EFFECTIVE CADMIUM CUTOFF ENERGIES 3445603614140

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. I

zyx zyxwvu ORN L-2823

UC-4

- Chemistry-Genera

EFFECTIVE CADMIUM CUTOFF ENERGIES

zyx

R, W, Stoughton J. Halperin Mo P o Bietske

.

U N I O N CARBIDE CORPORATION for the

U.S. A T O M I C ENERGY C O M M I S S I O N

.

1

L E G A L NOTICE

zyxwvutsrqpo zyxwvutsrqponm zyxwvutsrqpo

T h i s report was prepared a s an account o f Government sponsored work.

N e i t h e r the U n i t e d States,

nor t h e Commission, nor any person a c t i n g on b e h a l f of t h e Commission:

A.

Makes

ony warranty or representation, expressed or implied, w i t h r e s p e c t t o t h e accuracy,

completeness, ony

or u s e f u l n e s s of the information c o n t a i n e d i n t h i s report, or t h a t t h e u s e o f

information.

apporatus,

method,

or process d i s c l o s e d

i n t h i s report may n o t i n f r i n g e

p r i v o t e l y owned r i g h t s ; or

8 . Assumes any l i a b i l i t i e s w i t h respect t o the use of,

or for damages r e s u l t i n g from t h e u s e of

ony information, apparatus, method, or process d i s c l o s e d in t h i s report.

A s used i n the above, "person a c t i n g on behalf of the Commission"

i n c l u d e s any employee or

contractor of t h e Commission, or employee of s u c h contractor, t o the e x t e n t t h a t s u c h employee or

contractor

of the Commission, or employee of s u c h contractor prepares,

disseminates, or

provides access to, any information pursuant t o h i s employment or contract w i t h t h e Commission, or h i s employment w i t h such contractor.

1

z

om2823

zyxwvu

DATE ISSUED

zyxwvuts zyxwvutsr zyxwv zyxwvutsrqponm OAK RIDGE PTATIOTJAL U B O W O R P

Oak Ridge, Tennessee operated by

UT?IOIT CAR3ZDE CORPO€U!ITOT? f o r the Ud S + AT01!IC EIERGY COPdNISSION

'

8

3 4 4 5 6 0363434 0

-2

zyxw

zyxwvu

-

zyx zyxwvu Effective CadmLum CytofZ Ehergies

R . W . Stoughton, J. Halperir,, and Marjorie P, Lietzke

Abstract

Effective cutoff energies for poir-t

_1.I/. absorbers

inside of spherical

and cylindrical cadmim f i l t e r s have been calculated f o r thermal reactor neutrons. plus a

The neutron s p e c t m was assumed t o consist of a Maxwellian

1/E component,

and the parmeters varied were the thickness of

f i l t e r , the Maxwellian tenrperature and the b ~ w e l l i a aLo

_1/E flux r a t i o .

Because of the s e n s i t i v i t y of the el’fective cutoff t o Maxwellian f l u x parameters for t h i n f i l t e r s it i s recornended %‘fiatf i l t e r thicknesses of about 40 m i l s be used.

Forty mil f i l t e r s show effective cutoffs a t about

zyxwvuts

0.50 t o 0.55 ev. for temperahres up t o about 500°A ( o r about 0.045 ev).

Effective cutoff energies f o r boron f i l t e r s were also calculated for purposes of comparison.

The cutoffs f o r cylindrical cadnium f i l t e r s

should be applicable to a properly designed experLxen+ual f a c i l i t y .

-3-

zyxwv zyxw zy

z zyxw zyxw zyxw h t r o d u c t ion

For many yems cadm3m has been used as a fiJ,ter for thermal neutrana in maswing t h e r m 1 vs epithermal reaction r a t e s f o r reactor spectrum neutrons. Yaa e f ' f e c t l v s Cd cutoff er,ergy kras been estimateil as several

depenaing on the t h i c h e s s ~f the f j l t e r .

Hughes

a

e s t h a t e d about 0.4Q and

0.57 ev for 10 and 30 m i l cadmium -t;taFcknesses, -respe:tiveljr,

calculated r e l a t i v e number of neufxoos transmi3Aed vs enezgy Dayton and Pettus

tenths ef an ev

from a p l o t of %he

.

More recently

calculated effective Cd cutoff energies f o r flat f i l t e r s

of ,large area f o r both a monodirectional and an isotropic flux. only a

& flux,

w i t h lower wii upper lj.aits of 0.025 ev

%he upper liiit was not

and energy.

They assumed

aQa 10nev (althorn

important) i n the* numerical integrations over the angle

They defined the effective cutoff energy as the cutoff of a perfect

( I n f i n i t e l y sharp) f i l t e r that allows t h e same tu"al xmiber of-absorptions by the f i l t e r e d sample as does the gLven cailmkm ffl%er. In - h e i r calczila%irms they

assumed that the f i l t e r e d sanple had a The purpose of thLs paper is

tb

& cross

sectian.

calculate ef"fec-i;5.-veCd cutoff enezgies, as absorber and for an idealized

defined by Dayton and Pettus, f o r a 12ypo-khetical&l

zyxwvu z

Two geometrical configurations have been conside;-ed:

spherica4. and cylLndrica1

f i l t e r s (one cm dim. by two cn high.) ix resctor ixz*adiai;ions. Fdihfle %e ampl.es

occurred) and rather smal.1 3x1 ares,.

Xt c a s be s$mm that if a point san2le is moved

a signtficant distance f r D m the cen%er of the cyl-bdrical s h e l l i t s correaponfiir&

effective C d thickness is changed very l i t t l e .

For example, i f t h e p0b-k is moved

along the axis half way t o ogle of %he f a c e s (i. .e.

to one q w t e r '3f t h e height from

the nearer face) the effective Cd thickness is changed about G.$.

Eence a th4.n

zyxwv zyxwvu -4-

f i n i t e sample which approximates an i n t e p a l of such points should shov very

zyx zyxwvu

rxarly the sane effective cutoff as does the central point.

Actually an e f -

fective thickness could be calculated and a correction made, i f desired. the case of the spherical f i l t e r s the correction would be larger.

In

From an

experimental point of view, however, the cylindrical f i l t e r s are easier to make and to use, i n addition L ' o allowing an effective cutoff which is r e l atively insensitive t o position of sample.

Effective cutoff energies were also calculated f o r boron f i l t e r s LEIorder t o compare the variation of effective cutoffs with f i l t e r thickness and spectral parameters t o t h a t of cadmium.

zyxw zyxwvu zyxw zyxwv

I n general r e a l fiYcers such as caclnriurn a.~ad boron o n l y approxiaate o m defined perfect f i l t e r .

An additional factor t h a t a f f e c t s the u s e m e s s of a

f i l t e r is the sharpness w i t h iflich the t r t z x i t f o n fi-on opacity t o transparency i s made a t the cutoff.

A siaple measure of t b . i s efficiency was made here by

calculating the f'raction of %he ",tal number of reactions occurring i n t h e l / v t e s t sample a t energies below -

.O3

294

Fig. 2.

.04

.O5

.06

580 MAXWELLIAN TEMPERATURE

filter

(E,) for

.O8

.O 7

870 (OA)

Effective Cadmium Cutoffs for Spherical Shells.

l/V

absorbe

.09

3

4160

zyxw zyx

are given i n Table 1 f o r two values of Em (0.0253 and 0.05 ev)

-

.

Here the

f i r s t column gives ?he actual thickness, the second gives the effective

thickness and the last column gives the energy a t which 50% of the neutrons a r e transmitted.

The corresponding thickness r a t i o (effective/actual) f o r

a cubic f i l t e r i s about 1.20.

Some calculations were also carried out under conditions which should have given r e s u l t s i n agreement with those of Dayton and Pettus

12). Using

zyxwvu zy -

the sphere model, described above, with no Mxwellian ( i . e . , r = 0 ) and with

a lower l i m i t of the I & flux a t 0.025 ev the r e s u l t s should have agreed with

t h e i r monodirectional flux calculations f o r very t h i n samples (see the t h i r d

and fourth columns of Table 11). The data of Dayton and Pettus were read from

*.

a graph but should be accurate enough t o indicate a d i s t i n c t difference

Their

resonance parameters f o r Cd were s l i g h t l y different from those used i n t h i s paper, but hardly enough t o account f o r t h e difference i n results.

-

-

Reactior, rates per unit energy vs E and t o t a l reactions below E have been calculated f o r the

l/v absorber

as a function of energy for 10 and 40 m i l cad-

-

The solid curves i n Figs. 3 and 3a show

mium filters, Em = 0.0253 and r = 20.

-

-

the fractions of the t o t a l number of reactions occurring a t energy E per unit energy; the dotted curves show the fractions of the t o t a l reactions which

-

occur between energies zero and E.

*A

The t o t a l number of reactions occurring

recent comunication ( 2 June 1959) from W . G . Pettus contained some recal-

culated values and these ( i n the case of the beam flux) were much closer t o the r e s u l t s obtained in t h i s work than were Dayton's and Pettus' original values.

(See Table I1 and r e f . ( 2 ) ) .

-15-

zyxwv

zy zyxwvu

zyxw zyxwvu zyxw zyxw Table 9

Approximate vs Accurate Effective Cadmium Cu-toffs for Cylinrters

( a b . = 2) f o r

Em = .0253

lo

Eff 0 1

sphere

cylixder

cake

10

122

20

24,4

30

36.6

40

48.8

60

732

100

122.0

approx.

-P = 20

-16-

zyxwv

zyxw zyxwvutsr zyxwvut Table I1

Effective Cd Cutoff Energies for Monodirectional F l u Lower Limit in ev

Cd Thickness (mils ) 10

0.0253

zy

Dayton and Pettusa

This Paper

5 x

1/E F l u

0.025

0.025 -

0 -237 0.26 0.362 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

20

.431

.429

.34

40

,520

.520

.42

60

.584

583

47

100

.679

679

56

a

V a l u e s read from a graph

m.

zyxw zyxw

- 17-

U N C L A S S I FlED O R N L - L R - DWG. 39143

-

T

I

I. 3

T

1.2

1.1

zy

1.0

lu

3.9

6

cr

zyxwvutsrq zyxwv zyxwvut W

0.8

z

3

u)

c

s zyxwvutsrq 0.7

.o $ t

L

2Q.'

0.6

X-

cn z 0.6 0 -I o

1

IC

a

0.5

E LL

0

0.4 z 0 -

-Reaction

I I I

I

I I

I

I

Rate --- Fractions of Reactions

/o = 10 mil

-Reaction Rate ---Fractions of Reactions

/o =40mil

o

0.3

2 LL

0.2

0.1

I I

0.0

zy

zyx I-

A

I111111

lo2

I(

I I111111

103

I I1

io4

E,

(40 mil)

Fig. 3. Reaction Rates and Fractions of Total Reactions Below Energy E for Spherical Cadmium Shells.

zyxw zyxwv zyxwvutsrqponm - 18-

-

I

l1111l1

I

I

I I I1111

I I I IIll

I

UNCLASSIFIED ORNL- L R - DWG. 38934 I 1 1 l 1 1 1 I I I I I III

-

-

-

-

10’

zyx

IO0

l‘

zyxwvutsrqp >

.-c u)

t

3

h

L

W

L

t .-

a L

0

W

zyxwvu [r

W

z W

zyxwvutsrq lo-’ 3

13w

m m

I I I I I I I

z

10-2

0

I-

o

a w

I

I

I I

[r

I

LL

0

zyxwvutsrqponm zyxwvutsrqponmlkjihg IO-^ z 0

I-

i

0

a

I I

I

-

= 40 mil

---

= 10 mil

I I IIII

T

E

io0

I

I IIIIII

10

I

I1l111

40

I (40ECmil ) EC

(10 mil )

Fig. 3a. Reaction Rates and Fractions of Total Reactions Below Energy Cadmium Shells.

E for Spherical

zyxwvu zyxwv zy zyxwv zyxwv zyxw zy z

a t all energies was noxmaLized to uni"cyo Acreactions in the 10 than tn the 40 mEL caae,

of course tihere m e more

As seen

i n F i g e 3 about 6 ~ of $

the total reactions occur belaw the cutoff wit& Maxwellian neutrons I n the

BI the 40 mil. case very few reactions inm~,ve

case of the 10 mil khicknesh.

and only a few percent of t h e reactions w c u r be3.0w6EG.

MaxweUan neu-ns

-

The c a l c U t e d r e s u l t s f o r boron spheres m e presented

Boron Spheres.

i n Appendix B. Cd Cylinders.

The results for the cylindrical shells are Shown fn Fig.

4

4

The cutoffs are seen to be sfmilas t o but a l i t t k e higher than those for the spherical f i l t e r s , as expected.

Again a thickneas of abaut 40 m i l s is indi-

z

cated in arder that We cutoffs be insensitive to We flux r a t i o a t the lower Maxweuian teaperatures.

Since the melting point of cadmtum mtal i s 321%

0

(594 A) the higher temperatures ~ R be Y unrealistic; however cadmpum i n some chemical form could be used as a f i l t e r a t higher temperatures by c l a d d b g Vdues of E

it w i t h sume high melting material.

-

in Fig. 5 f o r r =

G

VS.

C d chiokness are

sWm

0

0,

E and

30 for

% -

= 0,0253 ev.

The fractions of the total reactions by the

& sample below the

effective I

cutaff are shown i n F&g, 6.

-

ing Em a t an;y thickness. creases wi-bh;

For r $

A t low

'c

E;m

0,

this fraction is increased by Fncreas-

( i . e e 2 mound 0,0253 ev), the fkaction in-

*-

only f o r t h i n f i l t e r s ; a t the higher Em values the fraction in-

creases w i t h r f o r all thicknesses.

A t En = 0.075 ev a dfsfinct rnihbtum

OCC'UU"~

d

in the fraction curve at about 15 mjls Cd,

A t Ea = 0.1 ev the mFn39aum &s broader -..-

and l&s d k t j h c t , See Appendix C f o r calculated values for cylindrical. Cd fil%wse

zyxw zyx

- 20 -

UNCLASSIFIED O R N L - L R - DWG. 381408

.8

.7

nils Cd

........ r = 12

00

-

............

60

.6

-

zyxwvuts zyxwvu ..................................

40

-T > Q,

..................................... ..*""*: _---------_

.5 30

............................

.......................................................................................... 20 -lu" .4 - - - - _ _ ---_---__ -- _ _ _ _ _ _--------------

v

. 3 -1 5

.2 10 .02

.03

294O

Fig,

.O 4

.O 5

.O 6 E,(ev)

-

.07

.08

580" 870° MAX WELL1AN TEMPERATURE ( O A )

.09

zyx .I 0

1160"

4. Effective Cadmium Cutoffs for Cylindrical Filters (Height/Diameter = 2).

-21

-

zyxw zyxw zyxwvutsrqponm - 22 -

0.L

0.:

zyxwvu

zyxwvutsr

z

0 -

I-

o 0.2

a

LT

LL

0.4

zyxwv \&-,

I-= 0

20

40 mils Cd

60

=.0253 ev

80

400

Fig. 6. Fractions of Reactions Below Cadmium Cutoff for Cylindrical Filters (Height/Diameter = 2).

Boron Cylinders. VS.

zyxwv zyxw zyxwv zy z zyxwvu -

Figs. 7a and 7 b show typical curvEs for Ec and FRACE

thickness, respectively, f o r boron and cadmium. As expectad, there is

as expected the boron shows a much W g e r FRAW

no leveling off of Ec w i t h increasing thickness i n the case of Boron.

Also

.wlan cadnlium azld shows t b e

effects of the Ma%wellim neutrons over a wider range of thioknesses.Also see Appendix D. Conclysiow

Effective cadpl;lwn cutoff energies have been calculated for a wide va;riety of Maxwellian neutron temperatures, r a t i o s of Maxwellian to epithe-1 and thicknesses of Cd f i l t e r s .

flux,

Beaause of the sensitivity t o Maxwellian flux

zyxw zyxwvu

parameters for thin filters (less than about 30 m;uS) it is recanmended that f i l t e r s of about 40 mils be used i n Cd r a t i o work.

Depedlng on the exact

conditions the effective cutoffs for 40 mil C d l i e between 0.50 and 0.55 ev f o r MaxweUm texperatures of 300 t o

5008.

The vaLues presented here Shou3.d

hold t o a good approxirpation for s m a l l samples centrally located inside cyl i n d r i c a l cadmium f i l t e r s .

I " I

+,

-

- 24 -

zyxw

zyxwvu zyxwvutsrqp

zyxwvutsrqpon z UNGLASSI FI ED ORNL-LR-DWG. 3 8 1 3 8 A

-B

6-

---- Cd

-

5-

T >

a, v

zyxwvutsr zyxwvutsrqponm zyxwvu 4-

-

lu” 3 -

I I

I

-

2-

I

I -

-

‘-___________--------------.*/’

,

I

1

I

10 20 30 40 50 60 70 80 90 400

I

I I 10 20 30 40 50 60 70 80 90 100

mils Cd 4

I

Fig. 7a. Effective Cutoffs for Cadmium and Boron Filters for E = 0.0253 ev and r m = 20.

Fig. 7b. Fractions of Reactions Below Effective Cutoffs for Boron and Cadmium Filters for E = 0.0253 ev and r = 20. m

-25-

zyxwv

zyxwvu zyxwv zyx Acknowledaements

We wish t o thank J. E. Murphy and C . S . W i l l i a m s of the Central D a t a

Processing Department of the O a k Ridge Gaseous Diffusion P b t f o r i n % e r e s t b g discussions on numerical integration and f o r helpful suggestions.

zyxw zyxwvutsrq zyxwvuts zyxwvu zyxw zyxwvu zyxw References

1, D e J, Hughes, " P i l e Neutron Research", pp. 131-2, AddisonrlJesby

Fubl, Co., 2.

Cambridge, Mass.,

(1953)0

I. E, D q o n a.nd W, G, Pet%us, Nucleonics

3. C. H, Weetcott, J. Nuclear Energy 4.

3

a No.

12, po

86 (1957).

59 (1955).

D. J, Hughes and R e B. Schwartz, "Neutron Cross Sections", U. 8. A.l;aanics Energy ~aaranissionDocument BNL-325, second mition, (1958)

zyxw zyxwv zyxwvuts zyxwv zyxw -27-

Appendix A

Wfective Cadmium Cutoffs Ec (in ev) for Spherical F i l t e r s o r Unidirectional Beams

12 EC

0253

10

15 20

30 40 80 100 120

.0300

10

15 20

30 40 50 60 80 100

120

.ob0

10

0.141 0.283 0.396 0.478 0.519 0.552 0.583 0 635 0.680 0 -719

0.158 0.285 0.395 0.477 0 . 5 ~ 0 555 0.584 0.635 0.679 0 -719

-

0.196

0.302

20

391 0.474 0.516

100 120

0.459 0.163

Ec

0.126 0.235 0.375 0.477 0.518 0.552 0.583 0 e635 0.680 0 -719

30

m C T

0.585 0.241

EC

0.118 0.202

0 * 351 0 475

ERACT

0.678 0.323 0.115 o .069

zyxwvu zyxwvu

15 30 40 50 60 80

20

FRAm

0

0

551

0.581 0.634 0.680 0.720

0.082

0.067 0.068 0.071 0.073

0.074

0.455 0.162 0.083 0.068

0.144 0.245 0.374 0.476 0.520 0 * 555 0.584 0 9635 0 0679

0 *719

0.186 0.278 0 372 0.469 0.514 0 549 0 578 0 -633 0.680 0.720

0.0%

0.068

f

0.069

0.518 0 552 0.583 0 -635 Q .680 0 -719

0.581

0 J37

0.675

0.220

0 * 33-9 0

0,239

0.097

0.069

0 351 0.474 0.520 0.554 0.584 0 =635 0 -679 0 -719

0.181

0.265 0 * 357 0.462

0.511 0.547 0 578 0.632 0.679 Q -719

.UT

0.070

6280

Appendix A (Cont’d)

e

zyxwvut zyxwvutsr zyxwvut zyxwvutsrq m m

m m

zyxwvutsrqponmlkjihgfed KFU.GT

/

30

20

12

0500

10

15 20

30

40

0,387

0 0457 0 .so2

100 120

’

00222

01180 0.131 0 0105

10

0,540 574 0.630 0.676 0.716

0.308 0,373 0 446 00493 0 532 0 566 0,625 0,672 0.714 0

0

‘9

15

0

30 40 60 100 10

15 20

30

40 60 100 10

15 20

30

40 60 100

331

0.376 0.1~32 0.467 0 536

20

.loo0

Ec

zyxwvutsrq 50

60 80

.0600

0.230 0.3U

Ec

zyxwvut zyxwvut zyxwvuts 0.650

0,288 0 353 0 392 0 435

0,286 0e 1 8 8 0.165 0.206

0 Q47L 0.529

0,623

0 317 0 4 365 0

0.395

Oe49 0 477 0 526 0 597

0.245

0,2hl 0,202

Q.197

0.286 0.349 0,386 0 428 0. J+60 0.514 0,606 0 0 317 0 364 0 394 0 e 434 0 467 0 * 517 0 * $93

zyxw zyxwvu zyx zy -29-

Appendix B

Effective Boron Cutoffs Ec (in ev) for Spherical F i l t e r s or Unidirectional Beams

r = nv0/@, =

Em

(4 0253

l0

(*./m2) 20

50 100 150 200 300 500

0350

20

50 100 150 200

300 500 .0500

20

50 100 150 200 300 500 *

0750

20

50

100 150 200

300 500 .loo0

20 50 100 150 200

300 500

12

EC

FRACT

0.384 0.545 0.0715 0.1672 0.524 0.5936 0.441 1.422 0.399 3.864 0.373 11.16 0.368 0.0353

0.0432 0.0858 0.1681 0.4192 1.139 3.615

0.356 0.538 0.571 0.492 0.430

E

C

20 FRAm

0.367 0.569 0.638 0.563 0.472 0.393 0.369

11.11

0 -369

0.0541 0.1060 0.1879 0.3177 0.7782 3.000 10.92

0.324 0.517 0.603 0.561 0.485 0.404 0 371

0.0537 0.331 0.1046 0.538 0.1794 0.655 0.27~. 0.637 0.4997 0.553 2.586 0.429 10.74 0.373

0.0699 0.288 0.1360 0.483 0.2318

0.610

0.3389 0.621 0.5126 0.571 2.174 0.454 io .23 0.380 0.0840 0.1626 0.2728 0.3826 0.5230 1.483

9.155

0.263 0.455 0.599 0.641 0.623 0.510 0.395

EC

me2

0.0349 0.399 0.0347 0.407 0.0692 0.587 0.0682 0.611 0.1372 0.599 0.1258 0.655 0.4227 0.490 0.2970 0.543 1.207 0.422 0.9990 0.449 0.377 3.600 0.383 3.743 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP 11.14 0.368 11.13 0.368

0.0428 0.0841 0.1507 0.2781 0.8512 3.344 U. .06

0.382

30

0.0696 0.1348 0.2246 0.3168 0.4321 1.520

9.613 0.0837 0.1615 0.2685 0.3691 0.4796 0.9321 8.027

0.0427

0.373

0.0832

0.586 0.682 0.627

0.1442 0.2295 0.6227 3.046

zyx z 0.293

0.497 0.641 0.680 0.648

0.506 0.38

0.267 0.465 0.625 0.687 0.689 0.584 0.413

11.00

0.0536 o.logg 0.~754 0.2531 0.3777 2.ll2

10.50

0.0694 0.1342 0.2223

0.3077 0.4030 1.049 8.925

0.0835 0.1610

0.2664 0.3629 0.4606 0.7403 6.881

0.518

0.406 0 * 370

0.336 0.550 0.685 0.690 0.618 0.458 0 - 376

0.296 0.505 0.662 0.716 0.703 0.561 0.398

0.269 0.471 0.639 o.‘p3 0.730 0.651 0.435

-30-

zyxwvu

Appendix C Effective Cd Cutoffs Ec ( i n ev) for Cylinders (Hei&t/Diam.

-

zyx = 2)

and Fractions of Reactions Below Cutoffs FRACT f o r Various Values of the Cnwacteristic Maxgellian Energy Em

zyxwvuts r = nv0/gr =

0

mils Cd

EC

12

FRAm

EC

30

20

FRAm

FRACT

EC

EC

FRACT

zyxwvutsrqp zyxwvuts Em = 0.0253

10

15 20

30

40 60

100

,378 .419 .452 .504 -547 .615 .718

,0612

.0640 ,0661 .0684 -0705 .0730 .0756

-173 .339 ,431 .503 .547 -615 -718

0358 .116 .0751 ,0692 *0705 .0729 *0757 Em

10

15 20

30 40 60 100

.go6 .342 ,429 .5oi 0545 .615 .719

.148 .298 .419 .502 .547 .615 ,718

=

=

LO

15 20

30 40 60 100

.260 -353 .415 .483 -531 .606 .714

.301

01552 .12i8

.io03 -0915 .089

00799

.137 .259 .404 .501 .547 .615 .718

.466 .161 .0877 .0726 -0723 .0736 a760

.i8i .283 .401 0497 .544 .614 .718

.582

.218

.0907 .0698 .0708 .0728 -0755

0.035 .189 .308 .416 ,499 ,545 .614 .718

.346 ,1190 .0789 .0711 -07x5 .0734 .0760

482 .161 .0819 ,0695 .0706 .0730 .0756

.565 .213

.0997 a0750 .0733 .071+1 .0762

0.05 .250 ,338 .401 .472 ,522 -599 .712

.398

.245 .479 .329 .25’2 .390 .188 .153 .120 .462 .143 .513 .122 .io5 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH .592 .lo0 e0910 .7o8 a 6 0 .0826 .202

-31(Appendix C continued) E, 10

15 20

30 40 60 100

.bo3 .446

.203 *I79 .i40

.336

234

.382

.2U

.412 ,456 .495 .547 .631

.yo

.210

10

20

.309

.249 -175 .198

15

100

0.075

zyxwvut .3U a375 .409 .454 .49i e555 .665

E,

30 40 60

=

,480

.540 .643

.304 .225 .248 .271 .266 .234

.177

.308 .366 *399 .441 .474 .529 .625

.344

.262

.289 .327 .326 .291 .219

= 0.100

.204 .197 .191 .225 ,236

.336 .381 ,410 .452 .488 ,539 .617

.267 .247 .244 .241 .23g *279 .304

Ec

mm

Ec

E~ = 0.70

#

-335

.go ,409 .450

.483 .534 .610

335 .270

,271 .q4 .274 -325 .370

zyxwvuts zyxwvutsr r = nv0/fir = 20

mils Cd

F!RAcT

Em = 0.20

10

15 20

FFUiCT

FRACT

zyxwvutsr EC

30 40 60

100

mils

Ec

# = 0.40

.403 .048 .4ll .37i .170 .390 -087 .450 .061 .456 .434 .lo2 .410 .185 .071 .485 .494 ,469 .115 .439 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA a198 .546 .550 .082 .484 .220 .520 133 .591 .089 .560 .596 .520 .236 .145 .678 ,622 .163 .657 .loo '575 .259 .792 -757 all9 .7i5 .192 .657 .286 Em = 3.0

Em = 10.0

Cd 10

15 20

30 40 60 100

,387 .0051 .5i7 ,0031 .631 .0049 .429 .0060 .716 .0063 .467 .0071 .834 . O083 *537 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA .oog8 .9lO .0095 .5g8 .0126 .995 .0104 .702 .0181 1.073 ,0103 .859 00273

= 1.0

.033 .036 .040 .Ob9 a057 .071 .OgO

zyxwv zyxwv

632-

zyxwvut zyxwvut zyxwvut Appendix C (Cont'd)

Miscellaneous Results

r = nvo/15, =

12

mils Cd

EC

FRAm

E, 25

35 80

0.475 0.526 0.670

EC

m C T

EC

0,468 0.525 0,670

0,070

0.074

0.072

0.070 0.074

0.473 0,524 0.670

35

80

0.454

0.108

0.508

0,095 0.081

0.665

E25

35 80

0,436 0,476 0.592

0.432 0.488 0,656

0.161 0.131 0.091

0.433 0,472 0,612

= U.100

0.200

OBL94 0.238

0.431 0.467 O.fl5

EC

0,072 0.071 0,075

m m

0.035

0.464 0.523 0,670

O&Q

0,07lb

0,075

Em = 0.075

E~ = 0.050 25

zy zyxw m C T

=

= 0,0253

0,069

30

I2

30

0.274 0,274 0,361

,

0.208

0.422

0,316

0,207

0,458

0,529

0.157

0,579

0.252

zyxwvu zyxw zyxw zy

Effective Boron cui;offs E~ (in ev) for cy1iniiers (ilei@;ht/biam. = 2)

and Fractions of Reactions belox Cutoffs FlRACT! far Various Values of the CharacterTstbc iyla;rweUau k r g y Em

n = 0.0253

E

-p__

20

422

30 50 80

, .Q40 *053 *0?9 0

100

0

125

440

.613 528

,618 --

173

623

150 200 300

500

1000

zyxw 0

039 053

0'77 QU5 .I49 535

9

1,631

.

5,160 15 292 611.227

zyxwvut zyxwvut zyxwvut zn = 0,050 --1_1__

20

30 50 80 100 150 200

3w 500 1000

062

0082

.EO

9

0

D

176

221

454

10297

4 ,620 15.126 61e 310

061.

061

a372

zyxwv e

082

464

eo81

166

e

0

295 607

3 532 14.790 61 310

zyxwv zyxwvu zyxwv z

Appendix D (Continued)

r = nvo/fir

3.2

m C T

Ec

E~

20

30

50

80

100 150 200 300

500 1000

30

20

zyxwvutsrq

mg. B/m2

Ec

106

324 410

154

o 522

.080

= 0,075

e

333-

.4639 540 420

zyxwvu zyxwvutsrq zyxwv 0

220

264 406 0770 34 532 14,518 61,272

607 ,628 627 ,600 0479 e 393* 371+

e 671 e679 .681 539 404 374

zyxwvutsrqponm 0

8

Em = 0,100

20

30

50

80 LOO 150 200

300 500

1000

ma

0%

.E8 184 260 3O9 .442 638 2 570 1 3 e 494 61,189 0 0

298

.m .496 .594 628 645 645 539 .412 8

0

Q575

557 ~ 6 9 8 1 2 364 62,189

.620 43'9 376 0

zyxwv zyxw zyxwvutsr zyxwvuts zyxwvut zyxwvu zyxwvut zyxwvuts ORNL- 2823 Chemi.s t r y - General

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1, 20 3. 4-50 6.

.

0

.

,

42p' 43 0 44* 45 0 46 P,

47 B 48 0 49 P 50% 51%

-52-1020 103. 104. 1050 106 107 108e 0

T I A. Lincoln A. S. Householder C, S. H a r r i l l C. Eo Winters Ho E, Seagren D. P h i l l i p s D. S. B i l l i n g t o n J. A, Lane M. Je Skinner W. H. Jordan G o E o Boyd R. A. Charpie P. Mo Reyling R. W o S q . u h t o n J. Halperin M. P. Lietzke Bryce Crawford (consultant ) T. H. Davies ( c o n s u l t a n t ) C. E. Larson ( c o n s u l t a n t ) J. D. Roberts ( c o n s u l t a n t ) G. T. Seaborg ( c o n s u l t a n t ) ORNL - Y-12 Technical Library, Document Reference Section

zyxwvut zyxw 0

,/'

39 0 40. 41.

109 e 110 0

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