285-294. Mille, Matthew M., Jae W. Jung, Choonik Lee, Gleb A. Kuzmin, et al. 2018. “Comparison of Normal Tissue Dose Calculation Methods for Epidemiological Studies of Radiotherapy Patients.” Journal of Radiological Protection 38: 775–792. Somasundaram, Elanchezhian, Nathan S. Artz, and Samuel L. Brady. 2019. “Development and Validation of an Open Source Monte Carlo Dosimetry Model for Wide Beam CT Scanners using FLUKA.” Journal of Applied Clinical Medical Physics 20: 132-147. Smith, Terry, Nina P. Henss, and Maria Zankl. 2000. “Comparison of Internal Radiation Doses Estimated by MIRD and Voxel Techniques for a "family" of phantoms.” European Journal of Nuclear Medicine 27: 1387-98. Athar, Basit S., and Harald Paganetti. 2011. “Comparison of Second Cancer Risk Due to Out-of-Field Doses from 6-MV IMRT and Proton Therapy Based on six Paediatric Patient Treatment Plans.” Radiotherapy and Oncology 98: 87–92. Nedaie, Hasan A., Mohammad A. Mosleh-Shirazi, and M. Allahverdi. 2013. “Monte Carlo N-Particle Code - Dose Distribution of Clinical Electron Beams in Inhomogeneous Phantoms.” Journal of Medical Physics 38: 15–21. Ramos, Susie Medeiros O., Sylvia Thomas, Mirta B. Torres, Lidia V. de Sa, et al. 2017. “Anthropomorphic Phantoms-Potential for More Studies and Training in Radiology.” International Journal of Radiology and Radiation Therapy 2: 101‒104. “HUREL Computational Human Phantom Research Introduction.” 2018. https://www.google.com/imgres?imgurl=https://i.ytimg.com/ vi/vO4ERtTR0sk/maxresdefault.jpg&imgrefurl=https://www.youtub

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Shashi Bala and Ashwani Koul e.com/watch?v%3DvO4ERtTR0sk&h=720&w=1280&tbnid=JUUkt kcO4zmkxM&tbnh=168&tbnw=300&usg=AI4_-kRvnqjs8yqx XZZd7wbFzzYV11hUA&vet=1&docid=2AHElCZbRa9YM&hl=en-IN. https://www.wikiwand.com/en/Computational_human_phantom. Zaidi, Habib, and Xie G. Xu. 2007. “Computational Anthropomorphic Models of the Human Anatomy: The Path to Realistic Monte Carlo Modelling in Radiological Sciences.” Annual Review of Biomedical Engineering 9: 471–500. Caon, Martin. 2004. “Voxel-based Computational Models of Real Human Anatomy: A Review.” Biophysik 42: 229-235. Xie, Tianwu, and Habib Zaidi. 2016. “Development of Computational Small Animal Models and Their Applications in Preclinical Imaging and Therapy Research.” Medical Physics 43: 111-131. Zhang, Juying, X. George Xu, Chengyu Shi, and Martin Fuss. 2008. “Development of a Geometry-Based Respiratory Motion-Simulating Patient Model for Radiation Treatment Dosimetry.” Journal of Applied Clinical Medical Physics 9: 1-17. Besemer, Abigail E., You M. Yang, Joseph J. Grudzinski, Lance T. Hall, et al. 2018. “Development and Validation of RAPID: A PatientSpecific Monte Carlo Three-Dimensional Internal Dosimetry Platform.” Cancer Biotherapy and Radiopharmaceuticals 33: 155165. Bolch, Wesley E., Keith F. Eckerman, George Sgouros, and Stephen R. Thomas. 2009. “MIRD Pamphlet no. 21: A Generalised Schema for Radiopharmaceutical Dosimetry—Standardisation of Nomenclature.” Journal of Nuclear Medicine 50: 477-484. Snyder, Walter S., Henary L. Fisher, Martin R. Ford, and G. G. Warner. 1969. “Estimates of Absorbed Fractions for Mono-energetic Photon Sources Uniformly Distributed in Various Organs of a Heterogeneous Phantom.” Journal of Nuclear Medicine 5: 7–52. Hurtado, Jorge L., Choonsik Lee, Daniel Lodwick, Timothy Goede, et al. 2012. “Hybrid Computational Phantoms Representing the

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Reference Adult Male and Adult Female: Construction and Applications for Retrospective Dosimetry.” Health Physics 102: 124. Josefsson, Anders, Klaikangwol Siritantikorn, Sagar Ranka, Jose W. A. de Carvalho, et al. 2020. “Accuracy in Dosimetry of Diagnostic Agents: Impact of the Number of Source Tissues Used in Whole Organ S-Value-Based Calculations.” EJNMMI Research 10: 1-9. Mikell, Justin K., Armeen Mahvash, Wendy Siman, Firas Mourtada, et al. 2015. “Comparing Voxel-Based Absorbed Dosimetry Methods in Tumours, Liver, Lung, and at the Liver-Lung Interface for 90Y Microsphere Selective Internal Radiation Therapy.” EJNMMI Physics 2: 1-14. Ajaj, F. A. A., and N. M. Ghassal. 2003. “An MCNP-Based Model of a Medical Linear Accelerator X-ray Photon Beam.” Australasian Physical & Engineering Sciences in Medicine / Supported by the Australasian College of Physical Scientists in Medicine and the Australasian Association of Physical Sciences in Medicine 26: 140144. Battistoni, Giuseppe, Broggi Francesco, Brugger Markus, Campanella Mauro, et al. 2011. “Applications of FLUKA Monte Carlo Code for Nuclear and Accelerator Physics.” Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms 269: 2850–2856. Kraan, Aafke Christine. 2015. “Range Verification Methods in Particle Therapy: Underlying Physics and Monte Carlo Modelling.” Frontiers in Oncology 5: 1-18.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 8

DOSIMETRY IN COMPUTED TOMOGRAPHY Joel Vazquez-Bañuelos1,*, Guillermo Eduardo Campillo-Rivera1, Claudia Angelica Marquez-Mata2, Claudia Villalpando-Hernandez3, Angel Garcia-Duran3 and Hector Rene Vega-Carrillo3 1

Doctorate Program in Engineering and Applied Technology, Electrical Engineering Academic Unit, Autonomous University of Zacatecas, Zacatecas, Zac. Mexico 2 TecNM/Technological Institute of Aguascalientes Aguascalientes, Ags. Mexico 3 Nuclear Studies Academic Unit, Autonomous University of Zacatecas, Zacatecas, Zac. Mexico

*

Corresponding Author’s Email: [email protected].

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ABSTRACT On the planet is exposed to natural and artificial sources of radiation, which are responsible for the dose that living beings receive. The largest dose contribution is because of the X-rays used for diagnosis. In radio diagnosis, there are several techniques such as conventional radiography, fluoroscopy, Computed Tomography (CT), among others. The dose because of X-rays increases the risk for the patient that is compensated with the benefit provided by the image. For different X-ray techniques, there are a set of doses that are recommended as reference values, however, the dose for the scattered radiation reaching sensitive organs and tissues is not included. In CT a narrow X-ray beam is used to swipe a part of the human body getting details of the patient body with good resolution, here images can be obtained in two or three dimensions providing the evidence to improve the diagnosis or the analysis of the progress of treatment. During CT the X-ray beam collide with the entrance surface and goes deeper into the body, and radiation is scattered reaching the thyroid, salivary and mammary glands, eye lenses, and gonads and it is important to evaluate the radiation dose delivered. This chapter will include the production of X-rays, the technique of computed tomography, the equipment, and the procedures used to get the images. Also, the devices used for the dosimetry of the patient and the radiation worker will be described, in particular, the use of thermoluminescent dosimeters to measure the absorbed dose during CT due to the scattered radiation.

Keywords: CT scan, TLD-100, absorbed dose, effective dose

INTRODUCTION Radiation The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) the radiation is any emission and propagation of energy, through a vacuum or a material medium, whether in the form of an electromagnetic wave or in a particle. The radiation can be classified in different ways; by its origin radiation can be natural or artificial, by its nature it is electromagnetic and corpuscular, and according to its effect in matter is defined as ionising and non-ionising radiation [1].

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Ionising radiation has enough energy to rip off electrons from the atoms, the ionisation can be produced by the Coulomb interaction between the incoming radiation and the electrons in the atoms, this direct ionising radiation are charged particles like electrons (protons, positrons, heavy ions, alpha particles, muons and charged Mesons. The ionisation can be also produced by uncharged particles like gamma rays, X-rays, and neutrons [1].

X-Rays The X-rays were discovered. By serendipity, in November 1895 by the German physicist Wilhelm Roentgen, when he was working in the study of cathode rays. He was working in a darkened room with a cathode-ray tube and found that even covered with black cardboard the discharge tube when an electric discharge passed through the tube, a faint glow was in the room. He repeated the experiment, because he knew that cathode rays can only travel a few centimetres in the air; however, the result was the same as the first time. So he lit a match aiming to find a possible cause of the faint glow discovering that the light was produced in a small platinum-barium cyanide [BaPt(CN)4] screen sited on the table where the cathode-ray tube. He inferred that an unknown radiation was produced when the cathode-ray was on, naming this radiation as X-rays [2]. And summarised the properties of X-rays as follows:      

There are substances that are transparent to them. These do not reflect or refract and do not show interference effects. These can veil photographic plates. Electric and magnetic fields do not deflect them. These can discharge electrified bodies (positively or negatively). This cause fluorescence in many substances.

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Production of X-Rays X-rays are electromagnetic radiation whose wavelength varies from 0.1 to 10 nm and their frequencies go from 3E+16 to 3E+19 Hz. Due to these features, X-rays have a high penetration capacity in matter. The production of X-rays occurs inside a glass tube under vacuum, when a beam of energetic electrons bombards a metallic target (commonly Tungsten, Copper, Molybdenum and Rhodium), in Figure 1 is shown an X-ray tube [3].

Figure 1. X-ray production.

Figure 2 shows the X-rays energy distribution (spectrum) observed outside the X-ray tube, these photons are produced when a mono-energetic electron beam interacts with the target. The energy distribution is the combination of continuous and discrete X-ray, the continuous spectrum is due the scattering and slowing down of electrons with the atoms in the target, during these interactions part of the electrons energy is transformed into electromagnetic radiation, which is called Bremsstrahlung or braking radiation [3]. On the other hand, in the case of an electron-atom frontal collision, all the kinetic energy of the incident electron is converted into electromagnetic energy in the form of a single X-ray photon (discrete spectrum). The energy of the discrete photons is characteristic of the target material [3].

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It is well known that in an atom, the electrons are arranged in shells around the nucleus; where the most strongly linked are in K shell, the following are in shells L, M, N, and so on. When a high energy electron rips off an electron in the K shell, a vacancy is left in the shell that is filled by an electron from the L shell and the difference in the binding energy between the shell is released as a X-ray photon. This radiation that is characteristic of the target material is called the 𝐾𝛼 line. If the electron in M shell fills the vacancy in K shell, also a discrete energy photon is released, called the 𝐾𝛽 line. Thus, the transitions from L, M, N shells to the K shell give rise to the series of lines named 𝐾𝛼 , 𝐾𝛽 , 𝐾𝛾 , respectively, and is called series K [2].

Figure 2. X-ray spectrum of a metallic target.

As the voltage in the X-ray tube is increased, the kinetic energy of accelerating electrons is also increased and the end-energy of the Bremsstrahlung spectrum is also increased. However, there is a voltage (critical voltage, 𝑉𝑐 ) when the kinetic energy of accelerating electrons is large enough to dislodge electrons in the K shell of atoms in the target; the relationship between the critical voltage and the kinetic energy of the electrons is shown in equation 1. 𝑒 𝑉𝑐 ≥ 𝐸𝑘

(1)

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Here, 𝐸𝑘 is the energy needed to release an electron from the K shell, 𝑒 is the electric charge of the electron and 𝑉𝑐 is the critical voltage. The ionising photons associated with the K series are called hard X-rays, and those associated with the less energetic series (L, M, N) are named soft Xrays [2].

Mechanisms of Interaction with Matter X-rays are uncharged so they cannot be slowed down by ionisation as they pass through a material. In a solid they can cross several centimetres and in the air hundreds of metres, without affecting the material they cross and without undergoing any process. Due to this, they suffer other mechanisms that in the end make them disappear, transferring their energy [3]. The four mechanisms of interaction with matter are [4]:

Photoelectric Effect Occurs when a photon experiences an interaction with an electron from an atom where it is completely absorbed and disappeared (Figure 3). But the necessary condition that is required for a photon to interact through this mechanism is that the photon has an energy, hν, greater than or equal to the energy of the bond of the electron with the atom, ∅. Experimentally, it is observed that in this phenomenon the minimum necessary energy is slightly greater than ∅ since in addition to detaching the electron, it must leave the metal that is irradiated with photons, this energy is known as a work function, which it is different for each material. So the energy of the electron is: 𝐸𝑒 − = ℎ𝜈 − ∅ where ℎ𝜈 is the energy of the photon and ∅ is the work function.

(2)

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Figure 3. Photoelectric effect.

Compton Scattering It is an elastic collision between a photon and an electron, where the energy of binding of the electron to an atom is much less than the energy of the photon. Therefore, the photon does not disappear; it only transfers part of its energy to the electron. Then the amount of energy transferred from the photon to the electron is a function of the photon scattering angle (θ). Because all the scattering angles are possible, the greater the angle, the greater the energy transferred to the electron and, consequently, the lower the energy of the scattered photon. Figure 4 shows a representation of this mechanism.

Figure 4. Compton scattering.

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Pair Production Occurs when a photon exceeds twice the resting mass energy of an electron, 1.02 MeV. In this way, it manages to penetrate all the electronic layers and when it reaches the nucleus, it disappears spontaneously and its energy reappears as a positron (𝛽 + ) and an electron (𝛽 − ). This transformation of energy into mass must take place near a particle (nucleus), so that the amount of movement is conserved, which is why they go out in opposite directions, as shown in Figure 5.

Figure 5. Pair production.

Rayleigh Scattering This interaction is also known as Coherent scattering (Figure 6), here the photon does not excite or ionise the atom, in this way the photon conserves all its energy. This interaction is usually neglected because there is no energy transfer. During the transport of ionising photons in the matter, the probability of interaction per unit length is defined by total linear interaction coefficient, which is calculated by adding the probability that the photon interacts through the four interaction mechanisms: Photoelectric effect (𝜇𝑃𝐸 ), Compton scattering (𝜇𝐶𝑆 ), Pair production (𝜇𝑃𝑃 ) and Rayleigh scattering (𝜇𝑅𝑆 ) [4]. Therefore, the sum of probabilities of each of these mechanisms is known as the linear attenuation coefficient, μ, that is: 𝜇 = 𝜇𝑃𝐸 + 𝜇𝐶𝑆 + 𝜇𝑃𝑃 + 𝜇𝑅𝑆

(3)

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The X-rays and radioactive materials are widely used in medicine either for diagnosis or for cancer treatment. For diagnosis, the image produced by X-rays is very useful to evaluate the inner structures of the human body allowing a better diagnosis, also the image is used to keep track to the evolution of a particular treatment or pathology; therefore, the X-rays are the largest source of radiation exposure to artificial radiation to which humans are subjected [5].

Figure 6. Rayleigh scattering.

Some of the diagnosis procedures where X-rays are used are: Conventional radiography, dental radiographs, fluoroscopy, among others. Due to the type of images obtained in computed tomography (CT) the use of this technique is increased at daily basis [6].

COMPUTED TOMOGRAPHY Computed tomography (CT) was introduced clinically in 1971, and was only an X-ray modality that allowed only axial images of interest to the brain in neuroradiology to be obtained. But as time has passed, it has become a versatile imaging technique that allows obtaining three-dimensional images of any anatomical area, and that has a wide range of applications, to name a few: Oncology, vascular radiology, cardiology, traumatology, interventional radiology, among others [7].

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The term CT refers to an X-ray machine in which the radiographic plate (the chassis) was replaced by detectors. The function of these is to collect the data after irradiation of the patient in the following way: A narrow X-ray beam is projected towards the patient, rotating rapidly around him, at the same time that the detectors located on the opposite side collect the radiation running through it. The data collected by the detectors is sent to a computer that integrates and reconstructs the information obtained, displaying it on the monitor as an image [8]. The CT images are known as tomographic images, containing more detailed information than conventional X-rays. Once the computer collects several successive slices, a three-dimensional image of the patient can be formed by digitally stacking the slices, making it easier to identify and locate basic structures, for example, the brain, heart, musculoskeletal system or full-length images [7]. This process lasts a few minutes, but this depends on the type of study and on whether the contrast (oral or by enema) is necessary to help distinguish tissues and organs more clearly (Costa and Soria, 2015). This procedure is useful to observe the evolution of pathologies, to detect anomalies [7]. Another important use of CT is in radiotherapy with linear accelerators where the image is used in the planning procedure of the cancer treatment.

Figure 7. Obtaining a CT.

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Other advantages are the ability to rotate the 3D image in space or see the cuts in succession, it is non-invasive, high resolution and the information obtained is more detailed, allowing a better diagnosis [9, 10]. During a tomography, each time a rotation is completed, a crosssectional image or body slice is obtained, where the slice’s thickness of the tissue represented in each cut can vary from 1 to 10 millimetres, this depends on the type of CT scanner used. Figure 7 shows the process of obtaining a CT [8].

Figure 8. Tomograph.

Today, there are a variety of CT scanners, one of these can be seen in Figure 8. The main components of a computer tomography are the following [8]: 





Gantry: It is the donut-shaped structure; the examination table with the patient is introduced through the centre. Inside this are the X-ray tube, detectors, high-voltage generator and mechanical supports. X-ray tube: Produces the X-ray photons that will pass through the patient in a large number of projections throughout the 360° of its rotation. High speed rotors are used to control temperature and dissipate heat. Detector Set: These can be scintillation detectors, gas detectors, or semiconductor detectors. Its function is to collect the energy of the X-ray photons that have passed through the patient’s body,

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

 

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

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transforming it into electrical current that will reach the computer and will be converted into an image. Collimation: It is the geometric limitation of the X-ray beam on the Z-axis (slice thickness). It helps to decrease the dose received by the patient and improves the contrast of the image by reducing scattered radiation. High-voltage generator: All scanners operate on three-phase or high-frequency power. Support stretcher: Keeps the patient in a comfortable position and is built with a low atomic number material, it has a motor that moves it slowly and accurately. Computer: They use ultra-fast, high-capacity digital computers. Since around 30,000 equations are required to be solved at once and with all these mathematical calculations the image is reconstructed. Control console: Normally they use two consoles, one for the technician who directs the operation of the equipment and performs the appropriate reconstructions for each study; the other for the radiologist who consults the images, manipulates their contrast, size and general conditions of visual presentation. Image storage: There are different useful formats in radiology, but the most used is DICOM. Newer scanners store image data on computer hard drives and also send it to the digitised file system. Spatial resolution: It is the ability of any imaging method to discriminate images of small objects very close to each other, being a pixel and voxel dependent value. Contrast resolution: It is the ability to distinguish structures of different density. This is far superior to that of conventional radiographs due to the fan beam collimation, helping to significantly restrict the presence of scattered radiation. System noise: It is the variation of the representation values of each pixel on the same fabric that is below or above the average value. It will depend on the number of photons reaching the detectors (mA and collimation) and the noise inherent in the equipment (computational and electronic).

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Image Reconstruction After performing the study and collecting the data, image reconstruction is determined by the radiation dose emitted, the attenuation of the detected radiation, the location of the X-ray tube, and the detectors during the study. Some of the basic concepts for image reconstruction are matrices (axial images obtained), shown on the screen as if the patient’s body was being observed from the feet. The basic unit that makes up the matrix is the pixel (2 dimensions) and each one has a specific optical density. Another unit defined by the thickness of the cut is the voxel (volumetric pixel, three dimensions) and basically it is the volume of an organism tissue [8]. These concepts can be seen in Figure 9. Then the image reconstruction consists of assigning the value of the linear attenuation coefficient (μ) for each voxel from the multiple projections made on the object that reflects that voxel. For the reconstruction algorithms are used, which are in charge of solving the multiple mathematical equations required to convert the collected data into appropriate information for the visualisation of images. To this end, the following types of algorithms are used [8]:

Figure 9. Matrix, pixel and voxel in an image.

Interpolation Algorithms Interpolation is a mathematical method that allows the estimation of unknown data from known ones. And in image reconstruction, it allows,

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through mathematical processes, to obtain an image of a section of the body from a series of data that has not been acquired in the same plane in which the image is found.

Filtered Back Projection Algorithm This algorithm can be classified into three methods that are described below: 



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Algebraic methods: Once all the total attenuation values have been obtained, they pose the solution through a system of linear equations, assigning a partial attenuation value to each of the pixels in the final image. However, the limitation of this method is that only until all the data is collected can the image be reconstructed, so it is currently deprecated. Iterative methods: They find the solution through estimations, making an initial prediction of the matrix values, which is compared and corrected in repeated iterations with the data from the previous and successive cuts. However, the evolution in data acquisition made it necessary to search for other methods that would allow the image to be reconstructed with the least possible computational cost. Analytical methods: The solution is based on the principles of Radon’s theorem, which says that the value of an integrable function at an arbitrary point is obtained by integrating it along all the lines that pass through that point and by the simple and inverse Fourier transform.

DOSIMETRIC MAGNITUDES AND DOSE The term radiation dose is defined as the quantification of the effects or damages that ionising radiation (radioactive materials and radiation sources)

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produce in the human body [5]. The three basic dosimetric quantities are the following [11, 12]: The absorbed dose (D) measures the average energy absorbed per unit mass of a material and is defined as: 𝑑𝜀

𝐷 = 𝑑𝑚

(4)

where 𝑑𝜀 is the average energy absorbed per unit mass 𝑑𝑚 by an organ or tissue. Its unit is the Gray (Gy), 1 𝐺𝑦 = 1 𝐽/𝑘𝑔. However, it is important to note that the absorbed dose does not indicate the biological effect that radiation will have on the tissue. Since biological studies have shown that some types of radiation cause more damage than others for the same absorbed doses. For this reason, the equivalent dose (H) was developed and is defined as: 𝐻 = 𝐷 𝑤𝑟

(5)

where 𝐷 is the absorbed dose and 𝑤𝑟 is the weight factor for the type of radiation. Its unit is the sievert (Sv). Another magnitude that was developed is the effective dose (E), explains the fact that the same equivalent dose depending on the organ or tissue of the human body on which it affects, represents different degrees of risk for the individual. Is defined as: 𝐸 = 𝐻 𝑤𝑇 = 𝐷 𝑤𝑅 𝑤𝑇

(6)

where H is the equivalent dose and 𝑤𝑇 is the weight factor for the organ or tissue. Its unit is Sv. Figure 10 shows the average dose received by anyone in the world due to various sources [5]. In order to have a better overview of the doses received within medical uses due to different studies, Table 1 is shown [9].

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As can be seen, those with the lowest contribution in frequency of radiological examinations are angiography and intervention and CT. The latter represents only 7% but due to its characteristics it is the one that contributes the most to the collective effective dose with 60% [9], this being one of its disadvantages.

Figure 10. Contribution to the average dose received by people.

Table 1. Radiological examinations and contribution to the collective effective dose Radiological examinations Thoracic Angiography and intervention CT Skeletal Dental Others

Frequency 13% 2% 7% 33% 35% 10%

Contribution to the collective effective dose 3% 18% 60% 9% 0.2% 9.8%

To get an idea of the dose received in this technique, Table 2 is shown, which compares the doses received in different types of examinations on CT and conventional radiography [13]. Doses received on a CT are much higher than on a conventional radiography, therefore it is important to keep track of the dose, particularly

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that due to the scattered radiation. There are different devices used to measure the absorbed dose. These devices can be active or passive. Active (immediate) detectors are those that have associated electronics to provide information on radiation levels and give the reading instantly, such as gaseous detectors, scintillation detectors, and semiconductor detectors. On the other part, passive (delayed) detectors are what requires other equipment to obtain the reading, such as thermoluminescent dosimeters [4]. Table 2. Effective dose on CT and conventional radiography CT exam Head Chest Abdomen Pelvis

Effective dose (mSv) 2 8 10-20 10-20

X-ray exam Head Chest Abdomen Pelvis

Effective dose (mSv) 0.07 0.02 1.0 0.7

THERMOLUMINESCENT DOSIMETERS Thermoluminescence, or thermally stimulated luminescence, is the emission of light during heating of a solid insulating sample or a semiconductor, after being previously excited by radiation. The thermoluminescent material absorbs energy when exposed to radiation such as visible light, infrared, ultraviolet, and ionising radiation, storing this energy and releasing it when heated [14]. In medical practice, the use of dosimetry is a necessity to optimise the use of radiation, monitor the good condition of X-ray equipment and use radiological techniques appropriately and has a wide variety of applications such as radiotherapy, radiology diagnostic, nuclear medicine, computed tomography, among others. It has been pointed out that to determine the relationship between the optimisation of radiological techniques and the image quality it is necessary to carry on measurements in the aim to preserve the principles of radiation protection. Thus, one of the roles of thermoluminescent dosimetry in radiotherapy is to ensure the correct delivery of the dose to the tumour and

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at the same time validate the treatment plan so that the dose to healthy tissue is minimised [15]. The importance of thermoluminescent dosimetry is that the amount of light emitted is proportional to the dose absorbed by the irradiated material, but requires sensitive detection and precise measurements of ionising radiation [15]. Additionally, dosimetry can be performed in-vivo and invitro, with the use of thermoluminescent dosimeters (TLDs). However, inappropriate use of thermoluminescent materials can result in large uncertainties in dose estimation. That is why for optimal use the selection of the type of thermoluminescent material depends on the specific requirements of the desired application, since it is necessary to understand the advantages and limitations of these [16]. TLDs are natural or synthetic materials that have the ability to measure the energy absorbed from radiation, this is based on the fact that after having been exposed to radiation and heated below their incandescence point they emit light, where the intensity is proportional to the dose absorbed by the dosimeter. Today, TLDs are well known and meet the requirements for various practical applications in dosimetry [14].

Luminescence Process The energy bands theory of solids says that in an ideal crystalline insulating or semiconductor material, most electrons are in the lower band known as the valence band and are separated from the upper band called the conduction band, the separation or difference in energy between these two bands is known as the prohibited band (𝐸𝑔 ). Structural defects or impurities in the crystals give rise to the electrons possessing prohibited energies and this determines the fundamental properties of these materials [17]. A simple thermoluminescent model to explain this phenomenon is shown in Figure 11, where two levels are located, the first (P) is below the conduction band but above the Fermi equilibrium level (𝐸𝑓 ). At this level there is no creation of charge carriers (electrons and holes) because it is empty in the equilibrium state (it has not been exposed to ionising radiation),

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that is why it is a potential trap for electrons. The second level (O) is a potential hole trap and works as a recombination centre. Then when the material is exposed to exciting energy, an absorption of this energy occurs with ℎ > 𝐸𝑔 , resulting in the ionisation of valence electrons, producing charge carriers which in turn will produce free electrons in the band of conduction and free gaps in the valence band (transition to) after thermalisation. The charge carriers are then free to move around the two bands, recombining with each other or becoming trapped [17]. In the case of direct recombination, an amount of energy sufficient to excite a luminescent centre will be released, with the possibility that it will coincide with the recombination centre. But since the material is not a conductor almost immediately, the luminescent centre returns to its fundamental state under the emission of light. However, in semiconductors and insulators, a certain percentage of the charge carriers get caught, the electrons in T and the holes in R (transition b). The probability of escape will depend on the depth of the trap (E), energy necessary to release an electron from the conduction band. Some of the carriers can be easily released at room temperature or remain in them until they acquire the necessary energy [17]. When the temperature of the material rises, the probability of escape (transition c) and recombination (transition d) increases. After a certain temperature for each trap level, a significant release of charge carriers occurs, reflecting in the appearance of peaks in the intensity of the light emitted as a function of temperature, this curve is known as the glow curve [17, 18].

Glow Curve The probability of escape as a function of the temperature of the crystal is almost null at low temperature, because the charge carriers do not have enough kinetic energy to escape from the potential well of the trap levels. But as the temperature increases, the probability of release also increases and a fraction of the charge carriers arrive at the recombination centres. So the light intensity then peaks and then decreases due to the decrease in the

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population of trapped charges. The release process that results directly from the observation of the light signal is indicated in Figure 12 [18].

Figure 11. Energy band theory model.

Figure 12. Probability of leak, trapped charges, and luminescence.

Furthermore, if the crystal contains more than one trap level, this process will be repeated and at each level the brightness curve will be characterised by the maximum light emission temperature (T), the depth of the trap or

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activation energy (E) and the frequency factor (S) that indicates the probability of leakage from the potential well, as shown in Figure 13 [18].

Figure 13. Brightness curve of a crystal with various trap levels.

Currently, there are several types of TLDs commercially available for a wide range of applications: Personal dosimetry, medical dosimetry, environmental dosimetry, etc. But the most widely used is that of lithium fluoride doped with magnesium and titanium (NatLiF:Mg,Ti), known commercially as TLD-100. For medical applications they can be obtained in a variety of forms, such as extruded rods, pure powder, or hot-pressed chips. And it is popular for some of its properties such as low relative discoloration, acceptable reproducibility, and one of the most important tissue equivalencies [16, 19]. In general, any material that is intended to be used in medical dosimetry as a TLD must comply with the requirements shown in table 3. According to the recommendations of the IAEA the values of the uncertainty in the medical practice are marked by the contribution of clinical dosimetry that has become a relevant tool [15]. Table 3. TLDS necessary requirements for medical dosimetry Activity Diagnostic radiology Whole body dosimetry Radiotherapy

Dose Range (mSv) 0.001 – 10 0.01– 0.5 0.1 – 100

Uncertainty DS (%) ±3.5 -30, +50 ±3.5

Equivalent tissue Important Important Very important

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DOSIMETRY IN EYE LENS, THYROID AND GONADS DURING A COMPUTED TOMOGRAPHIC In the Oncology Medical Specialties Unit (UNEME-Oncology) located in the Municipality of Guadalupe, Zacatecas, Mexico Vázquez-Bañuelos et al. carried out a study that consisted of measuring the absorbed dose due to radiation scattered in the eye lens, thyroid and gonads in a phantom undergoing a radiodiagnostic study for chest CT, and with these values the effective dose was calculated, this research work is described in this section [20].

MATERIAL AND METHODS TLDs Calibration To measure the air kerma at the input surface in the organs mentioned above, TLD-100, manufactured by Harshaw, were used. The dimensions of these dosimeters are 3.2×3.2×0.9 mm [21] and have a Zeff = 8.2 that is very close to that of human tissue Zeff = 7.42 [22]. Before use, they must undergo a heating process to erase any signal they may contain [23]. Erasing has been made in a muffle Panasonic brand, warming them up at 400°C for one hour and then let cool to room temperature. It was subsequently calibrated by placing them inside polyethylene containers to maintain the electronic equilibrium conditions. And were exposed to a well characterised radiation field, in this case a 137Cs source. To make the necessary background corrections, 8 TLDs were used to measure the contribution of the background radiation. After being irradiated, they were read on a Thermo Fisher Scientific Model 3500 Harshaw TLD reader, heating them from 50 to 350°C with a gradient of 10°C/sec in a nitrogen atmosphere. With the data obtained and once corrected for the contribution of the fund, the calibration curve was obtained.

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Dose Measurement with Ionisation Chamber At UNEME-Oncology different quality control tests are carried out and one of these consists in placing a calibrated ionisation chamber in the secondary laboratory of the Institute National Nuclear Research (ININ) in the centre of a solid water phantom known as “Cheese phantom” (Figure 14). With the ionisation chamber in position, a computed tomography was obtained. In addition, the electrical charge released during the interaction of the X-rays with the gas in the chamber was measured; simultaneously, the temperature and atmospheric pressure were measured, and the absorbed dose at the centre of the phantom was calculated. The TLDs were used to measure the dose due to the X-rays of the CT equipment and in order to validate the calibration process, one of the TLDs was placed together to the ionisation chamber, in such a way that both were exposed to the same dose. To determine the dose from the thermosluminescent response, the calibration curve was used and the dose was compared with the dose measured with the ionisation chamber. To this, three tomographies were performed, in order to obtain statistically valid data.

Phantom Dose during CT When a CT scan is performed, the X-ray photon beam strikes the body’s surface, some of it is transported within the body, and another part is scattered as the beam penetrates. Depending on the type of CT study, one or more sensitive organs are exposed to scattered X-rays, in the case of a chest CT they reach the eye lens, the thyroid and the gonads [24]. To determine the absorbed dose in the organs mentioned above and once in the UNEME-Oncology, all the TLDs for handling and exposure were placed in polyethylene containers of a thickness greater than 2 mm to ensure electronic balance. The CT equipment used is a General Electric BrightSpeed CT scanner, shown in Figure 15.

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The equipment operating conditions were 120 kV and 240 mA. At UNEME, this equipment is used as a fundamental part for treatment with a TomoLINAC [25].

Figure 14. Collocation of the ionisation chamber and TLDs.

Figure 15. General Electric CT scanner BrightSpeed model.

Chest CT was performed on solid water phantoms to simulate the human body. The Cheese phantom was used to simulate the torso, it has dimensions of 18 cm high and 30 cm in diameter; for the hip and legs, a phantom in the form of a regular parallelepiped with dimensions of 12 cm in height, 15 cm in width and 55 cm in length was used. While the neck and face, a water phantom with plexiglass walls and dimensions of 14 cm high and 21.5 cm in diameter was used.

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Figure 16 shows the placement of the TLDs, the thyroid was taken as a reference point where three dosimeters were placed, 19 cm towards the central part between the eye lens two TLDs were placed in each lens, the first at a distance of 3.5 cm and the other at 4 cm in each lens. While at a distance of 65 cm from the reference point, five TLDs were placed in the position of the gonads as shown in Figure 17. The Cheese phantom had an 18×30 cm tomography taken following a 2.5 mm cut helical trajectory. And in order to have a good statistic in the thermoluminescent response, three tomographies were performed with the same operating conditions. Also, 4 TLDs were left outside the venue to measure the contribution of the fund.

Figure 16. Location of TLDs in eye lens and thyroid.

Figure 17. Location of TLDs in gonads.

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Once the TLDs were exposed, their reading was obtained on the HarshawTLD 3500 equipment with the same operating conditions described above. From each set of TLDs, the average of the thermoluminescent response was obtained, which was corrected by the average of the response of the TLDs used to measure background. The averages of the net response of the TLDs in each position were entered in the calibration function and the absorbed dose was calculated, and with it the effective dose (E) was obtained using equation 6.

RESULTS The calibration curve was adjusted by weighted least squares [26] and the calibration function (equation 7) was obtained, which allows calculating the absorbed dose from the thermoluminescent response. 𝐷 = 𝐴 + 𝐵 ∗ 𝑅𝑁

(7)

where D is the absorbed dose in μGy, 𝐴 = − (92.8 ± 2.9), 𝐵 = (151.4 ± 3.9) and 𝑅𝑁 represents the average net reading of the TLDs in nC. In order to validate the TLDs calibration process with a source of 137Cs. A dose with the ionisation chamber of 1.39 ± 0.07 cGy was measured, while the dose determined with the TLD was 1.29 ± 0.09 cGy, placed in the same position of the chamber. The dose measured with the ionisation chamber is approximately 8% higher than the dose measured with the TLD. So the difference between the doses obtained with the ionisation chamber and the TLD is not statistically significant, therefore, the values measured with TLDs calibrated with a source of 137Cs are reliable. Table 4 shows the average of the thermoluminescent response corrected by the background (net response), absorbed dose and effective dose for thyroid, eye lens right and left, and gonads in a phantom exposed to a chest tomography.

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Table 4. Net thermoluminescent response, Dye Organ Right eye lens Left eye lens Thyroid Gonads

𝑅𝑁 [nC] 3.83 3.65 36.01 1.36

D [mGy] 0.49±3E(-2) 0.46±2E(-2) 5.36±6E(-1) 0.11±9E(-3)

E [μSv] 58.44±4 55.19±2 214.33±26 9.03±1

In the table, it is observed that the highest effective dose due to scattered radiation on a chest CT is received by the thyroid, then the eye lens and finally the gonads. The probable explanation of the distribution of the dose is due to the fact that the distance between the area of dispersion (thorax) and the organ of interest is less in the case of the thyroid, then for eye lens and finally for gonads. Furthermore, it can be observed for the case of the eye lens that the dose in the right eye lens is slightly higher than the dose in the left eye lens, however, the difference is not significant. The average dose for this organ was 57 μSv, this result differs significantly from that obtained by Weis et al. who report a dose in a range of 2 to 20 μSv [27]. Also, it is different from that reported by Kalender et al. who found a dose of 240 μSv [28]. However, despite the fact that this work was performed on a simple phantom (not anthropomorphic), the effective thyroid dose was 214 μSv. This value is in the range of the values reported by Behroozi, Davoodi and Aghasi that is in the range of 310 μSv for men to 410 μSv for women [29]. Likewise, it coincides with the range reported by Weis et al. whose doses vary from 100 to 340 μSv [27]. Both carried out their work in male and female patients of different complexions, but even so in the case of the thyroid, the doses coincide with this study. Additionally, Kalender et al. obtained 3600 μSv through a computer program, where their team operated at 140 kV and 150 mA [28], while in this study the conditions were 120 kV and 240 mA, which is why their dose is much higher. Finally, in the case of gonads, a value of 9 μSv was obtained, which is different from the values reported by Behroozi, Davoodi and Aghasi, who, depending on gender, reported an effective dose between 81 and 112 μSv [29]. While Weis et al. report an effective dose in gonads that goes from 2

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to 3 μSv and for ovaries goes from 30 to 130 μSv [27]. So these values are different from what was found in this work, however, it coincides with the 10 μSv that Kalender et al. [28]. The probable explanation that the doses received in eye lens and gonads do not coincide with the values reported in the literature is due to the fact that in the phantom, the position of the TLDs in the organs did not reproduce the conditions of the patients.

CONCLUSION In this work, the absorbed dose because of the scattered radiation on the entrance surface of the eye lens, thyroid, and gonads has been measured when a phantom has been subjected to a chest CT. We have got the absorbed dose values using TLD-100. After getting the absorbed dose, the effective dose for each organ of interest has been determined, this dose allows to know the damage or radiological risk that is done directly to it, even though it is a healthy organ. According to the results, the most important conclusions are the following. 



As the distance between the organ of interest and the area of dispersion is reduced, the dose increases, for this reason, the thyroid receives the highest dose. The effective dose in the eye lens, thyroid, and gonads because of the radiation that is scattered during this study is approximately 57 μSv, 214 μSv, and 9 μSv respectively.

The contribution of this study is that the doses received in these radiosensitive organs are known when a chest CT is performed, which allows taking measures and improving safety protocols that reduce these doses to a minimum for patient protection since there is the possibility that they may cause considerable damage that will appear.

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United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). 2000. “United Nation Scientific Committee on the effects of atomic radiation report to the General Assembly. Vol 1, Annex B Exposures from natural radiation sources.” Accessed February 24. https://www.unscear.org/docs/reports/2008/09-86753_ Report_2008_Annex_B.pdf. [2] Acosta, V., Cowan, C. L., and B. J. Graham. 1975. Modern physics course. Oxford University Press. [3] Serway, R. A., Moses, C. J., and C. A. Moyer. 2004. Modern physics. Thomson. [4] Knoll, G. F. 2010. Radiation detection and measurement. John Wiley & Sons, Inc. [5] Nuclear Safety Council. 2010. “Radiation dose.” Accessed February 25. https://www.csn.es/documents/10182/914805/Dosis%20de%20 radiaci%C3%B3n. [6] Alharbi, A., and A. El-Taher. 2013. “A study on transfer factors of radionuclides from soil to plant.” Life Science Journal 10:532-539. doi:10.7537/marslsj100213.78. [7] Calzado, A., and J. Geleijns. 2010. “Computed tomography. Evolution, technical principles and applications.” Medical Physics Journal 11:163-180. https://inis.iaea.org/search/searchsinglerecord. aspx?recordsFor=SingleRecord&RN=42053070. [8] Costa Subias, J., and J. A. Soria Jerez. 2015. Computed tomography directed to superior technicians in image for the diagnosis. Elsevier. [9] Kalender, W. A. 2014. “Dose in X-ray computed tomography.” Physics in Medicine & Biology 59:R129-R150. doi:10.1088/00319155/59/3/R129. [10] Mokhtar, A., Elawdy, M., El-Hamid, M. A., Refaie, H., El-Diasty, T. A., and S. El Mogy. 2017. “Radiation dose associated with common computed tomography examination.” The Egyptian Journal of Radiology and Nuclear Medicine 48:701-705. doi:10.1016/j.ejrnm. 2017.03.005.

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[11] Durham, J. 2006. “Concepts, quantities, and dose limits in radiation protection dosimetry.” Radiation measurements 41: S28-S35. doi:10.1016/j.radmeas.2007.01.011. [12] Cember, H., and T. E. Johnson. 2009. Introduction to health physics. McGraw-Hill. [13] ICRP. 2000. Annals of ICRP 30, Publication 87: Managing patient dose in Computed Tomography. Pergamon. [14] Ranogajec-Komor, M. 2003. “Thermoluminescence dosimetryapplication in environmental monitoring.” Radiation Safety Management 2:2-16. doi:10.12950/rsm2002.2.2. [15] Rivera, T. 2012. “Thermoluminescence in medical dosimetry.” Applied Radiation and Isotopes 71:30-34. doi:10.1016/j.apradiso. 2012.04.018. [16] Moscovitch, M., and Y. S. Horowitz. 2006. “Thermoluminescent materials for medical applications: LiF: Mg, Ti and LiF: Mg, Cu, P.” Radiation Measurements 41:S71-S77. doi:10.1016/j.radmeas.2007. 01.008. [17] Bos, A. J. J. 2006. “Theory of thermoluminescence.” Radiation Measurements 41:S45-S56. doi:10.1016/j.radmeas.2007.01.003. [18] Balseiro Institute. 2020. “Radiation detection principles.” Accessed March 2. http://labrad.fisica.edu.uy/docs/Detectores_de_Radiacion_ Balseiro.pdf. [19] Fernández, S. D. S., Garcia-Salcedo, R., Mendoza, J. G., SánchezGuzmán, D., Rodriguez, G. R., Gaona, E., and T. R. Montalvo. 2016. “Thermoluminescent characteristics of LiF: Mg, Cu, P and CaSO4: Dy for low dose measurement.” Applied Radiation and Isotopes 111:50-55. doi:10.1016/j.apradiso.2016.02.011. [20] Vázquez-Bañuelos, J., Campillo-Rivera, G. E., Garcia-Duran, Á., Rivera, E. R., Arteaga, M. V., Raigosa, A. B., and H. R. Vega-Carrillo. 2019. “Doses in eye lens, thyroid, and gonads, due to scattered radiation, during a CT radiodiagnosis study.” Applied Radiation and Isotopes 147:31-34. doi:10.1016/j.apradiso.2019.02.012.

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[21] Thermo Fisher Scientific. 2020. “TLD-100 Thermoluminescent Dosimetry Material.” Accessed March 10. http://www.thermofisher. com/order/catalog/product/SNO10106. [22] Furetta, C., Prokic, M., Salamon, R., Prokic, V., and G. Kitis. 2001. “Dosimetric characteristics of tissue equivalent thermoluminescent solid TL detectors based on lithium borate.” Nuclear Instruments and Methods in Physics Research A 456:411-417. doi:10.1016/S01689002(00)00585-4. [23] Furetta, C., and P. S. Weng. 1998. Operational Thermoluminescence Dosimetry. World Scientific. [24] Bahreyni Toossi, M. T., Zare, H., Eslami, Z., Bayani Roodi, S., Daneshdoust, M., Saeed, Z., Sedighpour, M., Mohammadian, N., Hashemi, M., and K. Afsaneh. 2018. “Assessment of radiation dose to the lens of the eye and thyroid of patients undergoing head and neck computed tomography at five hospitals in Mashhad, Iran.” Iranian Journal of Medical Physics 15:226-230. doi:10.22038/IJMP.2018. 31353.1369. [25] Vega-Carrillo, H. R., Esparza-Hernandez, A., Garcia-Reyna, M. G., Reyes Rivera, E., Hernandez-Adame, L., and T. Rivera. 2018. “H*(10) due to scattered radiation on the cáncer-patient bodies treated with Tomotherapy.” Applied Radiation and Isotopes 141:206-209. doi:10.1016/j.apradiso.2018.04.015. [26] Vega-Carrillo, H.R. 1989. “Least squares for different experimental cases.” Mexican Physics Journal 35:597-602. http://ricaxcan.uaz.edu. mx/xmlui/bitstream/handle/20.500.11845/714/Least%20squares.pdf? sequence=1&isAllowed=y. [27] Weis, M., Henzler, T., Nance, J. W., Haubenreisser, H., Meyer, M., Sudarski, S., Shoenberg, S. O., Neff, K. W., and C. Hagelstein. 2017. “Radiation dose comparison between 70 kVp and 100 kVp with spectral beam shaping for non-contrast-enhanced paediatric chest computer tomography.” Investigative Radiology 52:155- 162. doi:10.1097/RLI.0000000000000325. [28] Kalender, W. A., Schmidt, B., Zankl, M., and M. Schmidt. 1999. “A PC programme for estimating organ dose and effective dose values in

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computed tomography.” European Radiology 9:555-562. doi:10.1007/s003300050709. [29] Behroozi, H., Davoodi, M., and S. Aghasi. 2015. “Radiation dose to the thyroid and gonads in patients undergoing cardiac CT angiography.” Iranian Journal of Radiology 12:e20619. doi:10.5812/ iranjradiol.20619.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 9

DOSIMETRY IN THE AREA OF DENTISTRY Guillermo Eduardo Campillo-Rivera1,*, Joel Vazquez-Bañuelos1, Claudia Villalpando-Hernandez2, Claudia Angelica Marquez-Mata3, Angel Garcia-Duran2, Eduardo Medrano-Cortes4 and Hector Rene Vega-Carrillo2 1

Doctorate Program in Engineering and Applied Technology, Electrical Engineering Academic Unit, Autonomous University of Zacatecas, Zacatecas, Zac, Mexico 2 Nuclear Studies Academic Unit, Autonomous University of Zacatecas, Zacatecas, Zac, Mexico 3 TecNM/Technological Institute of Aguascalientes, Aguascalientes, Ags, México 4 Dental Academic Unit, Autonomous University of Zacatecas, Guadalupe, Zac, Mexico *

Corresponding Author’s Email: [email protected].

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ABSTRACT Any inhabitant on planet earth is exposed to radiation from two types of sources, these are: natural and artificial. Natural sources are present in the air with Radon, in materials of the Earth’s crust, where we can find Uranium, Potassium and Thorium, both Radon and the aforementioned contribute to background radiation, and we can even find in the food we eat, among others. Artificial sources are used in education, industry, and medicine. Worldwide, the X-rays for diagnostics deliver the highest dose to the population due to the large number of radiological studies and interventions that are carried out every day. One of the areas where radiological studies are very concurrent is in dentistry. Here, various tests are carried out with the two equipment available for this area. Two of the most frequent studies done by dentists are: periapical radiography, this being an intraoral procedure and orthopantomography commonly known as panoramic dental radiography, is being an extraoral procedure. Both studies allow us to assess the patient’s oral health or plan the development of some treatment. At the time of carrying out any of these studies or their derivatives, the dose received by the area that is irradiated is known. This type of study brings with it a risk for the patient since they are exposed to X-rays, but the benefit is greater since a single study extracts enough information. Unfortunately, scattered radiation has not been given real importance in sensitive organs that are close to the X-ray beam. This can be translated as unwanted exposure to organs that are not considered in the study and despite the fact that the dose in these organs is small it is important to determine their values. This chapter will include the dosimetry that can be done in the area of dentistry, ranging from the dosimetry of occupationally exposed personnel radiation worker, as well as the dosimetry of scattered radiation that reaches sensitive organs during exposure to dental X-rays and the orthopantomograph. X-ray production, description of dental X-rays and procedures used for radiation workers and the patient’s dosimetry will be included. The use of thermoluminescent dosimeters, its operating mechanism, the different types of thermoluminescent dosimeters and the calibration process will be emphasized. The results obtained by the research group to measure the dose due to the scattered radiation during the obtaining of dental radiographs will also be included.

Keywords: x-rays, dental, dosimetry, orthopantomograph

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INTRODUCTION Radioactivity (radioactivity, nuclear decay) discovered in 1896 by Henri Becquerel, is a physical phenomenon where unstable atomic nuclei lose energy through the emission of radiation, the type of radiation they can emit are: alpha (α), beta (β + or β-) and rays γ. The type of emission and speed of each radioactive will depend on the type of nucleus and the available energy [1]. Radiation is the emission, transfer and propagation of energy, in the form of subatomic particles or electromagnetic waves, through any medium. The mechanisms of interaction of radiation and the medium will depend on characteristics such as: the elemental composition and physical state of the medium, the energy of the radiation, its mass and charge, in the case of particles. As well as, its frequency in the case of electromagnetic waves [2, 3]. Radiation is classified as follows: 



Non-ionizing radiation. - This type does not have enough energy to eject an electron from the orbit (ionization phenomenon) of the atoms on which they impact. Ionizing radiation. - This type of radiation if it has enough energy to expel electrons from atoms and molecules that impact or pass nearby, therefore, it can ionize matter.

Electromagnetic waves do not need a material medium to propagate. They have a constant speed of 300,000 km/sec in a vacuum. Electromagnetic waves are grouped into the electromagnetic spectrum and classified according to their energy, wavelength, or frequency, as shown in Figure 1 [4]. In this Figure it can be seen that, for a radiation to be ionizing, it must have a minimum wavelength of 10-8 m (X-rays), up to 10-15 m (cosmic rays). Before X-rays we can find ultraviolet radiation, microwaves, infrared, visible light, radio waves, among other electromagnetic waves that, due to

246 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. their extremely low frequency and their wavelength that varies from 10-8 to 107 m. this type of wave will not be ionizing [4].

Figure 1. Electromagnetic spectrum.

Both X-rays and γ-rays do not have a charge and therefore cannot be slowed down by ionizing a material as it passes through it. These can cross several centimeters in solids and a very large number of meters while traveling through the air as long as they do not have any interaction process since they do suffer any of these processes. These will deposit part of their energy as can be seen in Figure 2.

Figure 2. Interaction of ionizing photons with matter.

According to Turner and Saha the three interaction processes shown in the previous Figure are as follows [5, 6]: 

Photoelectric effect. - This happens when the photon meets an electron of a material and transfers all its energy to it, the initial

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

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photon disappears and the electron acquires the energy in the form of kinetic energy. This being enough to detach it from its atom and turn it into a projectile. Compton dispersion. - This happens when the photon has a collision with an electron of a material. In this case, the electron acquires only part of the energy of the initial photon and the rest is carried away by a secondary photon as a result of the collision. Pair production. - It happens when an energetic photon approaches the intense electric field of a nucleus. In this case the photon is transformed into an electron-positron pair, where the sum of their masses is 1.02 MeV, this type of interaction cannot happen if the energy of the photon is less than the mentioned amount. If the energy of the initial photon is greater than 1.02 MeV. Surplus will be distributed between the electron pair and the positron in the form of kinetic energy, being able to ionize the material.

X-Rays Production in Dental Equipment The X-rays were discovered by Wilhelm Conrad Röntgen in 1895. Xrays are known to have high energy and a low wavelength. These are formed within a vacuum glass housing made up of various elements known as the “X-ray tube” shown in Figure 3 and are formed in two ways. The first is the phenomenon known as direct collision or electronic transitions. This occurs when an electron beam collides with a metallic target ionizing its internal electronic layers, when the electrons rearranging the electrons will cause X-ray emission. The second way is through Braking or bremsstrahlung. This phenomenon occurs when very energetic electrons (of the order of 1 keV) hit a metallic target, the electrons pass near the nuclei that make up the material and are abruptly deflected by the electric charge of the material, with the change of direction the electron kinetic energy is converted to X-rays. Most X-rays are formed by this phenomenon [7, 8].

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Figure 3. X-ray tube and its components.

As seen in Figure 3, the X-ray tube is made up of a vacuum glass housing and inside this there are two poles (anode + and cathode -). This also has a small window through which the photons exit and this in turn contains a filter that has an equivalent of 2.8 mm thick aluminum that contains lowenergy X-rays and is not suitable for radiological studies. For cooling the tube contains a compartment with oil. So, the cathode is made up of a focuser and a filament, this is where an electron cloud is produced that, according to the current that is implemented, will be the number of electrons in that cloud (thermionic effect). These electrons will hit a metallic target that is found at the anode by means of a potential difference. The target is generally Tungsten, Rhodium, Copper or Molybdenum, and it is tilted so that the impact surface is wider and the photons are directed towards the aforementioned window. There are tubes that contain rotating anodes. The purpose of this is that, when the metallic target is focused and tilted when it is constantly bombarded, it will suffer wear on the focal spot where the electrons impact. So rotating the anode from time to time will prevent such wear [8, 9]. Some of the properties of X-rays are that they pass through matter and in this process the radiation is attenuated, they fluoresce in certain substances, they produce images on photographic films, the amount of

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radiation decreases with distance and produces changes in living tissues [7, 9]. Among the features of the X-rays are: 

  



Power of penetration: These can pass through the matter with great ease and this will depend on the implemented kilovoltage. That is, the higher the kilovoltage, the greater its penetration. It will also depend on the density of the matter and the average atomic number of the matter traversed, the lower these are, the X-rays will penetrate more easily. Luminescent effect: X-rays can fluoresce certain substances such as phosphors. Photographic effect: These produce images on photographic films. Biological effect: When the matter passes through, the radiation is attenuated, which represents that part of it is absorbed, this produces injuries in living organisms. Ionizing effect: X-rays can ionize gases.

Radiodiagnostic Equipment Used in Dentistry “Periapical” dental X-ray equipment - This uses an intraoral procedure that consists of placing radiographic plates of different sizes inside the mouth and these are printed from the outside by the team. The main components of this equipment are: the head, articulated arm, support (this only for mobile equipment), control panel and voltage regulators as can be seen in Figure 4. The head includes the X-ray tube, the articulated arm allows the head to be moved in different directions to be able to do the different types of exams with this equipment, the support keeps the equipment fixed when it is mobile, in case it is not, it will be fixed on a wall and, finally, there is the control panel, which allows the equipment to be manipulated from the moment it is turned on until modifying some exposure variables. This equipment has a switch that allows the equipment test to be triggered

250 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. remotely. The parameters in which it is generally used for dentistry are as follows: Voltage: 70kV, Current: 8 mA., Time: 0.6s per shot [10-14].

Figure 4. Dental radiography equipment and components.

Different tests can be done only using this device, which are: 





Interproximal. - These show the portions of the crown of the upper and lower teeth together, as shown in Figure 5 as it is an intraoral procedure and shows teeth from both jaws. To do the exam, they use a “bite Wing” Figure 6. This is where the film is placed, which the patient will keep fixed by biting it while doing the exam. Periapicals. - This type of examination is the most recurrent in this area and type of equipment, hence the nickname of “periapical equipment”, this is also an intraoral test very similar to the one mentioned above. The difference is that these show 1 or 2 complete teeth from the crown to the root, but only from one of the jaws as shown in Figure 7. So, instead of using the bite fin for this procedure, commonly the patient who holds the film with the index finger while doing the test Figure 8. Palatal or (occlusive). - This type of exam has two variants. The bottom shot and the top shot Figure 9, both capture all the upper or

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lower teeth together in one shot as shown in the example in Figure 10, while the film remains on the teeth bite surface.

Figure 5. Interproximal radiography.

Figure 6. Bite Wing for interproximal radiography.

Figure 7. Interproximal radiography.

252 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al.

Figure 8. Procedure for periapical radiography.

Figure 9. Variants for palatal radiography.

Figure 10. Palatal radiography.

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Figure 11. Orthopantomograph and patient preparation.

Figure 12. Radiograph with orthopantomograph.

Unlike the equipment and types of radiography already mentioned. The orthopantomography or panoramic dental radiography is an extraoral procedure. This equipment can only do one type of test and for that it requires a special machine that rotates around the head as shown in Figure 11 and captures the complete teeth of both jaws in a single shot Figure 12. The procedure to do this type Test is as follows; The patient is asked to remove prosthetics or orthodontic appliances and any objects that may be left over the scanned area of the test. This to avoid confusing information

254 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. when viewing the radiograph, the patient will be placed on the equipment so that his spine is erect and will be supported by the stabilizing handles. The patient must insert the bitten plate and will have the chin supported with the support, the head will be immobilized with the supports and, finally, the patient will keep the lips closed and press the tongue against the hard palate and should not move during the time taken by the exhibition, this can also be seen in Figure 11 [15]. According to Barros, panoramic dental radiography has several advantages and disadvantages, among the advantages we can point out the following [15]:          

Increased range of records in a single movie. Recognition of functional and pathological interrelationships, and their effects on the masticatory system. Possibility of comparison between both sides. Low radiation dose. On the other hand, its main disadvantages are: Less sharpness and loss of detail. Deformation and magnification of the image. Defective visualization of the breasts and the middle third of the face. Structures outside the examination layer can overlap normal bone structures and simulate abnormalities. In cases of large class II or III malocclusions, the frontal areas of the maxilla and mandible cannot be reproduced correctly in a single projection.

Dosimetric Magnitudes and Units Dosimetry is the calculation of the absorbed dose in tissues or in matter, which were processed directly or indirectly to ionizing radiation. Dosimetry then focuses on calculating the internal and external dose of cathodic

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radiation. Measuring this is important in order to have a proper adequate dose that you are working with. Exposure to radiation produces effects on tissues that are classified in two ways. The first are stochastic effects, also known as probabilistic and non-stochastic or non-probabilistic [16]. The probabilistic effects, these are those that will increase its possibility of appearance with the radiation dose. There is no established threshold for stochastic effects, as it is somewhat random as its definition indicates [17]. Exposure is a quantity that measures the ability of an X-ray beam to ionize a unit of air mass and is represented by the sign (X). It can also be specified as the amount of electric charge of any sign (Q) produced by a unit of air mass (m), as shown in equation 1.

(1) In the international system (SI), the coulomb (C) is used for each kilogram of air (C/kg air). But traditionally used is Roentgen (R), and it has an equivalence of 2.58 × 10-4 C/kg [16]. Being the exposure is very easy to measure and therefore it is widely used, but this by not considering the radiosensitivity of the organs and tissues that the radiation passes through, does not offer information on the damage that occurs in them. The exposure rate is the magnitude that is used to determine the exposure that is held per unit time. In radiology, it is common to measure the speed of exposure before and after making a shield [17]. Exposure and absorbed dose are numerically similar in radiodiagnosis, to transform the exposure into absorbed dose in the SI, they are transformed using conversion factors. That is why, instead of exposure, the magnitude known as kerma (kinetic energy released per unit mass) is used [18, 19]. The kerma in air (K) is the kinetic energy, in Joules, transferred by the X-ray photons (dE) to the electrons released per unit mass (dm) of ionized air, equation 2. Its unit, according to the SI, is Gy (which is equal to J/kg).

(2)

256 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. Where dE is the sum of the initial kinetic energies of all charged ionizing particles released by uncharging ionizing particles in a mass (dm) material [18, 19]. Absorbed Dose (D) is a controlled quantity in radiology and radiological protection, to measure the amount of ionizing radiation that a material or tissue receives. The absorbed dose is the average energy (dE) that is absorbed per unit mass (dm) at a certain point, equation 3. The unit used is July per kilogram (J kg-1) better known as Gray (Gy) [17, 1, 19].

(3) The equivalent dose (H) to an organ or tissue is the dose an organ receives, but it is corrected by a weighting factor of the type of radiation used and this in turn (WR), takes into account the biological efficacy for producing stochastic effects, equation 4. The weight factor for any photon has the value of 1. The unit is July per kilogram (J kg -1) and is called sievert (Sv) [20, 1]. 𝐻 = WR D

(4)

In Table 1, adapted from Andisco, it shows some effects on organs and tissues based on the average of the absorbed dose. These effects depend on the radiosensitivity of the organ or tissue type [18, 19]. The Effective Dose (E) defined by the International Commission on Radiological Protection, as the weighted sum of the equivalent doses to all relevant tissues and organs “in order to indicate the combination of different doses in different tissues in a manner correlation with total stochastic effects is possible.” The effective dose is a non-measurable quantity, instead a measurable quantity, the absorbed dose (D), is used, and this dose is multiplied by a weighting factor due to the type of radiation (WR) and a weighting factor due to the tissue type (WT) equation 5 [20]. 𝐸 = WR WT D

(5)

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Table 2 Andisco, shows the weighting factors for tissues or organs. The unit of the effective dose is July per kilogram (J kg-1) and it is given the special name of Sievert (Sv) [18, 19]. Table 1. Effects of the dose on some tissues and organs Organ Skin Skin Testicle Testicle Ovaries Ovaries Eye lens Bone marrow

Average Absorbed Dose [Gy] 5 2a5 >4 0.15 a 4 >3 > 0.6 >2 0.25

Effects Alopecia Erythema Permanent sterility Temporal sterility Permanent sterility Temporal sterility Cataracts Platelet decrease

Thermoluminescent Dosimeters and Their Quality Control Also known as TLDs. Thermoluminescent dosimeters take advantage of the property that some crystals have to change the energetic state of their electrons when they interact with an exciting agent such as UV light, X-rays, gamma rays, among others. These materials have a crystalline structure and are based on the ability of solids to absorb and store the energy deposited by ionizing radiation [21, 22]. According to Bos, for the thermoluminescence phenomenon to occur, the materials must meet the following requirements [23]:   

It must be either insulator or semiconductor material. During the exposure to ionizing radiation the absorbed energy must be stored in the material. Luminescence emission is caused by heating the material.

258 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. Once the thermoluminescent materials are exposed to the ionizing radiation, must be heated to a temperature below incandescence and it will be phosphorescent. They are used as thermoluminescent detectors (TLDs), as they run on the energy of the radiation they absorb. This energy produces excited states in the atoms that make up the material, these remain in that state until its temperature is high enough for it to return to a lower energy state, in doing so they emit light [24, 21, 25]. Table 2. Organ and tissue weighting factors Tissue/organ Mammary glands Red bone marrow Colon Lung Stomach Gonads Thyroid Bladder Liver Esophagus Skin Brain Bone surface Salivary glands Rest of the organism

Weighting factor (WT) 0.12 0.12 0.12 0.12 0.12 0.08 0.04 0.04 0.04 0.04 0.01 0.01 0.01 0.01 0.12

It is important that thermoluminescence is not confused with light emitted by a material as it is heated to incandescence. a solid will emit infrared radiation that will increase in intensity as its temperature increases. This is known as thermal or blackbody radiation [26-28]. Thermoluminescence is known as the emission of light from a solid, either from insulating or semiconductor material that has ever been radiation. This type of material absorbs energy received from an exciting agent such as visible light, ultra violet, ionizing, etc., storing this energy until the calorie is applied to release it. The importance of thermoluminescence for its use in radiation dosimetry is in the fact that the amount of light emitted

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by the material is proportional to the absorbed dose of the same irradiated material [24, 21, 25]. Several models have been proposed to explain the phenomenon of thermoluminescence such as the Adirovitch model or the BraunlichScharmann model, but so far there is no one that is truly fully approved. Basic models assume that ionizing radiation produces free and hollow electrons, and some of these are trapped in energy levels within the forbidden band. Model of band theory is a simple and successful model that explains the phenomenon of thermoluminescence emission. In an ideal crystalline insulator or semiconductor, most of the electrons are in the valence band (BV). However, they can also occupy the conduction band (BC), these two bands are separated by the prohibited band (BP) where the energy difference between the bands before it is known as (Eg). In a simple thermoluminescence model, the prohibited band can be divided into two levels, one level below the conduction band and the other above the Valencia band and just in the middle of these levels is what is known as equilibrium level of fermi (Ef) Figure 13, adapted from [25]. In the model exposed in this Figure three main elements are taken into account, which are: traps (T), mobile entities (EM) also known as charge carriers (PC) and the recombination centers (CR). When crystals are ionizing radiators, they can create what are known as mobiles, these can be electrons or holes. The electrons in the material are free to move from the valence band to the conduction band. While the holes are only in the valence band, being able to move close to it. The moving entities created by ionizing radiation will remain in motion through the crystal until they can be trapped by metastable states, these can be defects created by exposure to radiation from the crystal or defects of the crystal lattice itself, or they can be captured by traps or if not captured, fall back into the valence band and these entities can recombine radioactively (fluorescence) or be captured in the luminescent centers. In order for the trapped electrons to be released, thermal energy will be gradually applied to them since they will be captured in traps or metastable states of different energies and will need different energy to be able to free

260 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. themselves and go to the conduction band again to later fall into the valence band, the electrons will recombine and emit photons of visible light. This light is emitted as the temperature is increased forming the glow or thermoluminescence curve. Each material has a unique glow curve; having from one to several peaks. The important thing about the thermoluminescence phenomenon in insulating or semiconductor materials is that it can be applied for the dosimetry of ionizing radiation since the amount of light emitted when heating these materials is proportional to the dose with which the same material was irradiated. It has also been shown that the area integrated under the thermoluminescence curve between two temperature values is representative of the light energy that is released or absorbed, which is proportional to the dose received by the thermoluminescent material [26, 28, 29, 8, 25, 30, 31].

Figure 13. Thermoluminescence process in a semiconductor.

There are different types of TLDs such as LiF, CaF2: Mn and Dy; CaSO4 (Dy); and Li2B4O7 among others, but one of the most used is that of lithium fluoride (LiF). This is a material that is commonly used for TLDs. They are used to detect exposure to ionizing radiation from beta particles and neutrons in nuclear reactors, in addition to gamma radiation. Lithium fluoride dosimeters are generally used for personal radiation detectors.

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Lithium fluoride is inert, insoluble, non-toxic, and its crystals are relatively hard and durable in air. There are different types such as TLD-100, TLD600, TLD-700, among others. Which only vary their isotopic concentration. In the case of Calcium Fluorides (CaF2), this type of dosimeter is known as window material in laboratory use, and is characterized by having sufficient transparency for the TLD to accurately record gamma radiation levels. This type of dosimeter is mainly used for the detection of radiation exposure in the environment [32, 33]. For a dosimeter to be considered as a potential thermoluminescent dosimeter, it must meet some properties, depending on the application it will be given, but generally the most desirable or ideal are [34, 35, 25]:            

A high concentration of traps and a high efficiency of light emission associated with the recombination process. A spectrum of emitted light in which the detector used presents a good response. That it presents a simple brightness curve, in case of having a complex brightness curve, that the main peak is well defined. The main peak must have an emission maximum located between 200 to 250ºC. They must have a good resistance to environmental factors such as light, humidity, organic solvents, etc. The material must not be damaged in the dose range to which it will be subjected. It must have a low dependency with the low energy photon response. A linear thermoluminescent response over a wide range of doses. It must not be a toxic material. It must have a good storage stability of the trapped loads, depending on the storage time and temperature. The thermoluminescent response must be independent of the dose ratio and the angle of the radiation. The minimum detectable dose should be as low as possible.

262 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. 

It must have low levels of auto radiation along with the natural radionuclides present in the material.

All of the above characteristics would be for an ideal material, but there is still no material that meets all of these. This is a limitation when selecting the appropriate material to work with. As long as the material meets the main characteristics; this will depend on the use to be made of it. They can be used as thermoluminescent dosimeters. Among the main characteristics that are evaluated for a TLD are [34, 35, 25]:       

The homogeneity of the batch The fading (decrease or loss of TL response of a material) Linearity Minimum detectable dose (DMD) Energy response (proportionality between absorbed energy and released light) Reproducibility Stability (without obligations to undergo chemical or chemical changes during use)

TLD Calibration For the measurements of the research group in the Odontology Academic Unit Guadalupe campus, Zacatecas, of the Autonomous University of Zacatecas. Thermoluminescent type 100 dosimeters (NatLiF: Mg, Ti) were used, these have a Zeff = 8.14, which is close to that of human tissue (Zeff = 7.42) and these have a measurement of 0.3175 x 0.3175 x 0.0889 cm from the company ThermoFisher Scientific [36-38]. Before using thermoluminescent dosimeters, any signal they may have due to accidental exposure or the background itself must be erased. To do this erase, the TLDs must be heated for one hour to a temperature of 400ºC in a flask like the one shown in Figure 14, and they will be allowed to cool

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to room temperature, covering them from any exposure such as fluorescent or solar light [36, 37].

Figure 14. Muffle Panasonic.

Figure 15. Polyethylene cylinders.

After the dosimeters are to room temperature. These will be inserted individually into polyethylene cylinders, such as those shown in Figure 15. Each cylinder is inserted into a vial; the vials were placed in a circular arrangement of 5 and 10 cm radius in the center of which the 137°C source was placed. They will be exposed inside the cylinders to achieve electronic balance.

264 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. For calibration of thermoluminescent dosimeters over a wide range of doses, they were exposed to a gamma radiation field for periods of 10, 60, 300, 900, 1800, 5400 and 15060 seconds over the course of two days. The calibration arrangement that the research group used for its tests is shown in Figure 16.

Figure 16. Experimental setup for TLD calibration.

Figure 17. Harshaw TLD reader model 3500.

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Dosimeters appear to be read on a ThermoFisher Scientific Harshaw TLD 3500 reader shown in Figure 17; the reading parameters used in said reader were from 50 to 350oC with a thermal gradient of 10oC/sec in a Nitrogen atmosphere. With the reading values, the average and the deviation of the thermoluminescent response in nC are obtained for each dose. This was correlated with the air kerma values in μGy and the linear equation that correlates the thermoluminescent response with the dose was calculated using weighted least squares [39]. The weighting factors used in the weighted least squares adjustment were the reciprocal of the sum of the variance of the air kerma and the thermoluminescent response. It is important to determine the Minimum Detectable Dose (DMD) because the scattered radiation dose levels are small. To determine DMD, the criteria indicated in the literature were used [29, 36, 37]. In this one batch of 100 TLD was lost, they were erased by heating them to 400oC for one hour, once timed they were read and their thermoluminescent response was obtained. Then the mean (B) and standard deviation (σB) that were substituted in equation 6 were calculated. DMD= 3 σB F

(6)

Where, F is the factor that converts the thermoluminescent response in nC to air kerma units in μGy. Since TLD children detected electron equilibrium conditions during use, kerma in air was converted to an absorbed dose. The value of F is the slope of the calibration curve.

DOSIMETRY IN DENTAL X-RAYS Dosimetry for Patients and Occupationally Exposed Personnel in the Dental X-Ray Machine For patient dosimetry, a head phantom and a tripod were used as the base to place the phantom at the required height of the dental X-ray machine,

266 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. the dose was measured, in terms of kerma on the input surface to get the absorbed dose (D). For occupationally exposed personnel a water plate phantom was used. For both cases, a batch of 40 TLDs was used, which were placed in eleven packages. Seven of the packages had 4 TLDs placed, while the remaining seven, only 3 TLDs were placed. For the phantom that the patient emulates, 2 radiographic images were taken, one on the left and one on the front. In each of the positions mentioned, the TLD’s were exposed to 10 shots from the dental X-ray equipment, whose operating conditions were 70 kV and 8 mA.

Figure 18. Lateral radiography.

In the lateral take of the dummy 3 packages were placed which contained 4 TLD’s. These are located, one on the input surface of the beam (cheek), one on the lens and one on the thyroid, as can be seen in Figure 18 adapted from [40]. For the front shot, see the place in 3 packages with 4 TLDs. One on the input surface of the beam (chin), one on the lens and one on the thyroid. This accommodation can be seen in Figure 19 adapted from [40].

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Figure 19. Frontal radiography.

Figure 20. Packing in a water plate phantom during lateral radiography.

To determine the dose on the entrance surface of the technician or dentist who takes the X-ray, a package of 4 TLDs was placed on the same plane of the X-ray tube exit beam in a phantom of water during the taking lateral, as shown in Figure 20 adapted from [40]. Finally, to make corrections for the background radiation, a package with 3 TLD’s was used to measure it. it remained away from the irradiation area. It should be reiterated that for this work only the absorbed dose (D) was measured.

268 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al.

Dosimetry for Occupationally Exposed Patients and Staff in Orthopantomography For measurements made on the orthopantogram, 4 TLD packages were used for the patients. These packages were placed in the organs that can be reached by scattering the radiation at the time of taking them, they were placed in: lens, thyroid, mammary glands and gonads with great care so that they do not interrupt the X-ray scan and therefore Therefore, it affects the same, this can be seen in Figure 21.

Figure 21. Placement of patient packaging on an orthopantomograph.

Measurements were made on a Vatech Pax-i 3D Digital 3D Model panoramic dental radiography machine. Where its parameters were: voltage 50-90 kv, current 4-10 mA and a time of 10.1 sec and an image range from 5x5 to 12x9 cm. In total, 5 patients agreed to put on the packaging. 3 men and 2 women whose ages ranged from 17 to 50 years old and their complexion was varied and only one shot was performed on each. To make the correction for background radiation, use a 4 TLD package that was away from the X-ray machine area.

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The radiation worker dosimetry was carried by a package with 4 TLDs. This packaging was carried during a working week and this was replaced by another when the proposed exposure time expired; this was done twice. The packaging can be seen in Figure 22. For TLD readings from the dental X-ray machine, orthopantograph, and occupationally exposed personnel, the procedure is the same. The packages with the TLDs were removed from the points of interest and transported to the laboratory of the Academic Unit of Nuclear Sciences and were read with the Harshaw 3500 machine whose parameters were given in the calibration topic. The TLD readings are individual, the results of each reading and each package are promised, background corrected and their standard deviation obtained.

Figure 22. Personal dosimeter in occupationally exposed personnel.

Because the packages are made of polyethylene, they assure us the condition of electronic balance. So for both machines the kerma on the input surface is taken as the absorbed dose (D). and for the orthopantomogram dipper, equations 4 and 5 will be used, exposed in the topic of “magnitudes and dosimetric units” and with them both the equivalent dose for occupationally exposed personnel and the effective dose for radiosensitive organs that are close to Scattered radiation. The results of both dental X-rays machines are shown in Tables 3 and 4 respectively.

270 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. Table 3. Dosimetry in a dental x-ray machine TLD position Beam input Thyroid Eye lens

Doses in lateral radiography (mGy/shot) 2.778 ± 0.317 0.040 ± 0.005 0.039 ± 0.005

Doses in frontal radiography (mGy/shot) 2.709 ± 0.394 0.137 ± 0.015 0.031 ± 0.004

While the absorbed dose received by the water plate phantom representing the technician in the dental X-ray machine was 3.61 ± 0.44 μGy/shot. In this case, the POE is the students, and since they did not have a control over the tests they do annually, the statements made by Loya et al., where a dental student during his training taking x-rays performs 304 shots. In addition, the dentist is considered as non-POE, the maximum allowable dose is 1 mGy/year [41]. Table 4. Dosimetry in orthopantomograph Organ Eye lens Thyroid Mammary glands Gonads

Absorbed Dose [μGy] 87.4 ± 3.31 94.64 ± 29.17 49.94 ± 5.06 55.19 ± 16.39

Effective Dose [μSv] 10.5 ± 0.40 3.79 ± 1.17 5.99 ± 0.61 4.42 ± 1.31

Radiation Worker Effective Dose The effective dose measured in the two weeks for occupationally exposed personnel is 0.60 μSv/day. Assuming you work 5 days a week, you are supposed to work 2,000 hours a year; implying that the effective dose rate is 3.0 μSv/week. Multiplying this value by the weeks of the year we have the value of 144 μSv/year; this value is very small and the result is consistent with that indicated by Pakravan et al. [42]. This effective dose rate is approximately 153 times less than the 20 mSv/year recommended as the maximum dose allowed by ICRP [17].

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CONCLUSION From the results got in the studies of the dental X-ray machine, the most important conclusions are:  



The highest doses are at the entrance surface of the beam, while the nearby radio sensible organs presented the lowest doses. In the study carried out on the X-ray dental machine, the exposed values do not exceed the value recommended by the Official Mexican Standard NOM-229-SSA1-2002, said value is 7 mGy for intraoral radiographs [43]. The dose received by the operator, in this case, dental students and practitioners, is 9.744% higher than the shown limit value of 1 mGy/year, so it is recommended to reduce the dose received in students as soon as possible. This can be accomplished by implementing control of shots made by a practitioner. As well as principles such as shielding and distance.

From the results got in the orthopantomogram, the most important conclusions are: 





The absorbed dose measured in this work does not exceed the guideline levels for dental radiographs, ranging from 5 to 7 mGy, recommended by the International Atomic Energy Agency (IAEA) In a panoramic dental radiograph, the X-ray beam is collimated to the maxillary area and despite this, in its interaction with the maxilla, the X-rays are scattered reaching organs and tissues far from it. The POE´s annual effective dose is approximately 154 times less than the maximum allowable dose. Therefore, the exposure of the POE is negligible.

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274 Guillermo Eduardo Campillo-Rivera, Joel Vazquez-Bañuelos et al. [23] Bos, A. J. J. 2007. “Theory of thermoluminescence.” Radiation Measurements 41: S45-S56. doi:10.1016/j.radmeas.2007.01.003. [24] Ranogajec-Komor, M. 2003. “Thermoluminescence dosimetryapplication in environmental monitoring.” Radiation Safety Management 2: 2-16. doi: 10.12950/rsm2002.2.2. [25] Rivera, T. 2011. “Thermoluminescence in medical dosimetry.” Proceedings of the ISSSD 2011: 164-176. https://inis.iaea.org/ collection/NCLCollectionStore/_Public/43/009/43009447.pdf. [26] Bos, A. J. J. 2006. “Theory of thermoluminescence.” Radiation Measurements 41: S45-S56. doi:10.1016/j.radmeas.2007.01.003. [27] Reddy, S. S., Nagabhushana, K. R., and F. Singh. 2016. “Thermoluminescence studies of γ-irradiated Al2O3: Ce3+ phosphor.” Nuclear Instruments and Methods in Physics Research B 379: 146-151. doi: 10.1016/j.nimb.2016.03.051. [28] McKeever, S. W. 1988. Thermoluminescence of solids. Cambridge University Press. [29] Furetta, C., and P. S. Weng. 1998. Operational thermoluminescence dosimetry. World Scientific Publishing Company. [30] Bhatt, B. C., and M. S. Kulkarni. 2014. “Thermoluminescent phosphors for radiation dosimetry.” In Defect and Diffusion Forum Vol. 347: 179-227. doi: 10.4028/www.scientific.net/DDF.347.179. [31] Bos, A. J. J. 2017. “Thermoluminescence as research tool to investigate luminescence mechanism.” Materials 10: 1357 (Pp. 22). doi:10.3390/ma10121357. [32] Karzmark, C. J., White, J., and J. F. Fowler. 1964. “Lithium fluoride thermoluminescence dosimetry.” Physics in Medicine & Biology 9(3): 273. https://iopscience.iop.org/article/10.1088/0031-9155/9/3/302/ meta. [33] Balseiro Institute (IB). 2018. “Radiation Detectors.” Accessed October 20 http://labrad.fisica.edu.uy/docs/Detectores_de_Radiacion _Balseiro.pdf. [34] Christensen, P., Bøtter-Jensen, L., and B. Majborn. 1982. “Thermoluminescence dosimetry applied to radiation protection.” The

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In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 10

EVALUATION OF SOME IGNIMBRITE ROCKS AS GAMMA RADIATION SHIELDING MATERIAL: A FLUKA SIMULATION STUDY E. Kavaz1, , M. Dal2, Z. Kuluöztürk3 and N. Demir4 1

2

Department of Physics, Ataturk University, Erzurum, Turkey Department of Civil Engineering, Munzur University, Tunceli, Turkey 3 Health Services Vocational School, Bitlis Eren University, Bitlis, Turkey 4 Department of Physics, Uludağ University, Bursa, Turkey

ABSTRACT In this chapter, the protection capacity of four different rock types (traditional, black, yellow, and grey ignimbrites) commonly used in the building industry against gamma radiation has been discussed using the FLUKA simulation method. Experimental analyses for determining the mass attenuation coefficients (μρ) of the rocks were performed by employing 60Co and 133Ba radioactive sources for 0.356, 0.662, 1.172, and 

Corresponding Author’s Email: [email protected].

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E. Kavaz, M. Dal, Z. Kuluöztürk et al. 1.330 MeV photon energies. To verify the results, the μm values at the same energies were simulated with FLUKA codes and theoretically generated with XCOM. Then, for a wider energy range, 0.015-15 MeV, the μρ values were obtained and various parameters, linear attenuation coefficient (μρ), mean free path (MFP), energy absorption and exposure buildup factors (EABF and EBF) and HVL, that are important in gamma shield design have been found for all of the samples. From the results obtained, it has been observed that the chemical composition and density of the rocks affect their radiation protection abilities. It has been revealed that black and ordinary ignimbrites with high CaO and Fe2O3 contents got the smallest HVL, MFP, EBF, and EABF values while having the largest μρ and Zeq values. Among the selected samples, the black ignimbrite is the sample with the best gamma shielding features.

Keywords: ignimbrite, FLUKA, gamma, shielding

INTRODUCTION Ionising radiation plays an extremely important role in medical and technology applications and is increasing day by day. Exposure to ionising radiation causes some negative biological effects such as cancer, mutation etc.., and the degree of these effects depends on the dose and duration of radiation absorbed [1]. For this reason, the radiation shielding becomes essential in many applications. Considering the importance of building materials in the design of various nuclear and medical facilities, many researchers have conducted extensive studies on how to improve building materials such as cement, concrete and brick used in the construction of these facilities [2–4]. Previously, Kavaz et al. [5] investigated experimentally gamma and neutron security qualities of Portland cement samples doped with Brass and Cu metal. They obtained that brass and metal additives improve the shielding ability of the cement samples against ionising radiation. Obaid et al. [6] showed that concretes obtained from heavy aggregates are more successful at reducing gamma radiation. They revealed that feldspathic and compact basalts, volcanic rock, dolerite and pink granite are more efficient than sandstone and concrete for gamma protection applications. Akkurt et al. [7] examined the radiation attenuation

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and mechanical properties of igneous rocks. Akkurt et al. [8] and Oto et al. [9–11] demonstrated that some minerals such as zeolite, magnetite, limonite and colemanite with heavy element contents enhanced the radiation shielding capacity of concrete. As can be seen, it is important to consider the possibilities of producing new protective materials to increase the efficiency of radiation attenuation. The province of Kayseri (in Turkey) is covered with a lithology of volcanoes. The northeastern extension of the Ecemiş fault zone in the southeast of Kayseri controls the formation of the Erciyes Stratovolcano on the one hand and the formation of the Erciyes pull-apart basin. The magmatic rocks that penetrate the study area affect the Permian limestones and form skarns in their contact. Mount Erciyes volcano constitutes the last volcanic activity in the region. Different colours of this volcanism are widely used as building blocks in the region [12]. Ignimbrite attracts attention as rocks formed by volcanic activity in the region. Ignimbrite rock is used as sustainable natural building materials in Turkey, in the construction sector due to being economical and easy to obtain [13]. For this purpose, in the current research, radiation shielding capability of four different ignimbrite rocks (Kayseri-Tomarza-Emirüşağı ignimbrite (I1, black), Kayseri-Tomarza-Koçacak ignimbrite (I2, yellow), KayseriTomarza-Koçacak ignimbrite (I3, grey), Kayseri-İncesu-Beğendik ignimbrite (I4, light brown)) extracted from the province of Kayseri in Turkey and is widely used in the construction industry were investigated. In order to determine the photon shielding ability of the ignimbrite samples in the study, the mass attenuation coefficient (μ/ρ cm2/g) were achieved experimentally, theoretically with the XCOM programme and generated by FLUKA Monte Carlo Codes. Next, HVL, Equivalent Atomic Number (Zeq), Mean Free Path (MFP), Exposure buildup factors (EBF), Energy Absorption Buildup Factors (EABF) were calculated for photon energies of between 0.015 MeV and 15 MeV.

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MATERIALS AND METHOD The physical properties and chemical compositions of ignimbrite rocks used in this study are listed in Table 1. It is seen that ignimbrites in the Kayseri region are in different colours. Ignimbrites are lithologically silicacontaining rocks and the density of ignimbrites ranges from 2.45 to 2.55 g/cm3. SiO2 (wt%) content of Silicate rich ignimbrites varies between 62.5071.50.

FLUKA Simulation Implementation for the Gamma Attenuation Coefficient Simulations to determine the radiation shielding properties of ignimbrite stone samples were performed using the FLUKA (FLUktuierende KAskade) version 2011.2x.7. A detailed description of the models used in FLUKA, the structure of the code and the application areas can be found in ref [14, 15]. In order to simulate in the FLUKA code, the input file must contain the radiation source, the elemental material composition, the geometry structure, and some physical parameters. The elemental compositions of the samples implemented in the FLUKA simulations with their densities are listed in Table 1. The sample geometry in simulation is taken as a cylinder of 5 cm radius and threshold values for particle energy production and transport were defined as 1 keV for photons. The USRBDX card obtained the transmission values for gamma sources with energies of 356, 662, 1173, and 1330 keV from the stones with different sample thicknesses. In order to obtain good statistics, a total of 5x105 primary were used with five replicates for each energy and stone sample. All the details required to calculate the gamma attenuation coefficient of a shielding material using FLUKA code are given in previous studies [16–18].

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Table 1. The physical properties and chemical compositions of the samples Compound (wt%) Na2O MgO Al2O3 SiO2 P2O5 K2O CaO TiO2 MnO Fe2O3 Density (g/cm3) Location

I1 3.8 1.1 16 62.5 0.2 3 3.2 0.1 0.1 5.7 2.55 Kayseri-TomarzaEmirüşağı

Type of building stones Petrography of building stone

Black ignimbrite Vitric tuff 80% feldspar, 10% pyroxene, 10% opaque minerals)

I2 4.7 0.3 13.9 71.5 0.1 4.1 1.1 0.4 0.1 2.4 2.45 KayseriTomarzaKoçcağız Yellow ignimbrite Vitric tuff (90% feldspar, 10% opaque minerals)

I3 4.8 0.3 14 71.5 0.1 4.1 1 0.4 0.1 2.8 2.54 KayseriTomarzaKoçcağız Gray ignimbrite

I4 4.6 0.8 14.5 67.5 0.1 3.6 2.2 0.7 0.1 5 2.50 KayseriİncesuBeğendik İgnimbirite

Vitric tuff (70% feldspar, 20% pyroxene, 10% amphibole crystals)

Vitric tuff (80% feldspar, 10% pyroxene, 10% opaque minerals)

Experimental Procedure The mass attenuation coefficient (µρ) values of the ignimbrite samples were acquired for the gamma-ray energies emitted from 60Co and 133Ba radioactive sources. A NaI(TI) detector was employed to determine the amount of gamma-ray photons that passed through the samples. The transmission spectra of the samples under study were saved with a multichannel analyser and MAESTRO software. The measurements were lasted 1000 s and were repeated two times to reduce the errors.

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Theory The mass attenuation coefficients (μρ) were calculated by the following equation that is based on the Lambert-Beer law: (1) where ρ is the density of the medium, I0 and I are incident and transmitted intensities and x is thickness of the sample. Figure 1 shows the ln (I0 / I) plot as a function of the thickness for 356 keV photon energy. The slope was calculated from this graph and replaced by Eq. 1. For the I3 sample, the linear correlation between the sample thicknesses and the ln (I0 / I) values is shown in Figure 1, and the R2 value is above 0.9. μρ can be theoretically calculated using the mixing rule with WinXCOM software[19];

(2) HVL is a very advantageous parameter to study photon protective capacity and estimate the penetration amount of gamma radiation in the sample. HVL is the thickness that reduces the incoming photon intensity by half and is calculated by enforcing the next formula; HVL = (ln 2/μ)

(3)

MFP (Mean Free Path) measures the travelled distance between two successive collisions by the gamma rays and can be obtained via the equation. (4) The buildup factor is a correction multiplier caused by secondary particles that are mainly related to Compton scattering. Energy Absorption

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and Exposure Buildup Factors (EABF and EBF) are obtained with G. P. Fitting Approach. Equivalent atomic number (Zeq) is determined by matching the (μρ)Compton/(μρ)Total ratio of the specific energy with the appropriate ratio of the element. For computing the EABF and EBF, the calculated Zeq values for the sample is then used together with G. P. fitting parameters which are taken from the ANSI/ANS database. More details were reported by many previous works [20–22]. In this work, EXABCAL programme [23] was used for buildup factor calculations.

RESULTS AND DISCUSSION To determine the gamma-ray shielding characteristics of four ignimbrite samples, the μρ values were computed from FLUKA simulation code and experimentally for 0.356, 0.662, 1.173, and 1.330 MeV. Moreover, for photon energies of 0.015-15 MeV and selected specific energies, MAC values were generated theoretically by WinXCOM It can be seen from Table 2 that experimental, theoretical, and simulation outcomes confirmed each other. Besides, Figure 2 depicts the changing trend of μρ values for ignimbrite samples versus the gamma-ray energy. One can notice that μρ values of rock samples are of the biggest values for low energy intervals. The cause for this fast decrement observed is that gamma photons interact with the sample depending on Z4-5/E3.5 in the photoelectric absorption (PEA) mechanism which has influence at low energies. Due to the varying of the cross-section of CS with Z/E, the dropping of the μρ values is more leisurely at medium energies. Since the chance of interacting with ignimbrite samples with gamma photons for Pair Production (PP) which prevails at high energies, depends on Z2, the μρ values are enhanced very slowly again in that higher energies. It can notice from Figure 2 and Table 2 that the μρ values of I1 and I4 (black and ordinary ignimbrites) are higher than the other samples.

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Figure 1. Graphic of ln (I0/I) as a function of the thickness of sample (I3) at 356 keV.

Figure 2. The change of ρ of the ignimbrite samples with photon energy.

HVL is a significant parameter for commenting on the material thickness required for any energy. The variation of HVL values of ignimbrite samples with photon energy is shown in Figure 3. According to Figure 3, the density and elemental concentration of the samples affect HVL

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values. While black ignimbrite owns the lowest HVL values with 2.55 g/cm3 high density, it is seen that the yellow ignimbrite has the highest HVL values. It is clear that three different photon-matter interactions are effective in the change of HVL values against photon energy, as in μρ values. Due to the increase of secondary scatterings in medium energies, it is observed that the required glass thickness increases. Table 2. The mass attenuation coefficients (μρ, cm2/g) obtained by FLUKA, WinXCOM and experimentally for the ignimbrite samples Mass attenuation coefficient (cm2/g) Energy (keV) Method I1 356 FLUKA 0.09898 XCOM 0.09994 EXP. 0.09420 662 FLUKA 0.07463 XCOM 0.07680 EXP. 0.07080 1173 FLUKA 0.05474 XCOM 0.05843 EXP. 0.05350 1330 FLUKA 0.05207 XCOM 0.05480 EXP. 0.05000

I2 0.0938 0.1000 0.0971 0.07179 0.07685 0.0758 0.05526 0.05847 0.05700 0.05184 0.05484 0.05380

I3 0.09323 0.09999 0.09770 0.07016 0.07684 0.07640 0.05598 0.05846 0.05730 0.05150 0.05483 0.05400

I4 0.09280 0.09994 0.09270 0.07232 0.07680 0.07600 0.05556 0.05843 0.05700 0.05204 0.05480 0.05400

Zeq (equivalent atomic number) values for the samples in regards to changing energy regions are indicated in Figure 4. It is recognised from Figure 4 that the Zeq values were enhanced with the impact of PEA at between 0.015-0.4 MeV. It is observed that Zeq values, which reach maximum values in medium energies, decrease rapidly after 1 MeV due to PP interaction process. It is explicit that black ignimbrite with the highest Fe2O3 content and density owns the largest Zeq values. Figs 5 and 6 display the variation of EABFs and EBFs of the ignimbrites against gamma-ray energy at several penetration depths. At low energy levels where PEA is effective, EABFs and EBFs are initially too small for all samples. It is seen that the buildup factors enhance as the penetration depth rises and they get maximum values around 0.2-0.4 MeV.

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Figure 3. HVL values of the ignimbrite samples.

Figure 4. Variations of Zeq versus gamma energy for ignimbrite samples.

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The increase in EABF and EBF values in this range can be attributed to the proliferation of secondary scatterings caused by CS. Then, beyond 0.4 MeV, the buildup factors appear to experience a rapid decline again. It is clear that as the amount of Fe2O3 in the sample composition grows, buildup factor values decrease. The smallest values of EABF and EBF belong to the black ignimbrite sample. In addition, changes in the EBFs of the ignimbrites versus penetration depth were calculated for the selected energies 0.15, 1.5 and 15 MeV as shown in Figure 7. The EBF values are raised in all energies against the depth of penetration for all of the samples. Black ignimbrite with the highest Zeq values possesses smaller EBF values than other samples at 0.15 MeV. The EBF curves separated depending on the elemental content of the samples for this energy. For 1.5 MeV and 15 MeV, the EBF values of all samples are almost the same.

Figure 5. Variations of the EABF with photon energy for ignimbrite samples at different penetration depths.

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Figure 6. Variations of the EBF with photon energy for ignimbrite samples at different penetration depths.

Figure 7. (Continued).

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Figure 7. Variation of the EBF with penetration depth for ignimbrite samples at 0.15, 1.5 and 15 MeV.

CONCLUSION In the current chapter, gamma-ray shielding qualities of several ignimbrite samples have been widely examined. The major shielding parameter, MAC, was acquired experimentally and by FLUKA codes in the energy range of 0.015 to 15 MeV. The simulated μρ values have concurred with the theoretical WinXCOM data. The highest μρ values were obtained for the black ignimbrite. Black ignimbrite with the highest Fe 2O3, CaO and TiO2 contents gets the lowest HVL values due to its high density. Additionally, Zeq, EABF and EBF parameters of the ignimbrites were acquired for 0.015-15 MeV photon energy intervals. While Black ignimbrite with the largest Zeq values takes the lowest EABF and EBF values, the photon buildup is more for yellow ignimbrite. As a result, Black ignimbrite was found to be the most effective material against photon radiation among the studied rock types. We believe that the results obtained from this study will make an important contribution to the literature in understanding the capacity of different building materials to reduce gamma radiation.

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Health risks from exposure to low levels of ionising radiation: BEIR VII Phase 2. 2006. [2] Akkurt, I., C. Basyigit, S. Kilincarslan, B. Mavi, and A. Akkurt, ‘Radiation shielding of concretes containing different aggregates,’ Cem. Concr. Compos., 2006, doi: 10.1016/j.cemconcomp.2005. 09.006. [3] Kharita, M. H., S. Yousef, and M. Alnassar, ‘Review on the addition of boron compounds to radiation shielding concrete,’ Prog. Nucl. Energy, 2011, doi: 10.1016/j.pnucene.2010.09.012. [4] Ling, T. C., C. S. Poon, W. S. Lam, T. P. Chan, and K. K. L. Fung, ‘Utilisation of recycled cathode-ray tubes glass in cement mortar for X-ray radiation shielding applications,’ J. Hazard. Mater., 2012, doi: 10.1016/j.jhazmat.2011.11.019. [5] Kavaz, E., S. R. Armoosh, U. Perişanoğlu, N. Ahmadi, and M. Oltulu, ‘Gamma-ray shielding effectiveness of the Portland cement pastes doped with brass-copper: An experimental study,’ Radiat. Phys. Chem., 2020, doi: 10.1016/j.radphyschem.2019.108526. [6] Obaid, S. S., D. K. Gaikwad, and P. P. Pawar, ‘Determination of gamma-ray shielding parameters of rocks and concrete,’ Radiat. Phys. Chem., 2018, doi: 10.1016/j.radphyschem.2017.09.022. [7] Akkurt, I., et al., ‘The properties of various igneous rocks for γ-ray shielding,’ Constr. Build. Mater., 2007, doi: 10.1016/j.conbuildmat. 2006.05.059. [8] Akkurt, I., H. Akyildirim, B. Mavi, S. Kilincarslan, and C. Basyigit, ‘Radiation shielding of concrete containing zeolite,’ Radiat. Meas., 2010, doi: 10.1016/j.radmeas.2010.04.012. [9] Oto, B., A. Gür, M. R. Kaçal, B. Doǧan, and A. Arasoglu, ‘Photon attenuation properties of some concretes containing barite and colemanite in different rates,’ Ann. Nucl. Energy, 2013, doi: 10.1016/j.anucene.2012.06.033. [10] Oto, B., Z. Madak, E. Kavaz, and N. Yaltay, ‘Nuclear radiation shielding and mechanical properties of colemanite mineral doped

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boron alloys,’ J. Alloys Compd., 2020, doi: 10.1016/j.jallcom.2019. 152946. [21] Tekin, H. O. and O. Kilicoglu, ‘The influence of gallium (Ga) additive on nuclear radiation shielding effectiveness of Pd/Mn binary alloys,’ J. Alloys Compd., vol. 815, 2020, doi: 10.1016/j.jallcom. 2019. 152484. [22] Ekinci, N., E. Kavaz, and Y. Özdemir, ‘A study of the energy absorption and exposure buildup factors of some anti-inflammatory drugs,’ Appl. Radiat. Isot., 2014, doi: 10.1016/j.apradiso.2014. 05.003. [23] Olarinoye, I. O., R. I. Odiaga, and S. Paul, ‘EXABCal: A programme for calculating photon exposure and energy absorption buildup factors,’ Heliyon, 2019, doi: 10.1016/j.heliyon.2019.e02017.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 11

INVESTIGATION OF GAMMA-RAY SHIELDING PARAMETERS OF MARBLES Nilgün Demir1,*, Zehra Nur Kuluöztürk2, Murat Dal3 and Bünyamin Aygün4 Department of Physics, Bursa Uludağ University, Bursa, Turkey 2 Vocational School of Health Services, Bitlis Eren University, Bitlis, Turkey 3 Department of Civil Engineering, Munzur University, Tunceli, Turkey 4 Department of Electronics and Automation, Agri Ibrahim Cecen University, Agri, Turkey 1

ABSTRACT In this chapter, the gamma-ray shielding parameters such as linear attenuation coefficient (LAC), HVL, mean free path (MFP), and mass attenuation coefficient (MAC) were investigated for various marble samples at Eskisehir and Usak province in Turkey. Investigated marbles are labelled that Sarıcakaya beige marble (E1), Sivrihisar beige marble *

Corresponding Author’s Email: [email protected].

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Nilgün Demir, Zehra Nur Kuluöztürk, Murat Dal et al. (E2), Supreme marble (E3), Usak green marble (U1), Usak white marble (U2) and Usak yellow marble (U3). These parameters were computed for four different energies gamma rays 356, 662, 1173, and 1330 keV, using the FLUKA and GEANT4 Monte Carlo codes. The obtained values were also compared with XCOM’s results.

Keywords: marble, gamma shielding, Monte Carlo simulation, gamma attenuation

INTRODUCTION Human beings are exposed to radiation from natural sources throughout their lives. However, with the development of modern technology (medical applications, nuclear experiments, particle accelerators etc.) it faces additional radiation effects for many reasons. One of the most useful ways to avoid these radiation effects is shielding. The shielding method can be implemented by using natural or composite materials. For this purpose, it is important to shielding properties of materials that will be used. Although materials of high Z atomic numbers, such as iron, lead, etc. have more effective shielding properties; it cannot directly be preferred in civil engineering because of its durability and high cost. The building materials commonly used, such as concrete, bricks, cement, and marbles and other natural stones have fewer shielding effects. This type of natural stone and marble can be doped to concrete or can be cladding on the built. These building materials are under the influence of radiation from terrestrial and cosmic rays. Therefore, the shielding parameters of these natural building materials are essential that examine. In the literature, it is possible to find shielding parameters for various natural materials using many experimental and computational methods [1-15]. Recently, computational methods, Monte Carlo simulation calculations, have started to be used more actively for investigating radiation shielding parameters [16-26]. This method, based on a random sampling of a given event, enables the simulation of the completely experimental system. Consequently, we can obtain the highest accuracy and precision, with more

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freedom and less cost, in the Monte Carlo sampling of a particle-matter interaction. FLUKA [27, 28] and GEANT4 [29, 30] are Monte Carlo simulation programmes that are frequently used for this purpose. The FLUKA code, a Linux-based programme written in FORTRAN language, is a user-adjustable programme that includes hadronic and electromagnetic interactions. An input file at the FLUKA includes the geometry, type, and characteristics of the source. It should be given the chemical and elemental composition of the medium and other related physical characteristics. It is used in many research areas such as shielding design, detector systems, cosmic ray studies, medical physics, dosimetry calculations, high energy experiments, and accelerator design [27, 28]. The GEANT4 (Geometry and Tracking) is a toolkit for Monte Carlo simulation, and is written in the C++ language. It simulates events over a wide range of energy that may occur in the passage of particles and photons through matter. The GEANT4 toolkit provides the user to design a large number of geometric models more easily, thereby simulating detector responses of materials in a variety of different chemical contents. It is used in particle physics, nuclear physics, nuclear medicine, particle accelerators, and space research to make many modelling for different particles [29, 30]. In this chapter, the gamma-ray shielding parameters of six different natural marbles, whose lithological and geological features are given later section, are investigated using FLUKA and GEANT4 simulation codes. For this purpose, the LAC, HVL, mean free path (MFP), and mass attenuation coefficient (MAC) were calculated for each marble types in the gamma energies of 356, 662, 1173 and 1330 KeV. The computed values were also compared with XCOM’s results [5].

MATERIALS AND METHOD Theoretical Background When the mono-energetic photon beam passing through in any medium, its intensity attenuates via the Beer-Lambert’s rule;

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(1)

where I0 is incident photon beam intensity, I is a transmitted photon intensity, and x (cm) is the thickness of the material. Thus, the linear attenuation coefficient of the material, μ (cm-1) obtained from Eq. (1). Mass attenuation coefficient μm (cm2/g) is found by dividing μ with the density of the material. Another of gamma-ray shielding parameter is the HVL calculated by using the following Eq. (2): 𝐻𝑉𝐿 =

𝑙𝑛2 𝜇

(2)

HVL is the thickness required to halve the incoming photon intensity. The mean free path (MFP) is defined as the average distance a photon can travel in the material between two successive interactions. It can be calculated by using the following Eq. (3): 𝑀𝐹𝑃 = 1/𝜇

(3)

Eskisehir, Usak Marbles Mainly, natural marbles are limestone, which contents carbonate. The Usak and Eskisehir marbles are widely used in Turkey in the building industry, production of decorative items, both in terms of durability and terms of aesthetics. The lithological and geological features of the marbles were discussed below, and their physical, geochemical structures and chemical contents were presented in Tables 1, 2, and 3 [11, 31]. Eskisehir, “Sarıcakaya beige” marble, is defined lithologically as neritic limestone. This rock is beige, yellowish, greyish in colour, medium-thick bedded, terrestrially massive, and highly durable carbonate rock. Eskisehir “Sivrihisar beige” marble is defined lithologically as pelleted intra micritic limestone. These rocks, which have massive, fragile, and

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unfossilised limestone character at the lower levels, dolomitic limestones with micritic fossils at the middle levels, at the upper levels have pinkish, beige, greyish, fossil micritic limestones character. Table 1. Chemical oxide contents of the Eskisehir and Usak marbles (%) Chemical content SiO2 Fe2O3 CaO MgO CO2 Density (g/cm3)

E1 1.20 0.25 54.40 0.60 43.55 2.70

E2 0.80 0.10 54.20 0.60 44.30 2.70

E3 0.56 0.57 53.25 1.42 44.20 2.76

U1 4.97 0.64 48.63 1.74 44.02 2.75

U2 0.02 0.12 52.16 2.56 45.14 2.74

U3 0.47 0.21 51.70 2.78 44.84 2.73

Table 2. Elemental contents of chemical compound for Eskisehir and Usak marbles (%) Compound Si Fe Ca Mg C O

E1 0.56 0.17 38.86 0.36 11.88 48.17

E2 0.37 0.07 38.72 0.36 12.08 48.40

E3 0.26 0.39 38.04 0.86 12.05 48.40

U1 2.32 0.45 37.74 1.05 12.01 46.43

U2 0.01 0.08 37.26 1.54 12.31 48.80

U3 0.23 0.15 36.93 1.68 12.23 48.78

Eskisehir “Supreme marble” is recrystallised limestone. There are Triassic aged metamorphic schists at the base. Generally, these marbles are grey, white colours and show red-pink-yellow veins, belts, and patches. Usak “Green marbles” are Paleozoic aged metamorphic rocks. It consists of calcite crystals, which is the size of 100-1000 micron, and very few biotite, quartz, and plagioclase microlites. Usak “White marbles” are in the form of lenses within the Paleozoic metamorphic schists. These show a catalytic texture, and it consists of calcite crystals, which are a size of 1-1.7 mm.

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Usak “Yellow marbles” have a catalytic texture. It consists of calcite crystals, which is a size of 0.1-0.8 mm and yellow-coloured recrystallised limestone. Table 3. The physical, mechanical, technological features of Eskisehir and Usak marbles Marbles Features Hardness (Mohs) Unit Volume by Weight (g/cm3) Density (g/cm3) Water Absorption at Atm. Pressure, By Weight (%) Water Absorption at Atm. Pressure, By Volume (%) Water Absorption at Boiling Water, By Weight (%) Water Absorption at Boiling Water, By Volume (%) Porosity (%) Compressive Strength (kg/cm2) Compressive Strength After Freezing (kg/cm2) Strength to Blow (kg.cm/cm3) Strength to Bending (kg/cm2) Modules of Elasticity (kg/cm2) Ratio of Fullness (%) Degree of Pores (%) Average Abrasion Strength (cm3/50cm2) Average Tensile Strength (kg/cm2)

E1 3 2.69 2.70 0.2

E2 5 2.69 2.70 0.2

E3 3.5 2.74 2.76 0.1

U1 4 2.73 2.75 0.102

U2 3.5 2.72 2.74 0.04

U3 3.5 2.71 2.73 0.142

0.4

0.4

0.3

0.280

0.109

0.387

0.2

0.3

0.1

0.60

0.053

0.103

0.5

0.7

0.2

0.165

0.145

0.282

0.4 1430 1250

0.4 1140 980

0.3 688 535

0.280 697 575

0.109 721 651

0.387 1060 1053

5.6 118 602000 99.6 0.4 12.42

20 122 785200 99.6 0.4 15.8

8 183 49400 99.3 0.7 25

15.57 138 101940 99.3 0.7 29.2

15.97 122 106123 99.3 0.7 25.2

13.57 212 156776 99.3 0.7 25

959

795

62

66

59

56

GEANT4 Simulation Code GEANT4 (Geometry and Tracking) is a Monte Carlo based tool kit that can simulate events that may occur in the interaction of particles and photons

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with a wide range of energy. The GEANT4 tool kit simulates the interaction of the radiation and particles coming into the detector, allowing much experimental geometry to be set up. Also, this kit offers many different experimental geometries establishing such as fast and accurate imaging techniques, ease of application in magnetic and electrical fields, shielding material design, and radiation perception. More than one file is needed to run the programme. These files were prepared in a source folder named src. Here each file contains different simulation settings. The materials used were uploaded to the file named Detector Construction.cc. Radiation related settings to be applied on the material are configured in the file named PrimaryGeneratorAction.cc. Physics List.cc file, a subfile, was prepared for operation. These files were associated with each other from running the simulation. Some chemical properties of the material to be examined are first defined in the detector construction library, then the type and energy of the radiation to be applied are selected using an interface and simulation is started. In this study, the GEANT4.10.3 version was used for gamma-ray at 356, 662, 1173, 1330 keV energies in simulation calculations. In the GEANT4 simulations, marble samples in which their chemical features and elemental compounds are given in Tables 2 and 3 were taken as a homogeneous mixture and in the dimensions of 10 × 10 × 10 mm3. Simulation geometry can be seen in Figure 1. These simulations were completed in five stages using the geometry above. 





Defined experiment geometry using material properties (DetectorConstruction.cc), radiation type, and properties (PrimaryGeneratorAction.cc) and mac files in the src folder in GEANT4 source files. The codes required to run the programme were entered from the terminal window by going to the folder where the files were prepared. System continued with simulation settings / run / initialise command.

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Nilgün Demir, Zehra Nur Kuluöztürk, Murat Dal et al.  

The number of particles to be sent was added with the simulation / run / beam on command. The results were read from the same terminal window.

Figure 1. GEANT4 simulation geometry.

FLUKA Simulation Code FLUKA (FLUktuierende KAskade) is a general purpose tool for calculations of particle transport and interactions with medium. You can simulate 60 different particle interactions with high accuracy from 100 eV energy photons to thousands of TeV energy hadrons using the FLUKA [28]. In the study presented in this chapter, simulations were performed with FLUKA version 2011.2x.8. A BEAM card was created that includes all characteristics of the source beam for the photon beam at 356, 662, 1173, 1330 keV energies. The source photon beam was directed to straight on the marble samples along the z-axis. In the FLUKA simulation, the chemical components, elemental compounds, and densities of the six marble samples (E1, E2, E3, U1, U2, U3) were defined, and its geometries are placed parallel to the z-axis by selecting a finite cylinder with a radius of 5 cm. The programme was started with 5x105 primary photons and run separately for each photon energy and marble sample. The EM interactions were activated during the simulation, the threshold energy of production and transport for photons was taken 1 keV. The photon numbers transmitted from the marble sample with several centimetres in thickness were computed by using a USRBDX card, and (I/I0) values were obtained. Thus, by plotting ln (I0/I) as a function of the sample thickness, the linear attenuation coefficient was calculated from the slope.

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RESULTS AND DISCUSSION For four different photon beam energies, its interaction with various marble samples was simulated separately with FLUKA and GEANT4 codes and transmission values (I/I0) were obtained. Linear attenuation coefficient (μ) was determined from the BeerLambert’s rule in Eq. (1). The obtained values of μ coefficient for each marble sample was compared with the theoretical values calculated from the XCOM database and are given in Table 4. Table 4. Linear attenuation coefficient μ (cm-1). Energy Method (keV) 356 GEANT4 FLUKA XCOM 662 GEANT4 FLUKA XCOM 1173 GEANT4 FLUKA XCOM 1330 GEANT4 FLUKA XCOM

E1

E2

E3

U1

U2

U3

0.2701 0.2682 0.2735 0.2100 0.2053 0.2092 0.1595 0.1489 0.1590 0.1495 0.1403 0.1491

0.2701 0.257 0.2735 0.2100 0.1934 0.2092 0.1595 0.1559 0.1590 0.1495 0.1405 0.1491

0.2755 0.2738 0.2796 0.2146 0.2053 0.2138 0.1627 0.1544 0.1625 0.1538 0.1431 0.1524

0.2743 0.2629 0.2783 0.2138 0.1950 0.2129 0.1622 0.1520 0.1619 0.1523 0.1432 0.1518

0.2736 0.2524 0.2773 0.2131 0.2122 0.2122 0.1617 0.1521 0.1613 0.1518 0.1394 0.1513

0.2728 0.2625 0.2763 0.2123 0.2084 0.2114 0.1611 0.1533 0.1607 0.1512 0.1433 0.1507

From the determined μ values, the mass attenuation coefficient (μm) has been calculated for each sample and the comparison of the results was given in Table 5. It is observed that the results obtained from both simulation codes and XCOM values are agreed. The mass attenuation coefficient is a more significant parameter than the linear attenuation coefficient because the density of the material is taken into account. The calculated μm values were

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plotted, as a function of incident gamma-ray energy, for Eskisehir and Usak marbles in Figures 2 and 3, respectively. As can be seen in both figures, μm is sharply decreased with increasing photon energy. This behaviour of μm can naturally be explained by the higher photon energy being more penetrated into the materials. Table 5. Mass attenuation coefficient μm (cm2/g) Energy Method (keV) 356 GEANT4 FLUKA XCOM 662 GEANT4 FLUKA XCOM 1173 GEANT4 FLUKA XCOM 1330 GEANT4 FLUKA XCOM

E1

E2

E3

U1

U2

U3

0.10006 0.09933 0.10130 0.07778 0.07604 0.07747 0.05908 0.05515 0.05888 0.05540 0.05196 0.05522

0.10007 0.09519 0.10130 0.07778 0.07163 0.07747 0.05909 0.05774 0.05888 0.05539 0.05204 0.05522

0.09982 0.09920 0.10130 0.07776 0.07438 0.07745 0.05897 0.05594 0.05886 0.05543 0.05185 0.05521

0.09997 0.09560 0.10120 0.07776 0.07091 0.07743 0.05898 0.05527 0.05886 0.05385 0.05207 0.0552

0.09988 0.09212 0.10120 0.07779 0.07745 0.07746 0.05901 0.05551 0.05887 0.05542 0.05088 0.05521

0.09998 0.09615 0.10120 0.07776 0.07634 0.07745 0.05918 0.05615 0.05887 0.05541 0.05249 0.05521

It can be seen from the data obtained that when the photon energy increases, around 1173,1330 keV, the μm coefficient remains almost constant for each marble sample since the interaction of pair production formation predominates. A comparison of mass attenuation coefficients simulated by GEANT4 and FLUKA for all marble samples and all photon energies is given in Figures 4, 5 in the form of a column chart. It can be seen from Figures 4 and 5, μm values of marbles are very close to each other because the chemical contents of samples are also very similar. Another critical parameter reflecting the shielding properties of materials is the HVL. The HVL values of Eskisehir and Usak marbles were obtained from Eq. (2) and given in Table 6. At the same time, the obtained HVL values were plotted according to the photon energy and given in Figures 6 and 7. It is

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seen that the HVL values increase with increasing photon energy. In contrast to μm, the shielding property of a marble sample with a low HVL value will be better. It has been observed that Eskisehir “Supreme marble” (E3) has the lowest HVL value. Although all HVL values are very close to each other, it can be said that the highest HVL value is observed in (E1) and (E2) marbles. A comparison of HVL coefficients obtained from GEANT4 and FLUKA for all marble samples and all photon energies is also shown in Figures 8 and 9.

Figure 2. Mass attenuation coefficient versus photon energy for Eskisehir marbles.

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Figure 3. Mass attenuation coefficient versus photon energy for Usak marbles.

Figure 4. The comparison of μm coefficient of all samples calculated with the GEANT4.

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Figure 5. The comparison of the μm coefficient of all samples calculated with the FLUKA.

Figure 6. Half value layer versus photon energy for Eskisehir marbles.

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Figure 7. Half value layer versus photon energy for Usak marbles.

Figure 8. The comparison of HVL values of all samples calculated with the GEANT4.

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Figure 9. The comparison of HVL values of all samples calculated with the FLUKA.

Table 6. Half value layer (cm) Energy (keV) 356

662

1173

1330

Method

E1

E2

E3

U1

U2

U3

GEANT4 FLUKA XCOM GEANT4 FLUKA XCOM GEANT4 FLUKA XCOM GEANT4 FLUKA XCOM

2.565 2.584 2.534 3.3 3.376 3.314 4.344 4.655 4.360 4.635 4.940 4.649

2.565 2.697 2.534 3.3 3.584 3.314 4.344 4.446 4.360 4.635 4.933 4.649

2.515 2.532 2.479 3.229 3.376 3.243 4.259 4.489 4.267 4.505 4.844 4.549

2.526 2.637 2.491 3.241 3.555 3.255 4.272 4.560 4.282 4.550 4.840 4.566

2.532 2.746 2.500 3.251 3.266 3.266 4.285 4.557 4.297 4.565 4.972 4.582

2.540 2.641 2.509 3.264 3.326 3.278 4.301 4.521 4.313 4.583 4.837 4.599

The mean free path (MFP) values obtained from Eq. (3) were given in Table 7. A material, which has the lowest MFP value, shows an effectively shielding property. It can be seen from Table 7 that (E3) marble has the lowest MFP.

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Nilgün Demir, Zehra Nur Kuluöztürk, Murat Dal et al. Table 7. Mean Free Path (MFP) (cm)

Energy Method (keV) 356 GEANT4 FLUKA XCOM 662 GEANT4 FLUKA XCOM 1173 GEANT4 FLUKA XCOM 1330 GEANT4 FLUKA XCOM

E1

E2

E3

U1

U2

U3

3.702 3.729 3.656 4.761 4.871 4.781 6.269 6.716 6.290 6.688 7.128 6.707

3.702 3.891 3.656 4.761 5.171 4.781 6.269 6.414 6.290 6.688 7.117 6.707

3.629 3.652 3.577 4.659 4.871 4.678 6.146 6.477 6.156 6.501 6.988 6.563

3.645 3.804 3.593 4.677 5.128 4.696 6.165 6.579 6.178 6.501 6.983 6.588

3.654 3.962 3.606 4.677 4.712 4.712 6.165 6.575 6.199 6.565 7.174 6.610

3.665 3.810 3.620 4.710 4.798 4.730 6.207 6.523 6.222 6.613 6.978 6.635

CONCLUSION In this chapter, the simulation results calculated with FLUKA and GEANT4 code the gamma-ray shielding parameters for six different types of marble in Eskisehir and Usak provinces in Turkey were presented. Linear attenuation coefficient (μ), mass attenuation coefficient (μm), HVL, and mean free path (MFP) parameters were computed at 356, 662, 1173, and 1330 keV photon energies. The simulation results were compared with the theoretical values calculated from the XCOM database and observed to be in good agreement. No very distinctive differences were observed between the μm coefficients calculated for each marble since the marble samples examined had almost the same chemical content. The lowest HVL and MFP values were obtained Eskisehir “Supreme marble” (E3), which is an indication that its shielding effect is better. These results indicate that FLUKA and GEANT4 Monte Carlo methods can be applied to predict shielding parameters for various materials known for their chemical content and density, and for various energies.

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Nilgün Demir, Zehra Nur Kuluöztürk, Murat Dal et al. Energy and Medical Applications.” Nuclear Data Sheets 120:211214. https://doi.org/10.1016/j.nds.2014.07.049. Ferrari, A., Sala, P. R., Fasso`, A., Ranft, J. (2005). “FLUKA: a multiparticle transport code.” CERN 2005-10, INFN/TC_05/11, SLAC-R773. Agostinelli, S. et al., GEANT4 Collaboration. (2003). Nucl. Instr. and Meth. A 506:250. https://doi.org/10.1016/S0168-9002(03)01368-8. GEANT-4 toolkit. http://geant4.fweb.cern.ch. (accessed July 14, 2013). Şener, M. F., Umut, M., Üzel, A. 2013. The conventional building stone of Turkey. Ankara: MTA.

In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 12

RADIATION SHIELDING CHARACTERISTICS OF BULK AMORPHOUS METALS FOR GAMMA RAYS, CHARGED AND UNCHARGED PARTICLES Ufuk Perişanoğlu Department of Physics, Ataturk University, Erzurum, Turkey

ABSTRACT In this chapter, nuclear radiation shielding qualities of some amorphous metals (Cu60Hf25Ti15)98Ta2; Ce65Al10Co20Zn5; Fe70Al5Ga2P11C6B4Nb2; Ti44Cu40Ni8Zr7Sn1; Ni60Nb37Sn3 encoded S1, S2, S3, S4 and S5 have been evaluated. For the determination of all photon shielding parameters, the mass attenuation coefficients (μ/ρ) of metallic glasses were determined for the 0.015-15 MeV photon energy interval. The largest μ/ρ values for the S1 sample ranged from 83.09036 cm2/g to 0.03721 cm2/g while the smallest μ/ρ values changing from 44.0296 cm2/g to 0.02841 cm2/g belonged to the S3 sample. Subsequently, EBF, HVL and 

Corresponding Author’s Email: [email protected].

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Ufuk Perişanoğlu equivalent atomic number (Zeq) values were obtained for the same gamma-ray energies. Besides, MFP (Mean Free Path) values of amorphous metals were compared with common used shielding materials'. It was determined from these results that the MFP values of metallic glasses were smaller than the known commercial glass samples and heavy aggregate concretes. Moreover, the defense of the proposed samples to the penetration of fast neutron and charged (alpha and proton) particles was interpreted by calculating macroscopic cross-section (∑R), mass stopping power (MSP), and projected range (PR) values, respectively. S 1 and S3 samples were found to have the best neutron retention ability due to their high density and light atomic element content, respectively. Finally, it was revealed that the charged particles had the shortest range in the S1 sample.

Keywords: metallic alloys, MFP, shielding, neutron, mass stopping power

INTRODUCTION The advancement of radiological methods, the changing of devices, and the use of high energy radiation beams for treatment purposes demand controls shielding the facilities and to limit the dose to be received from those facilities at an acceptable level. Considering the economic and social factors, it should be ensured that the radiation to be exposed in all applications to be kept as low as reasonably achievable (ALARA). For this reason, in order to reduce the radiation dose, appropriate shielding material should be placed between the source and the body [1]. The choice of shielding material varies depending on the type and energy of the radiation. However, the aim is to design a shield material that can be effective against all types of radiation. For this purpose, researchers recently carried out studies on many different types of shielding materials [2–4]. The earliest works on shielding were on concretes and concrete forming materials that have to be used in the design of the facilities. In many studies, it has been shown that concretes produced by adding heavy aggregates, various minerals and minerals become more effective in reducing photon and neutron radiation [5–8]. Alternative radiation shielding materials such as polymers, ceramics, and alloys to be used not only in facilities but also in radiation personnel equipment and other equipment have been proposed [9–

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12]. Although the attenuation performance of these materials has been convenient and cost-effective, new materials were surveyed due to some disadvantages such as crack formation, not being transparent, and water permeability. For this reason, due to its improved optical qualities, ease of production and diversity, glasses, especially heavy metal oxide glasses, have become very interesting as new shielding materials [13–16]. Metallic glasses, amorphous metals are a new family of metallic alloys with excellent properties such as high strength, hardness, corrosion resistance, wear resistance [17]. Their amorphous structure provides these advantageous features compared to crystalline counterparts with the same composition. Metallic glasses were produced only in strips and sheets until the 1990s due to high cooling speeds and dimensional restrictions. The discovery of multi-component alloys has been a turning point in this area and has made it possible to obtain metallic glasses in large volumes by conventional melting and casting methods [18]. For this reason, metallic glasses, which can be produced at low temperatures, have superior electrical, magnetic and mechanical properties, and have both glass and alloy properties, are very interesting for researchers. From this point of view, it may be useful to examine the nuclear radiation shielding parameters of metallic glasses with the desired properties for radiation shielding materials. Initially, for the five different metallic glass selected, the mass attenuation coefficients (μ/ρ) were achieved utilising WinXCOM software. Other μ/ρ based photon protection parameters, HVL, equivalent atomic number (Zeq) and Mean Free Path (MFP), of metallic glasses, were also determined for the energy range of 0.015-15 MeV. Besides, EBF values of the samples were computed by the EXABCAL programme. At last, effective removal crosssection (∑R) for fast neutron and PR and mass stopping power (MSP) for charged particles have been investigated within the kinetic energy range between 0.01–10 MeV.

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MATERIALS AND METHOD Five metallic glasses with compositions (Cu60Hf25Ti15)98Ta2; Ce65Al10Co20Zn5; Fe70Al5Ga2P11C6B4Nb2; Ti44Cu40Ni8Zr7Sn1; Ni60Nb37Sn3 encoded S1, S2, S3, S4 and S5 were selected from Ref.[19]. The density of investigated glasses are 9.467, 6.801, 6.371, 6.806 and 8.73 g/cm3 respectively. The mass attenuation coefficients (μ/ρ) were calculated theoretically calculated using the mixing rule with WinXCOM software [20].

   wi ( /  )i i

(1)

(1)

The photon attenuation feature of a sample is defined by a special parameter namely HVL, which reduces the primary photon intensity by half. [21]; HVL = (ln 2/μ)

(2)

MFP (Mean Free Path) presents the mean way travelled by the photon within two back-to-back collisions with the sample atoms, and is given as [22]. MFP  (1 /  )

(3)

The most important parameters employed in the investigations associated with photon scattering are the EBF and the energy absorption buildup factor (EABF) [23]. While EABF is a parameter correlated to the amount of energy absorbed in the matter in which the radiation interacts, EBF gives the quantity of potential interactions with air stretching the medium between the detector and the radiation source [24, 25]. The EBF and EABF values of the proposed metallic glasses were achieved by utilising the G-P fitting approach as declared earlier in numerous published works

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[26–28]. In this study, EXABCAL programme [29], which is very useful for buildup factor studies and gives correct results, was preferred for calculations of EBF values. The effective removal cross-section (Σ𝑅) presents the possibility of a fast neutron to perform the first collision, and the Σ𝑅 value of a composite material is calculated as below [30]; Σ𝑅 = ∑i 𝜌𝑖 (Σ𝑅/𝜌)

(4)

where ρ is the element density and (Σ𝑅/𝜌)𝑖 refers to the removal crosssection of the ith element. Charged particles like alphas and protons slow down as they move into the matter and the amount of energy drop varies depending on the change in their kinetic energies. It spends more energy near the electrons and cause more ionisation. The total energy lost per unit length, ie “Stopping Power” is found by the Bethe-Bloch formula [31, 32]; dE / dx 

4 N A me c 2 re 2 z 2



2



 2 me v3 Z ln 4 0 A ze2 f

(5)

e2

NA re  4 0 me c 2 is the Here   v c , N e  Z A  electron density and

radius of an electron. If the stopping power of the particle is known, the PR of the particle can also be obtained in the matter utilising the equation below[33]; R

0

0

E

dx dE dE   dE S (E) E 0

R   dx  

(6)

In the current study, proton and alpha mass stopping powers (MSP) and PR were achieved by SRIM-2008 codes [34].

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RESULTS AND DISCUSSION The mass attenuation coefficients (μ/ρ) of metallic glasses were determined by the WinXCOM programme for the gamma-ray energy interval of 0.015-15 MeV. Figure 1 represents the variation of the μ/ρ values of the chosen samples against the photon energy. The biggest μ/ρ values were gained for low energy intervals, 0.015-0.3 MeV for all the samples. As the photon energy rises from 0.015 to 0.3 MeV, the μ/ρ of the glasses declines quickly due to photoelectric absorption (PEA) interaction mechanism whose cross-section depends on Z4-5/E3.5. But in this region, unexpected increases in the μ/ρ values of S1, S2 and S5 samples are observed in the absorption edges of the elements Hf, Ce and Nb (65.35 keV; 40.44 keV; 18.98 keV), respectively. These abrupt increases are due to the PEA cross-section being larger in the absorption edge of Hf, Ce and Nb elements. The photons are almost completely absorbed in this interaction. The reduction in μ/ρ values of the samples is not rapid at the range of 0.3-2 MeV. This is the result of the CS cross-section which varies on Z/E. After 2 MeV, the photons are under the influence of pair production (PP), whose cross-section is proportional to Z2 when interacting with the sample. Therefore, an increase in μ/ρ values is observed for all samples. It can be seen from Figure 1 that S1 and S2 amorphous metals with high density and heavy element concentrations in their contents get the highest μ/ρ values. The largest μ/ρ values for the S1 sample ranged from 83.09036 cm2/g to 0.03721 cm2/g while the smallest μ/ρ values changing from 44.0296 cm2/g to 0.02841 cm2/g belonged to the S3 sample. HVL is an excellent parameter to decide the thickness of the material utilised for a given photon energy. The behaviour of the HVL values for the metallic glasses against gamma-ray energy is exhibited in Figure 2. While the HVLs of the amorphous metals were grown at low and intermediate energies, they were almost constant for the high energy zone due to PP process. The rapid rise in medium energies can be attributed to the increase of secondary scatterings in this region. S1 sample with the highest specific gravity possess the lowest HVL values in the chosen energy range.

Radiation Shielding Characteristics of Bulk Amorphous Metals …

Figure 1. The variation of μ/ρ values of the metallic glasses with photon energy.

Figure 2. The HVL values of the metallic alloys versus the photon energy.

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Figure 3. Variations of MFPs versus gamma energy for metallic glasses and various shielding materials.

MFP (Mean Free Path) refers to the path a photon takes between consecutive collisions. Figure 3 presents the comparison of MFP values of metallic glasses with commonly preferred shield materials, RS-360, 520 glasses [35] and barite, chromite and ferrite concretes [30] and Pd75Ag25 alloy [36]. Thinner MFP values make that material a better shield. As can be seen from Figure 3, the proposed metallic glasses have lowest MFPs than all the compared materials except the Pd75Ag25 alloy. Among the amorphous glasses selected, S1 gets the smallest MFP values. Even at the highest energies, a maximum of 3 cm MFP is observed for the S1 sample. The change of EBF with gamma-ray energy is presented in Figures 4(ae) for metallic glasses. In this work, EXABCAL programme was used for determining the G.P. fitting coefficients and equivalent atomic numbers (Zeq) employed to compute EBF values for within 0.015 and 15 MeV energy range. Remarkably, the smallest EBFs were gathered for S3 and S4 samples at low and high energy regions where PEA and PP interactions prevail. For S1, S2 and S5 samples containing high amounts of heavy elements such as Hf, Ta (for S1), Ce (for S2) and Nb,Sn (for S5), some sharp rises were observed at the absorption edges of the relevant elements at low energies.

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Figure 4 (a-e). Variations of the EBF with photon energy for the metallic glasses at several penetration depths.

For these three metallic glasses, EBF values increase due to the change of PP with Z2 at high energies. The EBFs touch the largest values at the

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middle energies due to Compton scattering, which provides photons to multiply through the samples. It can be observed from Figure 4 that while the EBFs get the lowest values for S1, the largest EBFs are observed for S3 samples.

(a)

(b)

(c) Figure 5 (a-c). Variation of the EBF with penetration depth for the metallic glasses at 0.15, 1.5 and 15 MeV.

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Figure 5(a-c) depicts the change of EBFs versus the penetration depths at three fixed energies. At 0.15 MeV, The EBF tends to remain stable after a small increase with increasing penetration depth and is almost zero for S1 and S2. The S3 sample takes the highest EBF values. By the force of the CS process at 1.5 MeV, the diversity in elemental composition mislays its effect, and the EBFs increase linearly with growing penetration depth. As in 0.15 MeV, S1 also owns the smallest EBFs in this energy. At 15 MeV dominated by PP, photon buildup is higher for samples with large Zeq at high penetration depths. It is seen that the biggest EBF values are obtained for S1 glass. Macroscopic cross-sections (∑R) of the metallic glasses for fast neutrons are depicted in Figure 6. It could be clearly found from Figure 6 that the neutron shielding capability of the S1 and S3 samples are better than that of others. The density of the S1 sample has a positive effect on the neutron shielding ability of the sample. Light elements in the S3 sample content improved significantly its neutron macroscopic absorption cross-section.

Figure 6. Effective removal cross-sections of the metallic glasses for fast neutrons.

Finally, the capacity of the proposed samples for shielding against alpha and proton particles was examined and the change of MSP against kinetic energy to determine the rate of kinetic energy loss of ions is shown in Figure 7 (a and b). MSP values of charged particles that interact with the sample

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initially enhance. After a while, the particle captures the electron and the MSP values reduce swiftly for both particles. Since protons are lighter than alpha particles, MSP values are lower compared to alpha particles. Lowest MSP values were gained for S1 sample. Figure 7 (c and d) shows projected ranges (PR) for alpha and proton as a function of kinetic energy. PR values for protons are lower than alpha particles for the examined glasses. The range of both ions is the shortest in S1 and S5 samples. All the results obtained revealed that S1 sample is the most effective shielding material for all types of radiation among the other amorphous metals.

(a)

(b) Figure 7 (a-d). (Continued).

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(c)

(d) Figure 7 (a-d). Variation of the proton and alpha mass stopping powers and projected range as a function of kinetic energy for the metallic glasses.

CONCLUSION In this chapter, nuclear radiation shielding features of five metallic glasses were studied. The mass attenuation coefficients (μ/ρ) of the metallic glasses were performed employing WinXCOM programme for a wide gamma-ray energy range. Other major photon protecting parameters, MFP,

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HVL, Zeq and EBF, were also found in an energy interval of 0.015-15 MeV. It was seen that the S1 sample, which owns the highest density, is quite powerful as a photon attenuator than others. It was also noted that MFP values of S1 and S2 samples were smaller than various shielding materials like heavy concrete and commercial glasses. The ∑R values of metallic glasses range between 0.108 - 0.162 cm-1. The best neutron attenuators were found as S1 and S3 samples according to others. Both ions were determined to travel smaller distances in the S1 sample.

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In: Computational Methods … ISBN: 978-1-53618-527-0 Editors: K.S. Mann and V.P. Singh © 2020 Nova Science Publishers, Inc.

Chapter 13

DETECTION FEATURES OF BORATE-BASED THERMOLUMINESCENT DOSIMETERS Carina Oliva Torres-Cortes1,*, Hector Rene Vega-Carrillo2, Antonio Baltazar-Raigosa1 and Luis Hernandez-Adame3 1

Doctoral Program in Engineering and Applied Technology, Academic Unit of Electrical Engineering, Autonomous University of Zacatecas, Zacatecas, Zac., Mexico 2 Academic Unit for Nuclear Studies, Autonomous University of Zacatecas, Zacatecas, Zac., Mexico 3 CONACYT-Northeast Biological Research Center (CIBNOR), La Paz, B.C.S., Mexico

ABSTRACT The human being is exposed to two types of radioactive sources, natural and artificial sources. The exposure to natural radiation is *

Corresponding Author’s Email: [email protected].

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Carina Oliva Torres-Cortes, Hector Rene Vega-Carrillo et al. continuous and comes mainly from cosmic rays, terrestrial gamma radiation, and gamma radiation caused by radon in the air and its progeny. In addition to having other percentages from internal natural radioactive sources, such as 40K. Artificial radioactive sources constitute a small portion of the total amount of radiation to which it is exposed, however, if there is not detection, control and quantification of this radiation, its consequences can be adverse. The human body does not perceive the radiation, so it is necessary to use equipment to detect and measure the absorbed dose in the organism. Within personal dosimetry, the development of thermoluminescent materials (TL) used for the detection and quantification of ionizing radiation continues to be a great challenge. During the passage of time, various TL materials or commercial thermoluminescent dosimeters (TLD) have been used which, although they have shown capacity, do not meet all the characteristics to be classified as an excellent TLD. This chapter presents some TL materials used as TLDs and recent advances in both the synthesis and characterization of the materials. Studies on Magnesium Borates are shown; MgB4O7 is considered one of the most promising phosphors for γ rays, heavy ions and neutrons. Likewise, the characterization of another phase of Magnesium Borate is also presented as TLD for γ rays, Mg2(B2O5). It should be mentioned that to these materials a doping is added, the type of doping and its concentration, have an important role in the production of TL and, therefore, also affects the detection of the radiation of interest.

Keywords: TLD, γ rays detection, neutrons detection, magnesium borates

INTRODUCTION Radiation is classified according to its energy, the ionizing radiation is made up of X-rays, γ rays, and the electromagnetic radiation from Cosmic radiation; also, ionizing radiation can be corpuscular, having mass and electric charge, as the alpha and beta particles being produced during the decay of natural occurring radioisotopes like 40K, U and Th [1, 2]. In several applications like industry [3], agriculture [4], medicine [5], educational and research centers [4] ionizing radiation artificially produced are used. Natural and artificial radiation sources contribute to the dose received by humans [5]. Regardless the origin of ionizing radiations is important to measure the absorbed dose and the radiation dose in the

Detection Features of Borate-Based Thermoluminescent Dosimeters 333 environment in the aim to survey the dose levels and to design procedures and protocols aiming to reduce the associated health risks. There are several devices and materials used to measure the radiation dose, like the thermoluminescent dosimeters (TLDs). In dosimetry and materials science, the development of materials to detect and quantify radiation dose by external exposure is of great interest. For such purposes, various compounds such as LiF, LiF:Mg,Cu,P, CaSO4, CaF2, K2Ca2(SO4)3, Al2O3:C, BeO, among others [6, 7, 8], are commonly used as materials thermoluminescent for the individual radiological surveillance of personnel working in radiology centers, radiotherapy and nuclear power plants [9]. Currently, there are several thermoluminescent dosimeters in the market used for this purpose (Bhatt and Kulkarni, 2014). TLDs such as TLD-100 [10], TLD-600 [11], TLD-700 [11], TLD-100H [12], TLD-600H [13], TLD700H [13], are used to quantify the doses due to γ rays, β particle, X-rays and neutrons (n), however, have several limitations regarding their stability, linearity, sensitivity and fading, which derive mainly from the degree of crystallinity, amount of doping and type of impurities, that make up each matrix [14, 15, 16]. In general, a personal dosimeter should have some characteristics such as a simple TL curve (with a single peak), high sensitivity, low threshold dose, little fading, linearity of the TL signal, equivalence to biological tissue (Zeff = 7.4), chemical stability, mechanical resistance, to environmental changes and magnetic fields [6, 14, 17]. Unfortunately, none of the available dosimeters have all these properties, the TLD-700H, TLD-100H and TLD600H have some of them, but their elaborate manufacturing process, highly toxic precursors, high cost and complicated availability, justify the constant search of materials for this use [15]. The TLD has advantages over other mechanisms of determination of the absorbed dose; these reside in the high sensitivity to different types of radiation, dose accumulation, small size, relatively low costs and greater understanding of the response to radiation of the characteristic peaks [18, 19, 20, 21].

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Research groups have been dedicated to the synthesis of materials that have ideal properties to be used as a personal dosimeter. In recent decades, interest has been placed on Magnesium Borate compounds, because they exhibit attractive physical, mechanical, and chemical properties and have diverse applications. They have a high resistance to heat, corrosion, mechanical resistance, insulation and elasticity. Due to these properties, they can be used as TL’s materials, catalysts for the conversion of hydrocarbons, additives in laser applications, reinforcement in electronic ceramics, broadband semiconductors and reinforcement compounds in plastics [22]. According to the phase diagram reported in [23], the thermally stable phases of Magnesium Borates are Mg3B2O6, MgB4O7 and Mg2(B2O5). MgB4O7 has been used as the TL matrix, it is considered a promising matrix for the dosimetry of γ rays, X-rays and neutrons [24], it is approximately 10 times more sensitive than LiF [25]. Its performance is increased with the incorporation of atoms in the crystal structure or as impurities with large effective sections (σ) such as 10B, this makes it become a material that is sensitive to slow neutrons with an effective section similar to that of 6Li and with a Zeff close to that of biological tissue (Zeff = 8.4) [26]. MgB4O7:Dy is recognized as a good thermolumines phosphor for personal dosimetry of γ rays, X-rays and neutrons because the 164Dy has a high cross-section, similar to that of 10B [27, 6]. Figure 1 shows cross-section of some neutron sensitive atoms. In [27], he proposed the incorporation of a co-dopant, Sodium (Na). Na as an additional dopant, increases the intensity of the TL in relation to MgB4O7:Dy. In MgB4O7:Dy,Na there is an improvement in its chemical and dosimetric properties for neutron detection. It has a simple glow curve, consisting of a well-defined main peak at around 163°C and another small high-temperature peak at around 300°C, using a heating rate of 2°C/s. Recently, they synthesized MgB4O7:Dy to be used as TLD for neutrons and  rays, the result showed that when doping with 1mol% it shows the best TL response, with a main peak at 220°C [28]. On the other hand, [29] synthesized MgB4O7:Dy using the solution-assisted method, and evaluated the low-dose TL response of β particle; The TL intensity was improved with

Detection Features of Borate-Based Thermoluminescent Dosimeters 335 4 mol% of dopant Dy3+. In the subsection of TL materials, the subject of TL matrices, especially MgB4O7 and Mg2(B2O5), is embroidered.

Figure 1. Total cross-section of atoms sensitive for neutrons.

For the development of thermoluminescent materials that can be used as TLDs in personal dosimetry, there are computational tools that allow predicting the performance against some type of radiation and optimizing the synthesis and characterization of TL materials. This chapter talks about the Monte Carlo (MC) method, specifically the MCNP5 code to predict the behavior of the MgB4O7:Dy y el Mg2(B2O5):Dy,Na.

THERMOLUMINESCENCE PRINCIPLE Thermoluminescence is a physical phenomenon that can be explained through band theory (Figure 1) [14]. The insulating or semiconductor material is exposed to an exciting source (i.e., ionizing radiation), to produce

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electron-hole pairs that can become trapped in energy levels introduced by defects in the TL material. So that the trapped charges can be released, it is subjected to a thermal treatment, giving rise to the TL, this process is represented graphically in a brightness curve, the intensity and the area under the curve are correlated with the absorbed dose [30, 31]. In Figure 2, the process carried out internally in the material is detailed. It begins by exposure to ionizing radiation that transfers sufficient energy to the valence band (VB) electrons to produce electron-hole pairs that, after the irradiation process, can witness two cases: (1’) direct recombination where a photon is emitted and does not contribute to the TL phenomenon, this occurs in approximately 10-8 s, or (1) electron-hole pair production and (2) the capture of charge carriers in the trap (T) located near of the conduction band (CB), where the electrons are trapped in metastable states, while the holes are in metastable states near the VB at the R level [32]. When the material is heated it provides enough energy so that the electrons are released from the traps and return to the CB (transition 3). The electrons in the CB tend to relax by direct recombination, however, some do so through discrete levels (transition 4 and R level), producing light emission (thermoluminescence) and is proportional to the dose absorbed by the material [32]. The separation between the VB and CB is called band gap (Eg), which plays a very important role in TL materials, because when there are structural defects in a crystalline material, and impurities are incorporated, the electrons can have prohibited energies and contribute to the TL phenomenon [32].

Radiation Dosimetry The applications of ionizing radiation require the adequate determination of the energy absorbed from the radiation field, to give it its intended use and protect radiologically those who use it [33]. For this purpose, dosimetry is the area of nuclear science that aims to quantify the energy received by some material (inert or alive) that has had interaction

Detection Features of Borate-Based Thermoluminescent Dosimeters 337 with any type of ionizing radiation [34]. The equipment used to measure and quantify this energy is called dosimeters; they are devices that directly or indirectly measure exposure, kerma, absorbed dose, equivalent dose, or related amounts of ionizing radiation [35]. Some of the techniques to measure radiation are the Fluorescence technique, Lyoluminescence method, Diffuse reflectance technique, thermally stimulated luminescence technique (TLD) and Optically stimulated luminescence technique (OSL) [33].

Figure 2. Thermoluminescence phenomenon according to band theory.

The potential of TLD use lies in several favorable characteristics, high sensitivity, small size, ability to cover a wide range of exposure, reuse, and insensitive to environmental conditions. The TL technique provides adequate passive measurement and has significant applications in radiation protection. TLDs have been widely used for in-phantom and in vivo dosimetry in medical applications, in personal monitoring of workers exposed to ionizing radiation, environmental dosimetry, space radiation measurements, and in radiation therapy applications against cancer [33, 35, 36].

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Currently, there are several commercial TLDs that are widely used in personal dosimetry, environmental monitoring, and clinical radiation dosimetry [8].

Gamma Rays Dosimetry The γ rays are part of the classification of ionizing radiation; they are electromagnetic radiation emitted by an unstable nucleus when a radioactive decay occurs, from an annihilation reaction or when an unstable nucleus enters a stable state [37]. The wavelength of γ rays is short so it can traverse space within the atoms of a detector. Therefore, the detection of γ rays strongly depends on the interaction that the photon has and that it yields all or part of the energy to an electron of the absorbent material [38]. There are a variety of γ rays detectors, however this chapter will focus on TL based passive detectors with applications in personal dosimetry. The field of application of TL dosimetry for γ rays and β particles have been highly developed [14]. According to an exhaustive review by [14], among the most used TL materials for their dosimetric properties are:       

Fluorides Sulfates Borates Sulfides Phosphates and halo-phosphates Metal oxides Different kinds of glasses and perovskites

The mentioned matrices combined with alkali or alkaline earth elements. For dosimetry, the most widely used TL or TLD detectors are those based on LiF, due to the close effective atomic number of human soft tissue, ranging from 8.14 to 8.65 [20]. Some LiF based TLDs are:

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LiF:Mg,Ti (TLD-100) This TL material has been the standard of thermoluminescence dosimetry for many decades [39]. It has a Zeff = 8.2 close to that of soft tissue, making it suitable for medical applications. The TL glow curve is complex, consisting of more than 10 peaks and sub-peaks [40]. One of the characteristics in common with the other two mentioned TL materials is the Mg dopant, which is responsible for capture centers to favor the thermoluminescence process. Mg2+ ions enter the crystal lattice as substitutes for Li+ ions. The concentration of Mg is important, in the case of TLD-100 a range between 0.01-0.02% and in LiF:Mg,Cu,P 0.2% has been reported [39].

LiF:Mg,Cu,P (TLD-700H or TLD-600H) TLD-700H corresponds to 7Li and TLD-600H to 6Li. The 7LiF:Mg,Cu,P material is sensitive to photons and β particles while 6LiF:Mg,Cu,P presents sensitivity to photons, β particles and slow energy albedo neutrons [41]. In general, it is a TL material that has high sensitivity and tissue equivalency, however, it shows a significant loss in sensitivity when it is synthesized at temperatures above 240°C [42]. Sensitivity is more than 20 times higher than TLD-100 [43].

LiF:Mg,Cu,Si It is a tissue equivalent TL material, 1.3 times higher when compared to LiF:Mg,Cu,P. It shows a main peak at 220°C. The optimal concentrations of the dopants are 0.2, 0.0125, 1.92 mol% respectively. The linearity range was 0.1-10 Gy [42]. Other of the groups of outstanding materials are the aim of this chapter, are magnesium borates. They have captured the interest of researchers for the chemical and physical properties they can present and the variety of applications in which they can be used. In particular, the materials MgB4O7:Dy and Mg2(B2O5):Dy,Na will be discussed. MgB4O7 is a promising matrix, when doped with rare earth elements it becomes a good TL material in thermoluminescent dosimetry. Some of the properties that make it attractive for this purpose are its Zeff close to that of

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soft tissue, low dependence on photon energy and the possibility that it is an adequate neutron dosimeter due to the high cross-section [44]. MgB4O7:Dy, is a TL material with an Zeff ~ 8.4, it is commonly used for medical γ rays and X-rays dosimetry. Its sensitivity is approximately 2.2 times higher TLD-100, however, it has been reported to have high fading, so the study of kinetic parameters is relevant [31]. The characteristics of a TL material strongly depend on the synthesis method used, the concentration of the dopants and the dosimetric conditions. Therefore, it is of great importance to find the interrelationships between the preparation methods, the defect structure and the TL properties of the material [45]. One of the decisive steps is the sintering heat treatment, because it can modify the obtained compound and the size of the particles. Typically, the way an inorganic material is obtained is as a polycrystalline powder. However, the final application determines the shape of the material [45]. According to the development of investigations in the synthesis of MgB4O7 the solid state reaction predominates, however, recently it has been dedicated to obtaining it by other methods. Table 1 shows TL materials based on MgB4O7 for detection of γ rays, where they mention the synthesis method used and the linear range of response to the absorbed dose in Gy. Recently there are two groups of researchers that synthesized MgB4O7:Dy, [29] synthesized by solution-assisted method, the annealing temperature was 800°C for 2 h, to obtain the glow curve, it was subjected to heating from room temperature to 450°C with a heating ramp of 2°C/s. The optimal doping concentration was 4 mol% and the main peak of the glow curve was 333°C. The TL material was irradiated with β particles from a 90 Sr/90Y source with a dose rate of 0.1099 mGy/s. A linear response of 52000 mGy was obtained. In [28], synthesized MgB4O7:Dy using a high temperature solid-state reaction method. The synthesis conditions were as follows: The stoichiometric mixture of reagents was stirred and heated to 90°C until the distilled water evaporated almost completely. Then it was subjected to another 400°C heat treatment for 4 h. It was allowed to cool and then grind it and subject it to another annealing step at 850°C for 12 h. The

Detection Features of Borate-Based Thermoluminescent Dosimeters 341 concentration of the dopant was 1 mol% and the material was exposed to 252 Cf source (0.08Gy/min). The results obtained MgB4O7:Dy (1 mol%) approximately 1.90 and 1.47 times higher than TLD-600 and TLD-700 respectively. The main peak of the glow curve was 220°C. It is important to mention that before each measurement of the TL response, they gave a heat treatment at 600°C for 1 h. They concluded that the synthesized compound can be suitable for neutron + gamma radiation and could be an ideal neutron dosimeter. In works made by our group was synthesized MgB4O7:Dy and Mg2(B2O5):Dy,Na with a doping concentration of 0.1 mol% for Dy and 0.5 mol% for Na. The synthesis method used was the chemical method by precipitation or wet reaction, MgO:H3BO3 1:4 with 8M HNO3 was mixed under constant magnetic stirring. HNO3 and water is evaporated in a drying oven for 24 h at 100°C. Several washes were done to get rid of the residual acid. Finally, the annealing stage was 800°C for 2 h and followed by a heating to 500°C for 1 h. It is important to mention that 13 TL materials were synthesized with a doping range of 0.01-1.5 mol% with respect to Dy and for Na the concentration was fixed (0.5 mol%) and those with the best response to were rays were MgB4O7:Dy 0.1 mol% and Mg2(B2O5):Dy,Na 0.1,0.5 mol%. Table 1. Thermoluminescent materials from MgB4O7 for γ rays TL material

Synthesis method SE

Radiation detection

MgB4O7:Nd/ X, γ and β MgB4O7:Nd,Dy MgB4O7:Dy P/SE γ rays /MgB4O7:Dy MgB4O7:Mn,Tb SE γ rays MgB4O7:Gd,Li SE γ rays MgB4O7:Dy,Na γ rays MgB4O7:Dy C γ rays MgB4O7:Dy P γ rays MgB4O7:Dy SE Neutron+γ radiation SE= Solid Estate, P= Precipitation, C= Combustion.

Linear response to absorbed dose (Gy) 5-40

Reference

10-100

[25]

0.1-5000 0.001-1000 0.00009-40 10-5000 -

[16] [46] [27] [7] [47] [28]

[24]

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In the same way the TL materials were obtained, no study has yet been done for the possible explanation of obtaining two different materials with the same synthesis method. However, according to works by other groups, possibly due to the concentration of the solvent, because the morphology of the polycrystalline depends on the solvents, which are promoters or inhibitors of nucleation. Furthermore, according to [48], excess MgO leads to the formation of Mg2(B2O5). Figure 3 shows the XRD where it is evident that only MgB4O7 was not obtained.

Figure 3. XRD diffractogram of a) XRD pattern of MgB 4O7 (JCPDS 00-031-0787) b) MgB4O7:Dy and c) Mg2(B2O5):Dy,Na.

The materials were irradiated 5.5 cm from a source of 529±26 MBq of Cs, for 30 minutes, the dose was 6.8±0.4 mGy. In the case of neutron irradiation, the samples were placed 2 cm from a 241AmBe source with an activity of 3.7 GBq for 17 h. The average neutron energy is 0.75 MeV, the applied dose was 3.1±0.1 mGy. The glow curves showed a better response to γ rays by Mg2(B2O5):Dy,Na 0.1,0.5 mol% that MgB4O7:Dy 0.1 mol%. La TL response in nC was of 88.07 and 36.56 respectively. The main peak temperature for 137

Detection Features of Borate-Based Thermoluminescent Dosimeters 343 the MgB4O7:Dy 0.1%mol was 252°C and for Mg2(B2O5):Dy,Na 0.1,0.5 mol% 222°C. Figure 4 shows the two glow curves of the materials synthesized by our group.

Figure 4. Glow curve the TL phosphors irradiated by γ-rays of an the 137Cs source with an estimated dose of 6.8 ± 0.4mGy.

Neutrons Dosimetry Neutrons are part of the nucleus of an atom, it is electrically neutral, that is, it does not interact directly with electrons, but it can interact with a certain probability, with nuclei that are in the center of the atom. Being free, the neutron is unstable, decomposing into a proton, an electron, and an antineutrino. The half-life of the neutron has been calculated to be approximately 15 minutes [49, 50]. The interaction of neutrons with matter is carried out through different reactions as seen in Figure 5. One of the most important parameters for neutron interaction is the cross-section, which indicates the probability of an interaction occurring between a neutron and a nucleus [51].

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Figure 5. Neutron interactions with matter.

Neutron applications are many. One of the oldest is neutron activation for analytical analysis, a powerful technique with high sensitivity, precision and multi elemental [50, 52]. Other applications are in medicine in Boron Neutron Capture Therapy (BNCT) to treat cancer, to obtain images, in national security it is used to detect nuclear materials, explosives and illicit drugs. In the treatment of radioactive waste, among others [50]. However, the production of unwanted neutrons can cause adverse consequences. Neutron induced biological damage is complex, because indirectly ionize, the effect of secondary particles after collisions and nuclear reactions produced by them on tissue is important, and this strongly depends on the energy of the neutrons, therefore, detection of them is important and decisive for the radioprotection [53]. One of the places of interest in the measurement of neutrons produced as secondary radiation is the radiotherapy rooms where high-energy linear accelerators are installed for the treatment of cancer. A LINAC (Linear Accelerator) when working above 10 MV produces undesirable neutrons, so it is necessary to have dosimetric materials with the appropriate characteristics for the detection of neutrons or photoneutrons [54]. For radiation detection it depends on the type of radiation and the energy, so measuring γ rays and neutrons is not easy. Until now, however,

Detection Features of Borate-Based Thermoluminescent Dosimeters 345 thermoluminescent dosimeters (TLDs) have regularly been the detector of choice for this. For neutron-gamma radiation, ICRU-recommended 6LiF and 7 LiF based TLDs have been used due to differences in nuclear reactions between these two isotopes [55]. The TL glow curve by 6LiF is essentially produced by charged particles arising from the 6Li(n, α)3H reaction with a thermal neutron cross section of 945 b. The 7LiF has a greater response to gamma rays, however, it is impossible to obtain a pure 7LiF dosimeter and the presence of 6Li will give a contribution of thermal neutrons to the response that can be significant and must be evaluated [55]. TL detectors have been used for neutron dosimetry for years. However, they have not been a great success so far. In this sense, materials containing 6 Li or 7Li and 10B simultaneously are more sensitive to neutrons, that is, LiF and Li2B4O7. When the material contains 10B it becomes sensitive to thermal neutrons due to the reaction 10B(n, α)7Li, it is important to mention that in the case of neutrons they are thermalized with hydrogenated materials such as polyethylene or other materials [14]. Among the materials studied for neutron detection are those that contain boron, such as boron carbides, boron nitrides, boron phosphides, Mg2B14, lithium borates and magnesium borates [56, 47]. Studies have revealed that the incorporation of rare earth ions increases the efficiency of TL in crystals. Thus, rare earth doping in compounds containing 10B (which has a high cross-section of thermal neutron capture) can offer highly efficient neutron detectors [56]. The 164Dy has a cross-section of high neutron capture (~ 2,650 b), in addition its natural abundance is high, approximately 28.2%, so it is attractive for neutron detection [57]. In works carried out by our group, magnesium borate TL materials (MgB4O7:Dy and Mg2(B2O5):Dy,Na) were synthesized in order to detect γ rays and neutrons, however, the results obtained for neutrons were not favorable, however, it has been working. They were irradiated with fast neutrons, so moderators are now being placed to thermalize them and see their behavior to thermal neutrons, which according to the literature and simulations using the Monte Carlo method will have greater sensitivity.

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It is important to mention that Mg2(B2O5):Dy,Na is a compound that has not been reported for dosimetric applications, however, the results obtained for γ rays were promising, and it is expected that for neutrons as well. The TL response obtained in nC for neutrons of the two synthesized materials was 2.64 for MgB4O7:Dy and 4.28 for Mg2(B2O5):Dy,Na.

Monte Carlo Simulation in Dosimetry The Monte Carlo (MC) method is a computational tool that allows to model complex systems, estimating solutions to mathematical problems using random numbers. Its genesis dates back to the 70’s, and is attributed to Comte Georges Louis Leclerc de Buffon. Snyder first introduced it to assess the fraction of photons and electrons emitted by radionuclides in source tissues, deposited in various target tissues at Oak Ridge National Laboratory. This is where medical internal dose radiation (MIRD) was defined [58]. The use of computational methods and the simulation of cases allows predicting different scenarios, that is, working with various radiation beams or different materials, which would be more complex or impossible experimentally. In addition, another advantage that it exhibits is that they provide faster results, however, the simulation could give erroneous results, due to the lack of knowledge of the working conditions, that is, the geometry of the problem, the physical-chemical characteristics of the materials, among others, it is concluded that an analysis with computational tools with the combination of an adequate experimental development will provide reliable results [59]. Particularly, in dosimetric applications in nuclear medicine by MC simulation, different tools are used to model real clinical situations and that accurately assesses the dose and can be compared with experimental data if required [58]. Regarding the use of the Monte Carlo method in TL materials, [60] estimated the responses of the TLD-100, OSL-Al2O3:C and RPL-GD201detectors. The required results were the absorbed dose, the energy, the

Detection Features of Borate-Based Thermoluminescent Dosimeters 347 angular dependence and the output factor for the γ rays from a 60Co source and the mean spectral energies of the 4, 10, 15, 18 and 25 MeV X-rays used in radiotherapy rooms.

Figure 6. Absorbed dose response per history to monoenergetic neutrons of MgB4O7:Dy and Mg2(B2O5):Dy,Na.

In [61] used the MC method to calculate and compare values obtained at different depths of measurement in water with respect to a reference depth to determine the absorbed dose. The calculation provides the correction factors at various depths. The results showed that at small dimensions, the effect of the thickness of the detector is more pronounced than the effective atomic number and the density of the TLDs studied (LiF:Mg,Ti, SiO2 and CaF2:Mn). The amount of disturbance was also evaluated and the conclusion they reached was that the effect of density is more evident than any other parameter of TL materials.

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In works made by our group calculated the absorbed dose response for γ rays, monoenergetic neutrons and isotopic neutron sources for two materials synthesized by us MgB4O7:Dy 0.1 mol% and Mg2(B2O5): Dy, Na 0.1,0.5 mol%. The results obtained in relation to the synthesized TL materials for neutrons are suitable for the detection and measurement of thermal neutrons (see Figure 6), with this, the necessary modifications can be made to irradiate the synthesized TLDs again and compare the simulated results with the experimental ones and obtain own TLDs to detect both γ rays from 0.511 to 18 MeV (according to the MC simulation) and thermal neutrons.

CONCLUSION In this chapter the subject of magnesium borate based TL materials for the detection of γ rays and neutrons was addressed, used as TLDs. The study of the different types of radiation and their interaction with matter is vital to decide what type of detector and what characteristics these materials must have in order for them to perform well. The field of dosimetry requires in-depth studies to contribute to radiation protection in any work area with ionizing radiation, because the effects of radiation on the human body can be adverse. Within the different applications of ionizing radiation (γ rays and neutrons, in this work), the measurement of the dose in radiotherapy rooms is relevant, due to the secondary or unwanted production of radiation as neutrons that do not detect, and much less control. The materials synthesized and studied by our working group are for this purpose. The development of materials for TLD, their characterization and their previous study using computational techniques or methods allow us to understand their behavior in the face of radiation and the scope they have for using them as a good TLD in the study radiation area.

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ABOUT THE EDITORS Kulwinder Singh Mann, PhD Assistant Professor, Department of Physics, D.A.V. Colleg Bathinda, Punjab, India Kulwinder Singh Mann, Ph.D. has been serving as Assistant Professor in Physics since Sept., 1998. He is a life member of Indian Society of Radiation Physics (ISRP) and Indian Association of Physics Teachers (IAPT). During his Ph.D. in Nuclear Radiation Physics, he has developed many computer program (toolkits) for investigation of gamma-ray shielding behaviours of building materials. He has published about 30 research papers in journals of high international repute and four books. The most recent book has been published with NOVA Science Publishers, USA consisting ISBN: 978-1-53616-993-5. He is an active reviewer of several journals. Currently he is working to develop an online platform for providing free research consultancy in calculation of various gamma-ray shielding parameters.

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About the Editors

V. P. Singh, PhD Department of Physics, Karnatak University Dharwad, India V.P. Singh, Ph.D. after completing his master’s degree in Physics from Lucknow University acquired doctor of philosophy in Nuclear and Radiological Engineering from Karnatak Universiy. He is having experience of Health Physics, Radiation Protection and dosimetry professions. He is the author of several scientific publications (journal articles: 100, book chapters: 4; book: 1; book edition: 2; abstracts: 37). He is reviewer/referee for high impact factor international journals in field of Physics, Nuclear Technology and Radiation Protection. He is member of various national & international societies. He is member of editorial boards of various Journals and member of national/international nuclear and radiation protection societies.

INDEX γ γ rays detection, 332 γ-rays, 35, 117, 152, 156, 170, 171, 246, 343, 354

A absorbed dose, 66, 69, 70, 71, 81, 88, 90, 93, 94, 115, 185, 186, 212, 225, 227, 232, 233, 236, 238, 254, 255, 256, 259, 265, 266, 267, 269, 270, 271, 332, 333, 336, 337, 340, 341, 346, 347, 348 ambient dose, 66, 70, 71, 72, 73, 77, 81, 87, 108 annihilation gamma rays, 120, 122, 136, 137, 140 attenuation, 2, 3, 4, 5, 6, 16, 34, 35, 36, 37, 39, 48, 49, 50, 51, 52, 53, 54, 55, 62, 67, 68, 69, 73, 74, 75, 76, 77, 83, 85, 87, 90, 91, 92, 94, 95, 96, 97, 101, 104, 109, 110, 114, 116, 117, 119, 120, 121, 122, 124, 129, 130, 133, 135, 137, 139, 148, 218, 223, 224, 278, 279, 280, 281, 282, 285, 290, 291, 293, 294, 295, 296, 300,

301, 302, 303, 304, 308, 309, 310, 311, 313, 315, 316, 318, 325, 326, 328, 329

B biological shields, 117 buildup factor, xi, 2, 36, 37, 38, 70, 87, 89, 93, 94, 96, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 121, 122, 123, 124, 126, 127, 128, 129, 130, 132, 133, 135, 136, 137, 138, 139, 140, 278, 279, 282, 285, 287, 291, 292, 316, 327, 328, 329

C composite shield, 114, 128 compton scattering, 2, 19, 29, 30, 32, 42, 59, 70, 75, 78, 79, 92, 106, 119, 120, 122, 135, 137, 139, 157, 158, 163, 217, 218, 282, 322 computational phantoms, 184, 186, 192, 193, 195, 197, 201 computations, 7, 40, 48, 58, 61, 67, 115

360

Index

cross-section, 1, 2, 3, 4, 7, 9, 16, 34, 44, 50, 59, 78, 79, 89, 91, 92, 107, 120, 160, 161, 162, 163, 165, 172, 221, 283, 314, 315, 317, 318, 323, 326, 334, 335, 340, 343, 345 CT scan, 116, 207, 212, 221, 233, 234

D dental, 219, 226, 244, 247, 249, 250, 253, 254, 265, 266, 268, 269, 270, 271, 272, 275 detection of gamma rays, 168 directly ionizing radiations, 117 discovery of γ rays, 155 dosimetry, viii, xi, 37, 40, 41, 42, 59, 61, 66, 68, 71, 74, 78, 79, 84, 86, 87, 88, 92, 111, 116, 117, 140, 148, 151, 152, 168, 171, 178, 180, 183, 184, 185, 186, 190, 191, 192, 193, 195, 196, 197, 199, 200, 201, 205, 206, 207, 208, 209, 211, 212, 227, 228, 231, 232, 240, 241, 243, 244, 254, 258, 260, 265, 268, 269, 270, 273, 274, 275, 295, 327, 332, 333, 334, 335, 336, 337, 338, 339, 340, 343, 345, 346, 348, 349, 350, 351, 352, 353, 355, 358

energy absorption buildup factors (EABF), 106, 110, 278, 279, 283, 287, 289, 292, 316, 328, 329 energy cut-offs, 43, 45 equivalent atomic number (Zeq), 32, 101, 105, 278, 279, 283, 285, 286, 287, 289, 314, 315, 320, 323, 326 exposure buildup factors (EBF), 22, 37, 38, 110, 125, 138, 146, 147, 148, 278, 279, 283, 287, 288, 289, 292, 313, 315, 316, 320, 321, 322, 323, 326, 327, 328, 329 E-Z graph, 5, 10, 16, 17

F five-layer shield, 139 flair, 46, 48 FLUKA, vii, viii, xi, 2, 12, 13, 37, 39, 40, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 82, 186, 196, 207, 209, 277, 278, 279, 280, 283, 285, 289, 291, 294, 295, 300, 301, 302, 305, 307, 308, 311, 312 FLUKA Monte Carlo codes, 279 FLUKA output, 40, 47 FLUKA simulations, 40, 47, 280 four-layered shields, 138

E G effective atomic number, 2, 3, 6, 12, 35, 36, 39, 48, 59, 60, 61, 94, 114, 116, 128, 129, 328, 338, 347 effective dose, 66, 71, 72, 73, 81, 82, 184, 185, 186, 189, 196, 212, 225, 226, 227, 232, 236, 237, 238, 241, 256, 257, 269, 270, 271 effective electron density, 2, 26 EGS5 code, 65, 66, 67, 69, 70, 71, 83 electron, 2, 26

gamma, vii, viii, ix, xi, 1, 2, 3, 4, 5, 6, 9, 10, 13, 16, 18, 19, 27, 34, 35, 36, 37, 38, 40, 41, 49, 50, 55, 59, 60, 62, 63, 65, 81, 83, 85, 88, 96, 99, 104, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 130, 134, 136, 137, 140, 145, 146, 147, 148, 155, 156, 159, 160, 161, 168, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 184, 187, 188, 194, 198, 199, 202, 204, 213, 257, 260, 264, 277, 278, 280, 281, 282, 283, 285, 286,

Index 289, 290, 291, 293, 294, 295, 296, 299, 302, 308, 309, 310, 311, 313, 314, 318, 320, 325, 326, 327, 328, 329, 332, 338, 341, 345, 349, 350, 351, 352, 357 gamma attenuation, 119, 280, 294 gamma photons, 19, 40, 50, 55, 118, 119, 122, 283 gamma radiation, 62, 63, 114, 116, 122, 156, 160, 168, 170, 260, 264, 277, 278, 282, 289, 328, 332, 341, 345, 349 gamma shielding, 278, 294 gamma-ray, xi, 1, 2, 3, 4, 5, 6, 9, 13, 27, 35, 36, 37, 38, 40, 41, 62, 63, 104, 110, 111, 145, 146, 148, 170, 174, 176, 178, 181, 187, 281, 283, 285, 289, 290, 291, 293, 295, 296, 299, 302, 308, 309, 310, 311, 314, 318, 320, 325, 326, 329, 357 gamma-ray shielding, xi, 1, 2, 6, 27, 35, 62, 63, 104, 111, 283, 289, 290, 293, 295, 296, 308, 309, 310, 357 gamma-ray shielding parameters, xi, 2, 35, 63, 290, 293, 295, 308, 310, 357 Geant4, xi, 39, 48, 52, 53, 54, 61, 63, 66, 82, 178, 186, 196, 294, 295, 298, 299, 300, 301, 302, 304, 306, 307, 308, 310, 311, 312, 327 glass system, 39, 48, 50, 51, 52, 53, 61, 327, 329 glasses, 21, 38, 42, 49, 52, 62, 63, 313, 315, 316, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 338

H half value layer (HVL), 39, 48, 55, 57, 58, 278, 279, 282, 284, 286, 289, 293, 295, 296, 302, 305, 306, 307, 308, 313, 315, 316, 318, 319, 326

361 I ignimbrite, viii, 277, 278, 279, 280, 281, 283, 284, 285, 286, 287, 288, 289 indirectly ionizing radiations, 117 interaction of neutrons with matter, 165, 343 international commission on radiological protection, 33, 71, 84, 185, 256, 273 ionising radiation radiation(s), 41, 88, 183, 184, 187

L linear attenuation coefficients, 74, 120, 121, 122

M magnesium borates, 332, 339, 345 marble(s), viii, 6, 35, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310 mass, 2, 3, 5, 6, 34, 35, 39, 48, 50, 51, 53, 54, 55, 75, 83, 85, 90, 91, 92, 96, 101, 120, 121, 277, 279, 281, 282, 285, 291, 293, 295, 296, 301, 302, 303, 304, 308, 310, 311, 313, 314, 315, 316, 317, 318, 325, 329 mass attenuation coefficient(s), 2, 3, 5, 6, 34, 35, 39, 48, 50, 51, 53, 54, 55, 75, 83, 85, 90, 91, 92, 96, 101, 120, 121, 277, 279, 281, 282, 285, 291, 293, 295, 296, 301, 302, 303, 304, 308, 310, 311, 313, 315, 316, 318, 325 mass stopping power, 314, 315, 317, 325, 329 mean free path (MFP), 35, 39, 48, 52, 54, 92, 93, 120, 121, 128, 278, 279, 282,

362

Index

293, 295, 296, 307, 308, 314, 315, 316, 320, 325 medicine, viii, 38, 66, 83, 88, 153, 170, 183, 184, 185, 186, 187, 192, 193, 197, 198, 200, 201, 204, 206, 207, 208, 209, 219, 227, 239, 244, 272, 274, 295, 332, 344, 346, 349, 350 metallic alloys, 178, 314, 315, 319 Monte Carlo, 2, 38, 39, 40, 42, 48, 52, 61, 63, 65, 66, 67, 70, 71, 72, 74, 76, 77, 79, 80, 81, 82, 83, 84, 86, 99, 103, 104, 107, 108, 109, 110, 111, 146, 147, 152, 171, 172, 177, 180, 184, 186, 194, 200, 201, 207, 208, 209, 279, 291, 294, 295, 298, 308, 310, 311, 326, 327, 335, 345, 346, 355 Monte Carlo code, 39, 41, 42, 48, 52, 61, 65, 67, 71, 86, 110, 146, 147, 171, 200, 201, 209, 279, 291, 294, 311 Monte Carlo method, 40, 65, 66, 67, 72, 74, 76, 77, 79, 80, 81, 82, 99, 103, 104, 109, 147, 152, 177, 291, 308, 310, 326, 345, 346 Monte Carlo simulation, 2, 38, 63, 70, 76, 82, 83, 107, 110, 200, 294, 295, 310, 311, 346, 355 multi-layer shields, 113, 114, 115, 128, 133, 138, 140 multi-layered shielding, 114, 126

N neutron activation analysis, 164, 170, 179, 180, 181, 354 neutron(s), 35, 66, 68, 77, 87, 90, 107, 108, 111, 145, 162, 164, 165, 166, 167, 170, 172, 173, 174, 176, 179, 180, 181, 278, 291, 314, 315, 317, 323, 326, 327, 328, 329, 332, 334, 340, 341, 342, 343, 344, 345, 348, 350, 351, 354, 355 neutrons detection, 332

nuclear radiation protection shelter, 3

O orthopantomograph, 244, 253, 268, 270

P pair-production, 120, 122, 124, 135, 136, 137, 139 PGNAA, 152, 170, 171, 179, 180 photoelectric effect, 29, 42, 92, 106, 118, 120, 122, 124, 158, 159, 163, 216, 217, 218, 246 photon atomic cross-sections, 120 photon buildup factor, 2, 87, 100, 101 photon dosimetry, 66, 68, 74, 78 photon interactions, 2, 10, 16, 17, 19, 42, 65, 66, 68, 70 photons, 4, 6, 19, 22, 23, 26, 30, 32, 33, 34, 35, 37, 40, 41, 42, 43, 45, 48, 50, 52, 55, 58, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 93, 97, 99, 106, 107, 109, 118, 119, 121, 122, 124, 128, 156, 158, 160, 161, 162, 163, 168, 172, 214, 216, 218, 221, 222, 246, 248, 255, 260, 280, 281, 283, 295, 298, 300, 318, 322, 339, 346, 355 polyester concretes, 40, 48, 49, 55, 56, 57, 58, 61, 63 polymeric materials, 7, 18, 20, 22, 25, 26, 28, 38, 39, 48, 63 polymers, 49, 58, 59, 60, 61, 311, 314 program BUF, 114, 116, 129, 130, 133, 136, 138, 139, 140 program code BUF, 116, 129, 138

Index R radiation dosimetry, 87, 117, 140, 152, 171, 183, 186, 258, 274, 338, 352 radiation interaction predictor for materials, 3, 9 radiation shielding, 2, 38, 40, 41, 59, 61, 62, 63, 65, 66, 67, 78, 79, 109, 111, 113, 115, 121, 152, 180, 185, 278, 279, 280, 290, 291, 292, 294, 309, 313, 314, 315, 325, 326, 327, 328, 329 radiation source, 44, 116, 164, 185, 190, 224, 239, 280, 316, 332

363 T Taylor approximation, 99, 114 thermoluminescent dosimeter(s)TLD, 190, 212, 231, 232, 236, 238, 241, 261, 262, 264, 265, 266, 267, 268, 269, 270, 275, 332, 333, 334, 337, 338, 339, 340, 341, 346, 348, 349, 350, 351, 353, 354, 355 three-layered shield, 115, 136, 138 TLD-100, 212, 231, 232, 238, 241, 261, 333, 339, 340, 346, 350, 355 two-layer shield, 115, 133, 137

X S scoring commands, 39, 47 shielding design, 2, 55, 66, 74, 81, 114, 152, 180, 295 shielding effectiveness, 2, 290, 292, 309 shielding parameter(s), viii, xi, 2, 3, 35, 39, 48, 55, 63, 199, 289, 290, 293, 294, 295, 296, 308, 310, 313, 315, 357 simulation method, 40, 48, 66, 277 single-layered shield, 113, 115, 130, 132 SVM algorithm, 8, 9

XCOM, xi, 7, 36, 39, 48, 58, 59, 60, 61, 64, 74, 75, 76, 84, 85, 204, 278, 279, 285, 294, 295, 301, 302, 307, 308, 311 x-ray discovery, 152 x-rays, 41, 88, 93, 99, 117, 118, 122, 124, 152, 153, 154, 155, 156, 177, 178, 184, 187, 188, 212, 213, 214, 216, 219, 220, 233, 244, 245, 246, 247, 248, 249, 257, 269, 270, 271, 273, 332, 333, 334, 340, 347