Gamma Radiation of an Atomic Explosion

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TRANSLATION SERIES

AEC-tr-4516 PHYSICS

GAMMA-RADIATION OF AN ATOMIC EXPLOSION By O. I. Leipunskii

Translated from a publication of the State Committee of the Council of Ministers of the U.S.S.R. on the Utilization of Atomic Energy, Moscow, 1959.

UNITED STATES ATOMIC ENERGY COMMISSION Division of Technical Information

A translation of: Gamma-Izluchenie Atomnogo Vzryva. O. I. Letpunskif. Izdatel’stvo Glavnogo Upravleniya po Ispol-zovaniyu Atomnol Energii pri Sovete Ministrov S.S.S.R., Moskva, 1959. Translated by the U. S. Joint Publications Research Service, New York, a federal government organization established to service the translation and research needs of the various government department^. In the interest of expeditious dissemination this publication has been re­ produced directly from copy prepared by the translating agency. Printed in USA. Price $2.75. Available from the Office of Technical Services, Department of Commerce, Washington 25, D. C. Issuance date: September 1961.

USAEC Division of Technicol Information Extension,-Oak Ridge, Tennessee

0. I . Leipunskii

GAMMA-RADIATION OF AN ATOMIC EXPLOSION

PUBLICATION OF THE MAIN ADMINISTRATION ON THE USE OF ATOMIC ENERGY OF THE COUNCIL OF MINISTER USSR Moscow 1959

TABLE OP CONTENTS Page NOTATION............................................................................................................ iv FOREWORD............................................................................................................ V il INTRODUCTION...................................................................................................... V l i l CHAPTER I . 1. 2. 3. 4.

Sources o f Gamma R a d ia tio n and th e Time o f T h eir E m ission................................................................................................... Gamma R a d ia tio n Due to F is s io n Fragm ents of U235 and Pu2 39....................... Gamma R a d ia tio n in th e C apture o f N eutrons by N itro g en . Gamma R a d ia tio n From A c tiv a te d E a rth .......................................

CHAPTER I I . 5. 6.

MAIN SOURCES OF GAMMA RADIATION IN ATOMIC EXPLOSIONS...............................................................

PROPAGATION OF GAMMA RADIATION IN ABSORBING MEDIA.......................................................................................

1 1 3 12 12 22

"Good" and "Poor" Geometry...................................... E lem entary P ro c esse s o f I n t e r a c t io n o f Gamma Quanta w ith M a tte r.................................. P ro p a g atio n o f Gamma R a d ia tio n From a P o in t Source In a Homogeneous I n f i n i t e Medium.............................. Power o f Gamma-Radiation Dose in A ir Over an E arth S urface Covered w ith Gamma-Radiation S o u rc es................... Dose Power o f Gamma R a d ia tio n Above a Plane Layer o f A bsorber, C ontaining Sources o f Gamma R a d ia tio n ......... A tte n u a tio n of a P a r a l l e l Beam o f O' Rays in a Plane L ayer o f A bsorber................................ Albedo o f *b d o ^ _ ,o p 5 o cd d o •" -H •o ^ © u -p >d © «h o,

o

U a3 O C0 © o -P

aJS- po- paJcCO 6 o o aMHri«d

o to^> -H3 ai &

«H

© £ P © Jh H

,£j £

Vi *d © O 05 o f t o5 cdVi

©o o© G ©,ci * k

o©*pg©©fl-P *H O

05 rH > O —

•P f t Vl f t O *H a) ^ O A 0

cm2/ g o f e a r th ... Energy o f em itted gamma quanta, Mev............. ....................... ...............................

46,5 18

16

A1

27,7

7,85 27

Does not 100 y ie ld T-rays — 2,3 min 27 sec 2,57-10-2 5,02 • 10—3 — 0,2

2,1- 10—4

—

0,215

4,2- 10-7

—

2,15 ■ 10-i

7,35-10~9

—

3,77 • 10“4

2.10-3

_

2,15 • 10~i

3,7. 10-5

—

3,77 • 10“4

1,7(70%)

—

1,8 (100%)

0,85

—

1,8

1,25-10 ~c

—

1,36 • 10~i

1,35.10-s

—

8,6 • 10~3

6,25*10-9

—

6,8 • 10-*

— — — — _

3,4 . 10“* 5,3 - Urn — — — —

Energy o f gamma r a d ia tio n per decay o f the Iso to p e , Mev/decay................ Energy o f gamma r a d ia tio n per neutron capture in the earth , Mev/cap. n e u tr o n ............................. .. Energy o f gamma r a d ia tio n em itted from gram o f the element by an ac­ t i v e neutron flu x of 1 neutron cm2, Mev/g element neutron/cm2...................... Energy of gamma r a d ia tio n em itted from 1 gram o f earth , a c tiv a te d by a neutron flu x of 1 neutron/cm2, Mev/g o f earth neutron/cm2 (G ij......... Gamma a c t i v i t y on in d iv id u a l e l e ­ ments per gram o f earth (Gj.) at d iffe r e n t in s ta n ts o f t i m e . . . . . ......... t = 0 hours t s 1 hour t = 4 hours t = 20 hours t = 200 hours t = 2000 hours

Si

I J

— — — — —

Table 7 C rust and Gamma R a d ia tio n from A c tiv a te d E a rth . Ca

Fe

4 ,8 5

3 ,7 5 \6

58 0 ,3 4

0 .0 0 3 2

4 7,1 d a y s

Na

2 ,8

2 ,6 2

23

15 h r s

1 ,87 • 10~« 1 ,2 8 • 1 0 -6

0 ,7

0 ,2 5

2 ,4 • 10-3

8 • 10 ®

2 ,4 3

26

6 ,9

1 ,7 • 10 i

1 ,26 • 1 0 '« 4 ,5 • 10-9

2 ,2 5

41

100

4 ,3 d a y s

Mg

K

•0,51

5 ,1 • 10~i

12,5 h r s 9,4 m i n 1 ,5 5 • 10-5 1 ,2 3 1 0 -3 0 ,0 5

1,97 -*• 1 O

O OO

1 ,2 7 • 10-3 2 ,4 2 • 10-* 3 ,7 4 • 1 0 -6

5 ,^ 4 6 m in 1,92 - 10-3 0 ,1 4

6 ,9 • 10-» 5 ,6 5 -1 0 -3 7 ,5 • 10~3 3 ,1 5 1 0 - 6

7 ,1 • 10 3

5 ,9 - 1 0 - s

5 ,6

3 ,3 - 1 0 - 5

5 ,3 • 1 0 -6

3 ,7 4 • 10-< 2 ,8 • 1 0 -5

0 ,4 3 • 10“ ' 5 ,1 • lO -i

0 ,7 5 50

11.3

1 ,0

Ti

1

0,84 (100%) 0 ,3 2 (70% ) 1.05(20% )

1 ,4 (100% ) 2 ,8 (100% )

1 ,5 (25% )

1 ,2

1,1

4 ,2

0 ,3 7

1 • 1 0 -6

3 ,1 5 • lO - i

2 ,0 5 • 1 0 -3 6 ,6 - 1 0 - 6

3 ,1 • 10-*

1 ,3 • 10-6

5 ,6 • 10 3

4 • 10“ 6

1 ,5 • 1 0-«

5 • 10“ »

1,57 • 10-3 - 1 ,0 5 • 10-6 3 ,3 - 1 0 - 6

2 ,5 5 2 ,5 5 2 ,5 5 2 ,5 3 2 ,5 3 7 ,5

O 1

1 ,4 (81% )

CO

0 ,2 (2 ,8 % ) 1,1 (56% ) 1 28 (4 3 % )

• • • • • •

1 0-i3 9 ,3 5 • lO -i* 2 ,0 — 10->3 1 ,9 — 1 0-i3 1 ,65 — 10-»3 8 • — 10~i3 2 • 10~i* —

• 1 0 -« • 10-8 • 1 0 -8 1 0-9 1 0 -ia —

17

1,0 5

1 ,4 5 -1 0 -6

1 ,6 • IO-10 4 ,0 - 1 0 - 9

0 ,2 2

3 ,1 5 - 10-5

2 ,0 5 • 10-6

1 ,5 6 • lO - i

4 • 10-8

—

____

____

—

___

—

____

____

____

___

—

—

—

—

—

C h a ra cteristic o f Element Abundance in the e a r th 's c r u st, p ercen t. ..................................... Mass number........................... .. Content and natu ral Isotope m ixture, p ercen t........................................................ H alf l i f e Ti / 2 .............................................. Decay constan t A, sec -*■........... .. A ctiv a tio n cross s e c tio n o f the is o ­ tope by thermal neutrons, aa c , b a r n .. A ctiv a tio n cross s e c tio n , c a lcu la ted fo r th e natu ral Isotope mixture OaC, barn........................................................... A ctiv a tio n cross se c tio n per gram o f ea rth . Sac* cm2/ g o f e a rth ........... .. Cross s e c tio n fo r the capture of therm al-neutrons by the n atu ral mix­ ture o f Iso to p e s, 0Cap* barn*................ Cross s e c tio n fo r the capture per gram o f ea rth , Soap* cm2/ g o f e a rth .............. Energy o f em itted gamma quanta, Mev...................................................................... Energy o f gamma ra d ia tio n per decay of the iso to p e , M ev /d e ca y .... . . . . . . . . . . . Energy o f gamma ra d ia tio n per neutron capture in the earth , Mev/cap. n eu tro n ...................................... .. Energy o f gamma r a d ia tio n em itted from gram o f the element by an A ctiv e neutron flu x o f 1 neutron/cm2, Mev/g element neutron/cm2........................ Energy o f gamma ra d ia tio n em itted from 1 gram or ea rth , a c tiv a te d by a neutron flu x o f 1 neutron/cm 2, Mev/g o f earth neutron/cm 2 (G i)........... Gamma a c t iv it y on in d iv id u a l elem ents per gram o f earth (Gj.) a t d iffe r e n t in sta n ts o f tim e...................... t = 0 hours t = 1 hour t = 4 hours t = 20 hours t = 200 hours t - 2000 hours

18

H 0,11

Mn

0,073 36

0,11

Does not Does not y ie ld y ie ld 7 -rays 7 -rays 2.67hr s 7,47. 10~* 12.7 12.7 1.05- 10-« 12.7

l ,9 • 10“i 3,3

io-i

4,1 • 10-* 2,2

10~i 1.05- 10-i 0,85 (69 %) 1,8 (18,5%) 2,13(12,5%) 1,2

2,55,10—5 1,7-10-1 1,27-10-1

9,5- 10“» 7.2- 10“» 3.2- 10~»

Table 7 (co n tin u ed )

0,075 19

0.037 37

100

s

Sum

0,037 37

—

0,017

-

— — -

Cl

F

24,6

10.7 sec 6,5 • 10~*

37.3 min 3,1 • !0-«

5,04 min 2,3 • 10“»

— -

0,000

0,56

0,14

-

t • 10~3

1,4

10~»

2,4

2,14 • !0-i

8,8

10 7

1,7 • 10—10 8,9 • 10“
R n

B,

R*

J

(7 .5 )

=■Jo Bj.

where Bj i s th e i n t e n s i t y b u ild -u p f a c t o r , equal to the r a t i o o f th e i n t e n s i t y of r a d i a ti o n to t h a t p a rt o f the r a d i a ti o n due only to the d i r e c t r a d i a ti o n J s * J0

Bj

J a — i n t e n s i t y o f s c a tte r e d r a d i a ti o n .

(7 .6 ) I t i s obvious t h a t

,u R

K j= B je

(7 .7 )

The e x p re ss io n s ( 7 .3 ) , ( 7 .4 ) , (7*5), ( 7 .6 ) , and (7 .7 ) a re w r itte n f o r th e i n t e n s i t y o f th e gamma r a d i a ti o n , but they can be g e n e ra liz e d f o r a l l e f f e c t s connected w ith th e a c tio n o f th e q u an ta. Then, in accordance w ith ( 7 .6 ) , th e c o e f f ic ie n t B can in g e n e ra l be ta k e n to mean th e r a t i o o f th e r e s u l t o f a d e f i n i t e a c tio n o f th e t o t a l flu x o f gamma-ray quanta to th e r e s u l t o f th e a c tio n o f th e flu x o f quanta due only to th e d i r e c t r a d i a ti o n . The s u b s c rip t o f th e c o e f f i c i e n t B w ill in d ic a te in t h i s case th e p a r t i c u l a r r a d i a t i o n a c tio n r e f e r r e d to . For example, Bn i s the r a t i o o f th e t o t a l number of quanta to th e number of quanta in th e d i r e c t beam; Bj — r a t i o o f th e t o t a l i n te n s i t y to th e i n t e n s i t y o f th e d i r e c t beam; Br ~ r a t i o o f the t o t a l dose power to th e power produoed by th e d i r e c t beam. One can in tro d u c e a ls o c o e f f i c i e n t s B f o r th e r a t i o o f th e re a d in g s of c e r t a i n in s tru m e n ts , e t c . S im ila r symbols a re used a ls o f o r th e a tte n u a tio n c o e f f i ­ c ie n t K. According to (6 . 11), th e dose power of i n t e r e s t to u s , P, i . e . , th e power o f th e absorbed energy, i s connected, in the case o f a m onoenergetic r a d i a ti o n , w ith th e i n t e n s i t y J ( in Mev/cm^) by th e fo llo w in g r e l a t i o n P = \^s J (1.4 8 x 10“ 5 i s M e v /c m ^ t o

th e

th e c o n v e r s io n d ose, r ) .

1,48

10“ *, r /s e c

fa c to r

fr o m

ab sorb ed

(7 . 8 ) energy

in

In th e case non-m onoenergetlc r a d i a ti o n , th e e x p re ss io n (7 . 8 ) must be re p la c e d by P = 1,48 • 10-* (V , (e)/(e) rfe, r / s e c .

(7 .9 )

i/

A fte r p a ssin g through the m a tte r, th e gamma r a d i a ti o n becomes

39

n on-m onoenergetic, even i f th e source i t s e l f , w ith a quantum energy £ q , i s m o noenergetic. In t h i s case th e f a c t o r (J.Q (£q) I s tak en o u ts id e th e i n t e g r a l sig n P ~ 1,48 • 10--* pt, (z\ ( J

Ve (*)o

dz.

(7 . 1 0 )

In accordance w ith (7 .1 0 ), ( 7 .A), (7*5) and w ith c o n sid e ra ­ t i o n o f th e g e n e ra l meaning o f th e c o e f f i c i e n t s B and K, we can w rite down th e fo llo w in g e x p re ss io n s fo r th e dose power from a m onoenergetic source w ith quantum energy £ q : P = 1,48 • 10- 5 G 471

Kr, r / s e o ;

P = P0 B, = 1,48 • 10- 5 — ’e -- --- e ~ n r ’ 4- a* Kr = B r e-''l ^ )R

(7.11) R, r / s e c ;

(7.12) (7.13)

As a lre a d y in d ic a te d , in a wide range o f quantum energy £ - jA(£)e i s p r a c t i c a l l y independent o f £ , th e r e f o re J ^ P , Kr » K j and The d e te rm in a tio n o f th e c o e f f i c i e n t s Kr (R, £ 0 ) o r Br (e o) i s a problem in th e th eo ry of m u ltip le s c a t t e r i n g o f quanta o r o f model ex p erim e n ts. T h e o re tic a l d e te rm in a tio n o f Br . F ig u re 13 and Table A22 o f Appendix I I g iv e th e c a lc u la te d v a lu e s o f Br [1 0 ]. In th e s e d a ta th e d is ta n c e from th e source R i s ex p ressed in u n i ts o f mean f r e e p a th o f th e prim ary r a d i a ti o n in th e medium Aq = 1/(a (^ o )# With th e space c o o rd in a te expressed in t h i s manner, th e m agnitude o f th e c o e f f i c i e n t o f a tte n u a tio n of th e r a d i a ti o n p e r u n i t le n g th o f a b sro b e r i s independent o f i t s i n t e n s i t y , and a l l th e laws o f a b s o rp tio n o f r a d i a ti o n in media w ith equal v a lu e s o f Z, but w ith d i f f e r e n t d e n s i t i e s , assume th e same form . T his r u l e i s r e ta in e d a ls o f o r su b sta n c es w ith d i f f e r e n t Z in th e c ase when only th e s c a t t e r i n g by th e fr e e e le c tr o n s i s o f im portance in th e i n t e r ­ a c tio n between th e quanta and th e su b stan ce (T able 1 2 ).

40

£, Mev

F ig u re 13. Dose b u ild -u p f a c t o r Br (Eg, pR) f o r gamma r a d i a ti o n from a p o in t source in w a ter a t d i f f e r e n t v a lu e s o f quantun energy e 0 [1 0 ]. According to t h i s r u l e , th e c o e f f i c i e n t s B f o r two ab so rb in g media a re e q u a l, i f th e th ic k n e s s of th e a b so rb e r i s ex p ressed in u n i ts A.q = I/(jl (Eq) . The r a t i o o f th e q u a n ti t ie s Xq fo r w ater and a i r a t 0°C and a p r e s s u r e 760 mm i s 860. When m easuring d is ta n c e s in o rd in a ry u n i ts of le n g th , th e c o e f f i c i e n t s B f o r w ater and f o r a i r a re equal a t d is ta n c e s from th e source d i f f e r i n g by a f a c to r o f 860. This r u l e se rv e s a s th e b a s is f o r th e p o s s i b i l i t y of s im u la tin g th e con­ d i ti o n s of p ro p a g a tio n gamma ra y s in a i r w ith th e a id o f s m a ll-s iz e w a ter m odels. The accu racy o f th e c a lc u la tio n o f Br and Bj i s e stim a te d by th e a u th o rs a t t 5 p e rc e n t f o r th e case o f ir o n and le a d a t s h o rt d is ta n c e s from th e source and a t 1 15 p e rc e n t f o r long d is ta n c e s . In th e case o f l i g h t elem ents such as w ater and aluminum, th e e s tim a te s a re ± 10 p e rc e n t f o r s h o rt d is ta n c e s and ± 2 5 - 3 0 p e rc e n t f o r long d is ta n c e s .

41

F ig u re 13 shows th e v a lu e s o f Br in w ater f o r d i f f e r e n t d is ta n c e s from th e source (th e v a lu e s of S a re marked on th e end o f each c u rv e ). From T able A22 o f Appendix I I and from F ig u re 13 i t i s seen t h a t as th e d is ta n c e from th e source i s in c re a s e d , th e c o e f f i c i e n t s Br a re c o n tin u o u sly in c re a s e d and th a t c o n seq u en tly th e r o l e o f r a d i a ti o n in th e p ro d u c tio n o f th e gamma-ray dose a ls o in ­ c re a s e s c o n tin u o u sly . For prim ary r a d i a ti o n € q = 0 .5 Mev, a t a d is ta n c e from th e so u rce o f 10 R/K q in w a te r, th e dose produced by th e s c a tte r e d r a d i a ti o n i s 80 tim es g r e a t e r th a n th e dose produced by the d i r e c t r a d i a t i o n . By I n te r p o la tin g th e d a ta o f Table A22 o f Appendix I I we can o b ta in v a lu e s o f Bj» f o r elem ents w ith d i f f e r e n t v a lu e s o f Z and f o r d i f f e r e n t quantum energy £ q . Thus, v alu es o f Br have been o b tain ed f o r Cq = 1 .6 and 2 .2 Mev, which a re c h a r a c t e r i s t i c o f gamma-ray so u rc es produced in th e re g io n o f an atom ic e x p lo sio n . The v a lu e s o f Br can be c a lc u la te d a ls o from i n te r p o la t io n fo rm u las. The v a lu e s o f Br g iv en in F ig u re 13 and in Table A22 o f Appendix I I make i t p o s s ib le to c a lc u la te th e doses o f gamma ra y s up to |*oR - 15 o r 20. At g r e a t e r d is ta n c e s from th e source i t i s d i f f i c u l t to so lv e th e k in e tic e q u a tio n f o r th e d i s t r i b u t i o n of gamma ra y s w ith a s u f f i c i e n t degree o f accuracy even w ith th e a id o f e le c tr o n ic com puters. At la r g e v a lu es o f f*oR» an asym ptotic form has been d e riv e d f o r th e a tte n u a tio n o f th e i n t e n s i t y and th e power of th e gamma-ray dose [9 ] . E xperim ental d e te rm in a tio n o f Kr» F ig u re 14 shows a com pari­ son .of th e r e s u l t s o f an e x p erim en tal d e te rm in a tio n o f th e c o e f f i c i e n t s o f a tte n u a tio n in sim u la tio n experim ents in w ater (acco rd in g to th e d a ta o f re fe re n c e s [ 11, 2 1, 2 2]) w ith th e th e o ­ r e t i c a l v a lu e s o b tain ed by form ula (7 .1 3 )• The law s o f a tte n u a tio n o f gamma-ray doses th ic k la y e r s a re n o t sim ple e x p o n e n tia l law s. The observed e f f e c t i v e l i n e a r c o e f f i ­ c ie n ts of a b s o rp tio n o f the dose power o f gamma r a y s , |xef f (th e change in th e lo g a rith m o f c o e f f i c i e n t o f a tte n u a tio n o r th e dose power p e r u n it le n g th o f a b so rb e r) i s not c o n s ta n t, b u t depends on th e d is ta n c e to th e so u rc e . At sm all d is ta n c e s , M"eff is c lo s e in m agnitude to Hoe ” ” th e c o e f f i c i e n t t h a t determ in es the a b s o rp tio n o f th e energy from the d i r e c t r a d i a ti o n . This i s n a tu r a l, f o r a t sm all d is ta n c e s from th e source th e double o r m u ltip le s c a tte r in g has low p r o b a b i l it y , and th e energy lo s s in s in g le s c a tte r in g o f r a d i a ti o n i s determ ined by th e c o e f f i c i e n t f^oe* For s o f t r a d i a ti o n , th e c o e f f i c i e n t |xef f a t sm all d is ta n c e s from th e so u rce may be even l e s s than J*oe» w^ en tk® flu * o f th e b a c k w a rd -sc a tte re d r a d i a ti o n from deep la y e r s o f th e a b so rb e r i s added to th e d i r e c t and s in g ly - s c a tte r e d r a d i a ti o n tr a v e lin g from th e so u rc e .

42

t

In-L

lr> lD K

F ig u re 14. C o e ffic ie n t Kr (€0 * >\)R) o f a tte n u a tio n o f th e dose of gamma r a d ia tio n from a p o in t source in w ater a t d i f f e r e n t quantum e n e rg ie s . For exam ple, w ith = 0.41 Mev and l e s s , a t a d is ta n c e HqR = 1 from th e so u rc e , th e gamma-ray dose n o t only i s not a tte n u a te d by th e a b so rb e r b u t, to th e c o n tra ry , i s i n t e n s i f i e d . As th e d is ta n c e from th e source i s in c re a s e d , Kef f in c re a s e s and approaches p.0 , i . e . , th e l i n e a r c o e f f i c i e n t o f a b s o rp tio n o f th e prim ary r a d i a t i o n . I t can be seen t h a t , over a wide range of source quantum e n e rg ie s , th e e x p erim en tal and t h e o r e t i c a l methods o f in v e s tig a tio n g iv e I d e n tic a l r e s u l t s w ith in the l i m i t s of e rr o r s o f c a lc u la tio n and m easurement. Since th e accuracy o f the t h e o r e t i c a l c a lc u la tio n s of th e v alu e of K f o r Eg = 0.41 Mev i s l e s s th an the accuracy of th e ex p erim en t, we s h a l l use th e ex p erim en tal d a ta in f u r th e r c a lc u la ­ tio n s f o r t h i s energy. From F ig u re 14 i t is seen t h a t w ith in a d e f i n i t e i n te r v a l of d is ta n c e s from th e source th e laws o f a tte n u a tio n o f th e gamma-ray d oses can be re p re s e n te d approxim ately by means o f th e e m p iric a l form ula 43

(7 .1 4 ) Using t h i s n o ta tio n , we in tro d u c e two c o e f f i c i e n t s cl and l*eff» which depend l i t t l e on th e d is ta n c e , in l i e u o f th e c o e f f i ­ c ie n t Br , which depends very s tro n g ly on th e d is ta n c e , and Jj.(Eq), which does n o t depend on th e d is ta n c e . The c o e f f i c i e n t i s in d e ­ pendent o f th e d e n s ity of th e su b sta n c e , w hile th e c o e f f i c i e n t p.ef f I s p r o p o rtio n a l to the d e n s ity p . T herefore th e e x p re ss io n f o r th e c o e f f i c i e n t o f a tte n u a tio n Kr can be w r itte n in th e form Kr = aee - ^ e f f R _ (Xe~ ^ A e f f

(7 .1 3 ')

in s te a d o f (7 .1 3 ). Formulas ( 7 .1 3 ') and (7 .1 4 ) a re c o n v en ien t to u se in th e case when th e y can be employed In th e i n t e r v a l of d is ta n c e s in which Oi and p ef f can be c o n sid ere d c o n s ta n t. F ig u re 15 shows th e v a lu e s o f & and p e f f *or a3-r ^o r two d is ta n c e in te r v a l s in which cl and f^eff were assumed c o n s ta n t. The d is ta n c e i n te r v a l s 400 - 1000 and 1000 - 2000 m eters were chosen such as to make form ula (7 .14) g iv e a r e s u l t a c c u ra te to i 10 p e rc e n t. I f the p e rm is s ib le e r r o r i s g r e a t e r , th e w idth o f th e i n t e r v a l w ith c o n sta n t Ct and |Aef f where (7 .1 4 ) i s v a lid * can be in c re a s e d . I n t e n s it y of gamma r a d i a ti o n in th e p resen ce o f a s p h e r ic a l c a v ity around th e so u rc e . A s p h e ric a l c a v ity around th e source i s th e s im p le s t model o f Inhom ogeneity o f a i r , o c c u rrin g in atom ic e x p lo sio n along th e p a th o f th e gamma r a y s , as a r e s u l t o f th e p ro p a g a tio n o f th e shock wave. In fo rm a tio n on th e p ro p a g a tio n o f r a d i a ti o n in a i r , i s ob­ ta in e d in t h i s case w ith th e a id o f sim u la tio n experim ents in w a te r. The re g io n o f r a r e f a c t io n around th e source was sim u la ted in w ater w ith th e a id of 10 empty aluminum sp h e re s , th e c e n te r o f each o f whloh a source was p la c e d . The r a d i i o f th e sp h eres were 1 8 .5» 2 9 .5» and 40 c e n tim e te rs , e q u iv a le n t to r a r e f a c t i o n re g io n s in a i r w ith r a d i i 160, 254, and 342 m e te rs . The m easurements were c a r r ie d w ith th r e e gamma-ray so u rces w ith Eq = 0 .4 1 , 1 . 25, a n i 2 .8 Mev.

♦ In C hapter I I I we s h a l l use form ula (7 .1 4 ) in s te a d o f (7 .1 2 ). 44

© .£ p

•• %4 © *H p © ©O O O £ •H Vi «H to Vi o fi O H © © > ^ O 3 ©p •H P 0 *H 05 P £ . . H aJ aJ O -h £ «H £ O ^ o * o cd H o fi © O U P «H

U

£ I

© ©

o 0 £

£ o

a—

Pi u 05 © P Vi qj

tOVi *H 00 O * H Vi «H o O HV P — © O Pi

P

©

pa> a> ©-3* > o H U© • a> £ a 3 ©t^-p © o

e ff

P ' - ' a -P © © © > © •H 0 H I ,£ P P £ £ 2 I P •H «H 0 a Vi o R cvi © o O Pit * o Vi •« Vi ^vo Vi £ P • ©Vt O © OJ ©

§

V-PIO C< O © V © CM

'E ©

U £ >>* © © p I

> ffld V

O © rl o n

P
- (?„) R, l.e ., m e te r

th e pR.

" o p tic a l th ic k n e s s "

in

th is

case

is

equal to

th e

para­

I f t h i s source i s surrounded by a c a v ity o f ra d iu s L, th e n we have p - 0 when R L, and consequently

47

R A=

jV

( P o ) ^ - dR =11 (p0) (R -

•

( 7 .1 7 ')

0 F ig u re 16 shows t h a t in th e case when the medium does not have a homogeneous d e n s ity i t i s n e ce ssa ry to use as th e param eter d eterm in in g th e v a lu e o f th e c o e f f i c i e n t s B and K th e v a lu e s (7 .1 5 ) and (7 .1 7 1) — th e " o p tic a l th ic k n e s s ," in s te a d o f |J-R or rA-« This o p e ra tio n i s approxim ate. The deg ree of approxim ation can he seen in F ig u re 16. The concept o f " o p tic a l th ic k n e s s " i s used in C hapter I I I in th e e stim a te o f the e f f e c t of th e shock wave on th e i n t e n s i t y o f th e gamma r a d i a ti o n . Notes on th e p ro p a g a tio n o f gamma r a d i a ti o n in a i r n e a r th e e a r t h . I f an atom ic homb explodes n e ar th e su rfa c e o f th e e a r th , th e n th e p ro p a g a tio n o f th e gamma r a d i a ti o n occurs under c o n d itio n s o f an inhomogeneous medium, l . e . , o f two h a lf spaces ~ th e e a r th and th e a i r . The e f f e c t o f th e e a r th on the p ro p a g a tio n o f gamma ra y s in e a r th has been In v e s tig a te d l i t t l e . The i n t e r a c t i o n between th e r a d i a ti o n and th e e a r th i s p a r t i c u l a r l y im portant when c a lc u la tin g the gamma-ray doses on th e su rfa c e o f th e e a rth — on th e boundary between th e e a r th and th e a ir. Let us c o n sid e r th e p o s s ib le d if f e r e n c e betw een t h i s case and th e case of p ro p a g a tio n o f gamma ra y s in a homogeneous a i r medium. In a homogeneous medium a t la rg e d is ta n c e s from th e so u rc e, th e i n t e n s i t y o f th e gamma ra y s i s determ ined e s s e n t i a l l y by th e s c a tte r e d r a d i a ti o n , which i s produced by a broad beam o f prim ary gamma r a y s . In th e p resen ce o f e a r th , p a rt o f t h i s broad o f gamma ra y s i s absorbed by th e e a r th in the d i r e c t v i c i n i t y of the source and does n o t p a r t i c i p a t e in th e c r e a tio n o f s c a tte r e d r a d i a ti o n . I f th e p o in t source and th e p o in t a t which th e r a d i a ti o n i s in v e s tig a te d a re lo c a te d a t th e le v e l o f the e a r th , th e n h a lf o f th e broad beam o f th e gamma ra y s tr a v e lin g in th e d i r e c ti o n from th e so u rce s t r i k e s th e e a r th and i s absorbed in i t . One can th e r e f o r e ex pect th a t in t h i s case th e t o t a l i n t e n s i t y o f th e gamma r a d i a ti o n a t la rg e d is ta n c e s from th e source i s ap p ro x im ately h a l f as sm all a s in th e case o f a homogeneous a i r medium. At sm all d is ta n c e s from th e source one can e x p e c t, to th e c o n tra ry , a c e r­ t a i n in c re a s e in th e i n t e n s i t y of th e gamma r a y s , by 10 o r 20 p e rc e n t, owing to th e p resen ce o f r a d ia tio n s c a tte r e d backward from th e e a r th . The c h a r a c t e r i s t i c fe a tu r e s o f th e p ro p a g a tio n of gamma ra y s in a i r over th e e a r th a re shown in F ig u re 17. The r a d i a ti o n s c a tte r e d in th e a i r , making up th e main c o n tr ib u tio n to th e dose a t la r g e d is ta n c e s , occurs only on th e upper h a lf o f th e space, whereas in th e case of a homogeneous a i r medium i t would a ls o come from th e low er h a lf space ( d o tte d ) . T h erefo re in th e case shown in F ig u re 17 th e dose i s ap proxim ately h a l f th e dose in an i n f i n i t e 48

homogeneous medium. I f th e source i s lo c a te d not on th e e a r th , but above i t , th en as i t s d is ta n c e from th e e a r th in c r e a s e s , th e i n f l u ­ ence on th e gamma-ray doses on th e s u rfa c e should d e c re a s e . The fo reg o in g q u a l i t a t i v e c o n s id e ra tio n s concerning th e p ro p a g a tio n o f gamma ra y s in a i r over th e e a rth have been confirm ed by e x p erim en tal d a ta . F ig u re 18 shows curves in th e a tte n u a tio n of th e gamma-ray dose I n t e n s it y acco rd in g to th e d a ta o f th e a u th o r and V. N. , Sakharov. The experim ents were c a r r ie d out w ith a source o f Co&0, lo c a te d a t a h e ig h t o f 1 m eter above th e e a r t h . A IR S c a tte re d r a d i a ti o n

F ig u re 17. F e a tu re s o f th e p ro p a g a tio n o f gamma r a d i a ti o n in th e case when the source and d e te c to r a re lo c a te d in th e boundary of th e a i r — e a r th h a l f sp a c e s. F ig u re 18. C o e ffic ie n t o f a tte n u a tio n o f th e dose of gamma r a d i a ti o n from a Co^O p o in t source when th e source and th e d e te c to r a re lo c a te d on th e e a r th — a i r boundary a t a h e ig h t of 1 m eter above th e e a r th (curve 2 ) . For com parison, th e f ig u r e shows th e a tte n u a tio n c o e f f i c i e n t s in a homogeneous a i r medium (curve 1) c a lc u ­ l a t e d from the m easurements in w ater and th e c o e f f i c i e n t s o f a tte n u a tio n of th e d i r e c t ray (curve 3 ).

49

S p e c tra l com position o f gamma r a d i a t i o n * In re fe re n c e [10] th e s p e c t r a l d i s t r i b u t i o n o f gamma r a d i a ti o n In an ab so rb in g medium was c a lc u la te d f o r d i f f e r e n t d is ta n c e s o f th e p o in t so u rc e . F ig u re 19 shows th e s p e c tr a l com position o f th e gamma r a d i a ti o n o f a monochromatic p o in t source o f u n i t a c t i v i t y ( 0 = 1 M ev/sec) w ith = 2 Mev in w a te r. The s p e c tr a l d i s t r i b u t i o n i s ex p ressed by th e fu n c tio n / le' f1 (eo)

(7.18)

Along th e a b s c is s a a x is i s p lo tte d th e quantum energy in Mev, w hile th e o r d in a te s r e p re s e n t th e v a lu e s o f th e fu n c tio n ( 7 .1 8 ), r e f e r r e d to th e i n t e n s i t y o f th e d i r e c t r a d i a ti o n of th e so u rc e , i . e . , th e v a lu e s f [€ , (j .(Cq )R ]/J o . J _ r), r / s e c ,

(8. 1)

where P i s th e dose power o f th e gamma ra y s in a i r and a l t i t u d e H above th e c e n te r o f an a re a on e a r th w ith ra d iu s r , on which th e gamma ra y so u rces a re uniform ly d i s t r i b u t e d . The a c t i v i t y o f th e s e so u rc es i s o'M ev/sec-cm ^, and |j.e i s th e l i n e a r c o e f f i c i e n t o f a b s o rp tio n o f energy in a i r . *0ne should ex p ect th e a n is o tro p y o f th e a n g u la r d i s t r i b u t i o n o f th e doses to d e c re a se w ith In c re a s in g R/A. **The c a lc u la tio n s were perform ed by V. N. Sakharov. 56

Table 18

Sq>

Mev

Altitude H of the point of measurement of the surface, meters

V alues o f th e c o e f f i c i e n t f(H , E q * r ) f o r th e c a lc u la tio n o f gamma r a d i a ti o n

25

0 ,7

—

1

f(H , E0 , r ) when th e ra d iu s o f th e gamm a-active su rfa c e 1b r m eters

1 .6

100

0,41

2 ,7 9 —

—

—

2 ,8 7

—

2 ,6 9 5 —

—

0 ,6 0 5

0 ,3 8

—

— 2 ,5 5 5

—

0 ,1 6 5

0 ,5 5

0 ,7 4 —

—

2 ,7 1,1 0 ,7 5 0 ,4 0 5

0,00205

0,00825

0 ,0 3 0 5

0 ,0 8 5

0 ,1 4

0 ,1 4 3 5

0,00105

0,00425

0 ,0 1 6

0 ,0 4 3 5

0,081

0 ,0 8 5

—

—

—

0 ,4 3 5 - 10-4 1 ,7 5 - 10-4 6 ,4 - 10-4 —

—

—

—

—

—

1

1,6

1,95

2 ,2 8

25

-

—

—

50

0,0535

1000 0 ,7

0 ,1 6 5

0 ,3 7

_

100

_

—

—

0 ,0 4 8 5

0,00 2 1 5 0,00 5 2 5 0,00625 — — 2 ,5 3 5 — 0 ,5 8 5

_

— — 2,71 0 ,7 6

_

0 ,00006 2 ,9 2 ,7 3 1,125 0 ,7 8 0 ,4 5 .

200

0,0022

0,0087 5

0 ,0 3 7 5

0 ,0 9 3

0 ,1 8

0 ,1 9 3

250

0,00125

0 ,0 0 5

0 ,0 1 8 5

0 ,0 5 2 5

0 ,1 1 6 5

0 ,1 3

300

—

—

—

—

0 ,0 9

0 ,0 1 3 5

0 ,0 1 8

500 1000 0 ,7 1 25 50 ■

—

oo

500

200

500

2 ,8

—

200

250 300

1,25

100

1,95 —

25 50

50

1 • io -


>>d

cl 0 0 a -h o 0 O 0 to rl ®'d (fl •P P< u O OVl^ 0 -P O U O

fri 0 Ce'««

i3,9mln 1,6

(c o n tin u e d )

0 5 to

OJ

Q

d •d 4^ 0 o fd •H N ^ « 0 5*P> 0 d 0 O 0 d o o A 0 d 0 > 0 o •P 0 0 0 0 «H «rl -p o «d -P 0 *♦-< 0 § S dfc A 0 Cl O 0 d * 0 0 4h •H C» P «H •H D* 0 d P i O fC! o-p 4h 0 ^d U* . C.

® a o O tt) S C*P 0 o to g a 30 *0 >* Ci «PO to4-1 »d H d© 4h •H -P Pi U 0 0 O © 5^ 0 ss co h •d d 0 Cl o d w 4> 0 0 O > dd •5 ° M0 0 4h

4h > O0 *a O «H to * tf K t CV) p* >> O O 0 * d 0 -P 0 H H 0 0 *HSX 0 -P d X H 0^ a o 3 «h © A a «p O •H >> 0 xS CO 0 I * 0 > 0d 0 P0 S

0

> 4-1

OO

0,9

0 ,1 4 2 0 ,2 7

0,22

0 ,3 2

Rb88

Kr88 Mo'01

i7.8min 1.7 2,8hrs l .7 I

i4.6min 2,2

1,8

2,8

20 2

0 ,9 5

7

1 ,8 5

1,8

0,028j

2 ,2 6

0,19 0 ,9 6 0

Kr8?

Te i*i m

78 min

2,35

30hr,8 2,4

2 ,4 3

2 ,3 1,89 0 ,4 0 5

2 .4 8

0 ,1 7 7

0 ,6 7

0 ,8 9

4 ,8

68

0 ,034

0 ,0 3 4

1,0

100 70

0 ,4 3 1,52

1,95

1 ,5

0,7 0,58 0,12

1,4

2,7

0 ,4 4

1,55

12.5 12.5 12.5 100

0,1 0,12

Te131

I

25min 2,4

2.48 0,16 100 0,64 45

0,39 0,72

La141

3,7hrs 2,4 i5.4min 2,65 2,7hrs 3,1

2,48 1.5 5 2,73 unknown3,2

0,19

Rb8»

Sr*s

Xe‘3« u min La143 19 . Baul 18 . Te133"» 62 . Te133 2. Te134 J13‘

44 . 52,5,

3 .4 3 .5

3,5 3,61 4,13

4 .3 4 .3

4.44 0,4 100 4.44 0,6 100 70 1.0 4,44 unknown4,85 0,86 30 1,1

4

4 ,3

4,7

1,7 0,19

2,4 3,8 unknown 2,8

1 ,7 8

121

1,8 2,7 3,0

7,5

1,25

1,25

1.6 unknown 2,0

© u© &a

© Vi

© © ft o p o © H

H Vi H © «

p § d © Vi d ,d P O P a © © ©H o >>PH © O © © OP p © 4-1

>>

oS © o d

© •d Vi O

o © © H

h

•d © o u © ^■P a*p d©>U

WU

d © d fa

A .d p «H

p p

p

VlH

©o

»d

6,8 1,4 100. 5,35 0,25 unkn.wn — 0,63 V — 0,87 » 2,53 5,E6 0.45J» 100 0,94 0,75C) 22 2,74 1,49 33

La>« prue

25 .

5,4

Ba'w

85 .

5,6

5,8

Y95

10,5,

5,6

CS>38

33 .

8,6

Ce>*s

1,8hr 1S 3,4

©

oso d © •d*H «H

d o

«rl © O

CCL

© © d d ©

Vi >

© «H o5 © o5* od oft +9 O © •H © © Vl > 4-1^ P © •> © O H CVJ 3d d©■d 05 d a «r O d f t 4-i H d 3 V >» O H »d o p a* P © H os o d-3* os o £-W & d © © d h « d P fe © Vi 4 n P o* ©>>ft o to a O P V d p p e* © d o u 3 *d © d >>4-i p h >> © U) © P O h d © © Vi H o H d \ H O © >> © H © S> © ©d © * d to ©d d © S \ p © > © d d © >Vi M © o o +

4,85

16,5min 4,7 5,2 74 .

CVI d © o o oft

6,8 _

O© » s

to u d © 6 H

I

5,4 unknow n

6,21

3,1

0,25 0,04

0,29

2,3

5,8 unknwn~

—

0,1631 26 1,05 0,6

1

122

12,8

p a r tlo le e * *

T a b le A1

unknow n

2,7 2,0

Table A2

Y ie ld o f -2 1,25

0,48 0,18 0,23 0,26 1,50 0,54 1,62 1,54 0,74 1,86 1,92 0,16 0,06

1,15

p r ite

0,290 51 0,300 16 0,660 11 0,720 11 3,3 0,455 100 0,750 22 1,49 33 80 3,7 0,52 95 3,1 0,25 3,7 0,551 91 3,87 0,53 91 0,85 5 1 1,4

2,28

__ 0,9 1,2

Y9i"» J133

123

1,86 2,14

Nd1*9

Y ield o f quanta w ith energy E«y percent o f number o f decays I n te n s it y o f r a d ia tio n o f the energy o f th e corresponding *Y quantum, M ev/sec per 10^ f i s s i o n s x 105 O verall I n te n s ity o f r a d ia tio n o f energy by th e .g iv e n iso to p e M ev/sec per 10^ f i s s io n s (x 103) Maximum energy o f p a r t i c l e s , Mev

Energy o f *Y quanta from fragm ents, Mev

F ra ctio n o f decays o f the Iso to p e In th e t o t a l number o f decays o f a l l the fragm ents, peroent A bsolute number o f decays per second per 10^ f i s s i o n s (x 10^

H alf l i f e

Iso to p e s

Table A2 (continued)

1,8hra

1,6

4,96 0,538 unknown 0,65 » 0,03 • 0,097 • .... 0,112 0 0,114 100 0,57 0,124 unknown ” 0,188, ■ 0,211 ■ 0,198 ■ — 0,226 0,240 • 0,266 V 0,422 o

Y*5 10,5 min Cb*™1 .u sec Cbw 74 min Zi” r/hrs rem 44 min Kr«* 76 .

1.8 2,0 1,8 2,0 2,3 2,7

Sr"

3

_ 5,59 unknc»wn 4,61 6,21 0,75 1 99 3,75 5,59 0.67 I 100 __ — 6.2in0 r ra d ia tio n — 7,23 unknown — 2,4 12,5 8,39 2,3 1,89 12,5 1.98 0,41 12,5 0,43 7 9,3 1.4 0,91 3,3 1,03 3,17 0,640 30 1,8 0,49 0,750 7 0,66 23 1.42 10,2 0,468 unknown 0,98 m 1,44 100 14,7 10,2 0,7 100 7,1 4,4 11,0 0,4 100 11,0 1,0 70 7,7 0,6 100 6,6

9,7 hrs

Csim 33 min

3,3

yo3 10 hrs Tei3im min Te133 62 2 .

3,3 3,55 3,55

1.5

0,57

i unkno1

8,36

__

1.3 1.9

—

unkno 3,0

4,81 7,79

1,6

14,7

2,6

7,1 18,7

3.1 1,6

| 124

4,5 h r s

KrM JI3J

11,9

2 ,8 .

3 ,9

6,68 .

4,2

12,3 13,0

Y'93 C ei« La>« La'

Sr” J134

I7 ,8 m in

4,3

3 ,5 h r s

4,5 5,6 6

1,8 . "4 m in

3 7hrs 2’.7 . 52 m in

Ba'9* 85 ra in

6,6 6,6 7,2 7,5

13,3 13,9 17,3 18,6 20,9 20,9 22,3 23,2

I n te n s ity o f r a d ia tio n o f th e e n e r g y o f t h e c o r r e s p o n d in g

a> O-H U to to >> 0 ^-* a «h •p,o ft 3 p S 0 •H «H OS tQ u 0 0 0 jsj o o

_ n o *y- — r a d ia tio n 0,028 68 0,23 1.3 u n k n o w n 2 ,4 1.1 1 0,35 1,8 u n k n o w n — 4,95 20 1,85

0,23 0,35

1,2 0,9

6,59

4,8

0,75 0,89 8,35

8,35

3,5

— -

_

unknow n

1,57

1,57

5,77

5,77

2 .4 | unknow n

0,98 0,15

1,13

2,8 0,95 0.6

2 7 100

unknow n— i 0,25 u n k n o w n

0,63 0,87 1.5

5

m to

unknow n-

0,86

30

1.1

— -26

1,78 0,163 1,05

125

0,6

—

1,7

2,0

2,0

2,3

Table A3 :y R a d ia tio n o f Fragments 20 Hours a f t e r F is s io n u(20 h rs ) = 1.57 x 10"2 Mev/sec x 10^ f i s s i o n s C o n trib u tio n o f r a d i a ti o n o f In d iv id u a l Iso to p e s to u(20 h r s ) , % Zr')7, Cb57'" , Cb9T Y*1 m .

I3aM0 l2,Sdays 1

Rh>0 T> 91

0,181 97,.c> 0,741 17,f) 0,780 2,5 ■ 15,8 no v rad laitlon 13,6

19,7

0,58 0,11

0,11

0,4

2,4 l.l 0,52 1,3 unknown . j l 1.8 126

1,1 1,7

0,52

0,9

cq

>P H b o) O q) (D O P p,

>P P o P © © a h P H O 0 2 O © tO a b

H H

Pi

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b O a> h Pi X 00 ^ ►> a) a o p 0 o *0 00 Vl © O H Vl

Vi

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8 day s

(D> P o c? P o o O P, H © H © © 'd P © •» © H ©b a Vi H b 3 Vi o *d o p 0

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5 IO P 4 © O b b © ©p H Vi >> P Vi,p o 4 o to g O P V b e- © b 3 t>>Vi h o p Pi H P p o © © Vi H O H O © >> © © * P tO © b V P © > © P P H © S

2.8 $.3 0.7 80,9 6.3 6.3

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to

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a 3 a H

h p

b ©

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o o

0,59 1.65 0,03 8,25 0,50 0,14

11,16

0,6

100 30 10 100 70

8,4 5,7 1,1 1,1 3,9

8.4 11,8

1.1 0.8

7 33 30 7 23

3,5 12,1 6,8 1,87 5.4

29,7

1,6

4,98 0,081

100 35

29.8 1,43

29,8 1,43

3.1 0,3

6,16 0,22 0,13 6,41 o,6 1,4

40 30 100 50

5.4 2.4 33,5 44.9

7,8

0,2

83,4

1,5

96

22,2

22,2

0,8

JI3*

2,4 .

5.4

Xe'as

9,2 »

7,8

9,25 0,25

Zr9T

17

.

8.4

9,96 no O' - rad ia tio n

J133

22,4 .

8.5

10,5 0,53 0,85 1,4

129

94 5 1

1,9 52,5 4.47 1.47

58,4

1.2

T a b le A4

(c o n tin u e d )

130

Table A5 O' R adiation o f Fragments 3 Days a f t e r F is sio n u(3 days) = 3*21 x 10"3 Mev/sec x 10^ f is s io n s Contribution o f r a d ia tio n o f In d ivid u al Isotop es to u(3 d a y s), fa Te133, J133..................................... 23,6 Zr97. Cb97mCb97 . . .18,2 Ba'40, l a 140 . . . . 17,3

H alf l i f e

Y ield o f y quanta w ith energy E m ti « 20,5 0,619 10,4 0,88 0,3 1,045 1,7 0,4 1.14 1,54 0,2 3,8 no P H U

a -----X oq vi cd © o q cd > ©o p ©

p

p

Pm147 2,6 Cs137 Ba137 Sr*> yso

33 .

15,6 18

18 2,6 min 19,9years22 61hrs

22

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2.9 no y r a d ia tio n 33 no y - r a d i a ti o n 33,5 0,661 100 40.9 no y r a d la tlo n I 40.9 no 7 - _ r a d ia tio n

144

00 q © o O ft rH P o p p

.q x cd o © p © p ©q •HP >> ©P P o > a 0) q od p O o q q © cd o © P p U p p Vi > P p © © OP Vi a a) a Vi cd q a p tf) ^ 3 O P U q Vi >> -=tco o* sPO P P ® oo ^ q cd O f r t PJCJHH © U cd O ©P cQ © JJH q q x ©>>©w Vi >> S Vi ^3 o* o to p o P . q PX) ft ©q q a >>Vi p P p © rH a Vi P o fcO® ©© O P o pq © >> ©P ©Ns, q ta © cdq> ©q \ p © > ® q q © > Vi M© a

© cd o cd © © CD Vi op ft Vi © 3 * © © Vi O rl 04 © p © o •* V. p % . A OpCD q _ p Vl p C ^ © O >>C X) o Vi Q o CO cd P «fll© O tf) W S3“rt O0 i cd O >q ©p as © tt)Vi pO OViVi ft q © ft q p © cdp o q q p o rH C w ftq © OO ©O cO © © l 0,65 3,15 0,54 Krs:- 9 ,4 years 1,7 ©

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p a r t i c l e s , Mev

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43 0 * A 0«rl Vl 0 A A Pi Vi A P gi *sfC0 rd O 43 43 A O O O4AP-^t *H#PrHrH v ^ *4 A A b A A O A 43 A P rH P UK ,Q v i >> a V P O4 A >>A ^ o to p O v 0 43,0 p , V i£ - A P 0 0 fp A >>o p «H >iO h a v i 43 tf)A A A O *H >> O rH V A A tO A rH H A A \ AA 43 a > A S 0 A A >V i m s: O O

2.98 no y - r a d ia tio n 2.98 no