Radiation attenuation in light materials with spherical geometry

~r9~

0 ~ 9 ( ~ ~

An~ Nuc1. Ener9y V0L 2~ N0. 11, pp. 947-954, 1996 C0pyd9ht • 1996 ~ f 1 e r 5e1en~ Ltd Pr1nted ~ 6reat 8f1~1m Af1d91a~ rem~ed 0306-4549D6 $15.00+0.00

7ECHN1CAL N 0 7 E RAD1A710N A77ENUA710N

1N L 1 6 H 7

MA7ER1AL5 W17H

5PHER1CAL 6E0ME7RY A. 5. M A K A R 1 0 U 5 t, A. EL-5AYED A 8 D 0 2, 1. 1. 8 A 5 H 7 E R 2 and W. A. K A N 5 0 U H t 1React0r and Neutr0n Phy51c5 Depa~ment, Nudear Re5earch Cen~L At0m1c Ener9y Auth0r1ty, CMr0, E9ypt 2Facu1ty 0f 5~enc~ 2a9a219 Un1ve~1t~ 2a9a21~ E9ypt (Rece1ved 18 March 1995)

A65Ua~--7he 5pat1M f1uxe5 and ener9y ~r16ut10n5 0f fa5t neutr0n5 and t0ta1 9amma ray5 6e~nd 5pher1cM 5~dd5 0f pdy~h~ene and 9raphffe have 6een carded 0ut. A Pu-a-8e 50urce ha5 6een u5ed ~ 5pher1cM 9e0m~ry. Mea5uremen~ and ca1eu1at10n5 0f the fa5t nen~0n 5pectra 6eh1nd ~fferent th1ckne55e5 0f p01yethy1ene and 9raph1te have 6een carded 0ut. A150 the t0ta1 9amma ray 5pectra 6eh~d ~fferent th1ckne55e5 0f p01yethy1ene and 9raphffe have 6een mea5ured exper1mentM1~ A fa5t neutr0n and 9amma ray 5pectr0meter w1th a 5f116ene cry~M Wa5 u5ed ~ the pre5ent mea5u~ment~ 7he unde51red pu1~5 0f neutr0n5 0r 9amma ray5 were prevented 6y a p~5e 5hape ~r1m1nat10n teehn~ue 6a~d 0n the 2er0 cr05f1n9 m~h0~ 7he cMc~at10n5 0f the fa5t neutr0n f1uxe5 we~ perf0rmed 6y u51n9 the AN15N We5t1n9h0u5e ver510n (AN15N-W) e0de w1th the EUR L18 1515 cr055 5ect10n 116rary. 7he 06ta1ned data were d15#ayed M the f0rm 0f 5peetra and f1ux d15tr16ut10n5 and attenuat10n curve5. C0mpar150n 6etween the mea5ured and ca1cu1ated fa5t neutr0n 5pectra f0r p01yethy1ene and 9raph1te 5h0w5 a ~a50na6~ a9reement f0r M1 ener#e5 and f0r a11 1nve5t19ated th1ekne55e~ A150 e0mpar150n 6etween pdy~h~ene, 9raph1te and water ~0m the rad1at10n m0derat~n and attenuat10n p01nt 0f f1ew have 6een carded 0ut.

1. ~7R0DUC710N Hydr0car60n mater1a1 1n the f0rm 0f p01yethy1ene (CH~ are u5ed a5 neutr0n 5h1e1d5 f0r m061L neutr0n 50urce5. P01yethy1ene mater1a1 w1th p = 0.92 9/cm ~ ~ u5ua11y ch05en a5 a p05f161e rep1acement 0f water f0r 0ther 5h1dd1n9 app11cat10n5 where the 5h1e1d ~ n0t exp05ed t0 h19h temperature5. 1n add1t10n R ha5 0ther m0re advanta9e5 than water due t0 ff5 ea5e 0f c0n~ruct10n and 5hap1n~ 1n add1t10n p01yethy1ene c0nta1n5 m0re hydr09en at0m5 per un~ v01ume ( ~ 7.8-8.0 x 10~ at0m5 0f hydr09erdcm 3) wh1~ ~ ~ 6.7 x 10~2 at0m5 0f hydr09en/cm 3 f0r water (Pr1ce et a1., 1957). 6raph1te ~ a 900d fa5t neutr0n m0derat0r and ref1ect0~ R ha5 a 10w capture cr055 5ect10n f0r therma1 neutr0n5. A150 1t5 9amma ray attenuat10n ~ 10w. Due t0 R5 ref1~ance t0 rupture and ma1nta1ned 5~en9th at h19h temperature5, 1t5 h19h mdt1n9 and 5u611mat10n p01nt5 and R5 h19h therma1 c0nduct1v1ty, 9raph1te ~ an attract1ve mater1a1 a5 a therma1 5h1dd (71pt0n,

1960; Jae9e~ 1975). Nuc~ar 9rade 9raph1te w1th denf1ty 1.718 9/cm 3 wa5 u5ed 1n th15 5tud~ 7he 5tudy 0f the 5pat1a1 f1uxe5 and ener9y d1~r16uf10n5 0f fa5t neu~0n5 ~ 0f 1n~re5t n0t 0 n ~ fr0m the p01nt 0f v1ew 0f the the0ry 0f neu~0n penetrat10n thr0u9h matter 6ut a150 fr0m the p01nt 0 f ~ e w 0fca1cu1at1n9 and def19n1n9 the 5h1e1d5 ar0und neutr0n 50urce~ A150 ff ~ 1mp0~ant f0r the purp05e 0f de~rm1n1n9 c e ~ n 1nte9ra1 charac~r15t1c5 0f the med1um. A150 the 5tudy 0f neutr0n5 and t0t~ 9amma ray f1uxe5 and ener9y d1~r16ut10n 15 very 1mp0~ant ~ 0 m the 5h1dd1n9 p01nt 0f f1ew 51nce ~ ~ve5 the m ~ n c0ntr16ut10n 0f the t0ta1 rad1at10n d05e at the 5h1e1d 5urface. 7heref0re ~ 6ec0me5 nece55ary t0 a55e55 the neutr0n and 9amma f1uxe5 a5 a funct10n 0f rad1at10n ener9y at the 5h1dd 5urfac~ 5er1e5 0f mea5uremen~ and ca~u1at10n5 have 6een carded 0ut t0 determ1ne the rad1at10n d1~f16ut10n thr0u9h 9raph1te and p01yethy1ene 0r p01yethy1ene added t0 0ther c0mp0und5 t0 f0rm d1fferent p01ymer5 uf1n9 d1fferent exper1menta1 9e0metr1e5 and d1fferent 947

948

7echn1Ca1 N0te

c0de5 f0r the ca1c~at10n5 (8ednar5k1, 1985; 5 e ~ m 0 t ~ 1985; 5a~0~ 1987; Kucha~ 1989; 5 ~ 6 a t ~ 198~ K0~9awa, 1990). 1n the p~5ent w0rk mea5u~ment5 w e ~ perf0rmed t0 de~rm1ne the rad1at10n d~tf16uf10n 6 e ~ n d ~fferent t~ckne5~5 0f p ~ y e t h y ~ n e and 9 r a p ~ u~n9 a p ~ n t 150~0p~ 50urce ( P u - ~ 8 ~ ~ 5pher1c~ 9e0m~ry. A150 ca~dat10n5 0f the fa5t neutr0n f1uxe5 and ener9y d1~r16uf10n5 6 e ~ n d ~ f f e ~ n t th~kne55e5 0f p ~ y e t h ~ e n e and 9raph1te have 6een carr1ed 0ut u~n9 the AN15N-W c0de w1th the EUR L18 1515 cr055 5ect10n5 ~6rar~ 7he m a c r 0 ~ 0 p ~ t 0 t ~ cr055 5eCt10n5 f0r fa5t neutr0n5, the hnear a~enUaf10n C0eff1~en~ f0r 9amma ray5 and the re1aXat10n ~n9th5 f0r neutr0n5 and 9amma ray5 have 6een 06ta~ed f0r 60th p ~ y e t h ~ e n e and 9raph1te and C0mpared W1th that f0r Water t0 de~rm1ne t h 0 r eff1c1enCy f0r the therma115at10n 0f fa5t neutr0n5 and attenuat10n 0f 9amma ray5.

7a61e 1. Neutr0n ener9y 9r0up ~ructure 0fthe EUR L18 1515cr055 5ect10n data 5et u5ed 1n the pre5ent w0rk

6r0up num~r 1 2 3 54 6 87 9 10 1211 13 14 15

Up~r ~er~ (Me~ 14.918 5A881 3~788 3.3287 22313 20190 1.3524 •7206 E-1~ ~6883 E-1 •7379 E-2 4.0868 E-2 21017 E-3 1~846 E-3 83153 E-6 ~1399 E-7

~ Read a5 ~7206 x 10 ~.

105 ~

•• •

M~d CMcu1Med

2 ~

~

~

C ~ 0 N 5

7he ~5t neutr0n and 9 a ~ a ray f 1 ~ ~ d ~ e ~ d1~r16uf10n5 6e~nd ~ m t~ckn~5 0f p 0 ~ h ~ e n e ~ = 5, 10, 15 and 2 0 ~ ) and 9 ~ e Q = 9 . 5 , 19 and 2 0 c ~ have ~ e n c a ~ e d 0ut. 7he mm~ were a ~ a n ~ d ~ a 5pher1c~ ~ 0 m ~ ~th a Pu-~-8e 50urce ~ a c e d ~ the 5phere cente~ 7he ~ neutr0n and 9 ~ m a ray f1uxe5 and ~ e ~ y d1~r16ut10n5 have ~ m ~ d ~9 a ~ ~ n and 9 ~ m a my 5 ~ m ~ ~th 5~ne c ~ ~ 0 x 40 m ~ . ~ r 1 ~ n a 9 ~ n 9 undef1~d p ~ 5 0f ~ ~ ~ ~ 0 ~ wa5 ~ e ~ d 6y a p~5e 5hape ~ r 1 m ~ n m ~ h 0 d 6a5ed 0n the ~ ~ ~ . A ~t~ ~ r 1 ~ 0f the 5 p e ~ r 0 m ~ 5et up and ~ r 1 m ~ a t 1 0 n ~ n ~ are 91ven 6y M c 8 ~ h et aL (1971). U n ~ 0f the ~ ~ ~ 5 ~e ~ ~ n 5 ~ e n e ~ y ~9r16uf10n5 wa5 ~ e d 0ut uf1n9 the ~ f 1 ~ ~ ~ 1~1). ~ e ~ m m a m ~ p ~ h~9ht ~ f 1 ~ 5 ~ ~ ~ ~ ~ • ~f16ut10n5 6y uf1n9 the matr1x ~ m~h0d (K0~v~0% 196~. C~c~n5 0f the ~ neu~0n f1uxe5 and e n e ~ ~9r16ut10n5 were c a ~ e d 0ut 6 e ~ n d ~ th~kne~e5 0f p 0 ~ e ~ e n e and ~ p ~ e uf1n9 the ~ n ~ verf10n 0f the AN15N c0de ~ 5 ~ ~ ~ n 9 1 ~ 198~ ~ r deep penetrat10n5. ~ e EUR ~ 8 1515 c0u~ed neutr0n and 9 ~ m a cr055 5~t10n ~ 6 r a ~ wa5 u5ed ~ ~ e pre5e~ c~c~at10n5. 7he c~c~at10n5 were carr1ed 0ut ~ r 5pher1c~ ~ 0 m ~ ~ 5~ ~0~m~0n. ~ e 50urce r e p r e ~ a f 1 0 n ~ the AN15N c~c~af10n ~ ~ k e n a5 ~ f 1 6 u ~ d v 0 ~ m e 50urce. 7he AN15N c~c~af10n were n 0 ~ d t0

~

104

"t (cm)

~

10 3

5

102

10~x10-1 -~%~.

~ 0

~-~.~.~ °. •

~£~ 10~

..... F.0~.. . . . . . . .

~ ~ ~= 100

15~

x1~ ~ % ~

"°, "0 •

~

~

"

....)10-2 0

1

1

1

[

1

1

1

1%1

1

2

3

4

5

6

7

8

1

9

10

E n (MeV)

N ~ 1. ~ u ~ ~d ~ N~ ne~mn ~ a • ~t th~kne~e5 0f pNy~h~ene.

6eN~d

91ve the t0ta1 50urce ~ren9th 0f the Pu-~-8e 50urc~ 7a61e 1 5h0w5 neutr0n ener9y 9r0up 5tructure5 0f EUR L18 1515 cr055 5ect10n f16rary (Herren6er9eL 1982). ~ RE5UL75 AND D15CU5510N

Mea5urement5 and ca1cu1at10n5 0f the fa5t neutr0n f1uxe5 and ener9y d1~r16ut10n5 6eh1nd d1fferent th1ckne55e5 0f p01yethy1ene (t = 5, 1~ 15 and 20cm) were 5h0wn 1n F19. 1. F19ure 2 5h0w5 the mea5ured

7ech~c~ Nme 105 ~

949

10 4 • ~

M ~ d

-

C~c~ed

-

--x--

2•1°°3•°4

Mea5ured

1

10 3

~~ ~

• • ~ • • • • ~ •• • ~ * ~

~

:111,"

10 3

~ ~ ~

27

••0 •0

10 0

°•~••

~

2

•

•

•

~

x~

x

,

•

•

10-1

"••

1

0

••

10 2

•

10 -2 0

1 1

[ 2

1 3

1 4

1 5

1 6

1 7

1 8

1 9

-

1 10

~ (MeV) N ~ 2 . Mea5ured and ca1cdated N~ neutr0n ~ectra~h1nd • ~rem ~ne55e5 ~ 9r~e.

~

.

•

2

10;

•

10 3

: ~

and c~cu1a~d fa5t neutr0n 5pectra f0r 9raph1te 0f 9.5, 19 and 27 cm th1ckne55. 1n each 0f the a60ve f19ure5 the neutr0n 5pectra have a p p r 0 ~ m a t e ~ the 5ame pr0f11e 0f the Pu-~-8e 50urc~ Each 5pectrum c0nt~n5 the 5ame maf1ma and m1n1ma 0f the 50urce. 7he neutr0n 1n~nf1f1e5 decrea5e w1th the 1ncrea5e 0f the ma~r1~ th~kne~. A re50na61e a9reement 6etween mea5ured and c ~ c u ~ d fa5t neutr0n f1uxe5 f0r p01yethy~ne wa5 06t~ned a5 5h0wn 1n F19. 1. 7he c~cu1a~d f1uxe5 f0r 9raph1te ~ h19her than the mea5ured v~ue5 at E~<3.3MeV. 7h15 may 6e attr16uted t0 de~ct5 1n the cr055 5ect10n data 5et f0r 9raph1te 1n the 10w neutr0n ener~e5 6e10w 3.3 MeV. 7he 109ar1thm~ ener9y decrement (x) and the f10w1n9 d0wn p0wer ~E~) f0r 9raph1te ~ ~55 than that f0r 0ther m0derat0r5 f1ke water 0r p01yeth~ene (Ether1n9t0n, 1958L 0 n the 0ther hand the m0derat1n9 rat10 (a~a~) f0r 9raph1te 15 h19her than that f0r water 50 ~ ~ expected that 9raph1~ m0derate5 fa5t neutr0n5 and ref1ected therm~ neutr0n5 m0re than 0ther kn0wn ref1ect0r5 re5u1t1n9 1n an 1ncrea5e 1n the pr0p0rt10n 0f the 10w ener9y neutr0n5. 50 the f1ux 1n~n5~y 0f fa5t neutr0n5 ~ak1n9 ff0m 9raph1~ ~ h19her than that 0f the 5ame th1ckne~ 0f p01yethy~ne a5 5h0wn 1n F195 1 and 2. F0r c0mpar150n5 ~ w0u1d 6e m0re appr0pf1a~ t0 c0nvert the exper1menta1 data (0.2MeV w1de 61n 5tructur~ t0 the c0rre5p0nd1n9 ca~u1a~d ener9y

10 4

"×N~1~

10 2

10 2

~

~

65 10 2

101 0

5

1 10

1 15

20

t(cm) F1~ 3. C ~ c ~ e d and avera9e mea5ured f1uxe5 ~ 9r0up5 1~5 f0r pdyethy~ne.

9r0up 5tructure (7a61e 1). 7h15 wa5 1nd~ated 1n F195 3 and 4 a5 an avera9e mea5ured f1ux 1n 9r0up5. F19ure5 3 and 4 5h0w that the fa5t neutr0n f1uxe5 decrea5e exp0nenf1a11y w1th the 1ncrea5e 0f the p01yethy1ene and 9raph1te th~kne5~ re5pect1ve1y. F19ure 5 5h0w5 the mea5ured 9amma ray 5pectra 6eh1nd d1fferent th~kne55e5 0f p01yethy1ene. 7he 5pectra are appr0x1mate1y f1mf1ar and have the character15t1c5 0f 9amma 5pectrum emRted ff0m the Pu-a-8e 50urce. 7he f19ure 5h0w5 that the 9amma ray f1ux 1nten~ty decrea5e5 w1th the 1ncrea5e 0f the p01yethy1ene th1ckne55 f0r a11 9amma ray ener~e5. 7he f19ure 5h0w5 a150 an 1ncrea5e 1n the 10w ener9y

950

7echn1ca1 N0~

105

104 ~

×-- M ~ d Ca1cu1ated

-

~ "" ~ ~ ~

--~--

cm)

-- 104

x~

~ ~ ~~ ,• , ~ ,

~

x~

"~

1] ".~

~ ~'~

~

~ x

10~

~2

104

" ~4 ~

.

103

~

, N

~

~

~

~ 1~3

10:

63 ~ ~ ~

102 66

~0~

102

1

1

1

1

10

20

~0

~0

t (cm)

,0,1-, 0

1

2

3

4

5

6

E~(MeV)

F ~ ~ CMc~Med and aver~e me~u~d f1~e5 M ~ 0 ~ 5 1~ ~r 9raph~

F19 5. Mea5ured 9amma ray 5pectra 6eh1nd d1fferentth1ckne55e5 0f p01yethyMne.

9amma ray5 due t0 the effect 0f 6u11d up fact0r wh1ch ~ m0re pr0n0unced at 10w ener91e5. C0mpt0n 5catter1n9 pr0ce55 ha5 the ma1n c0ntr16ut10n 1n the 1nteract10n 0f 9amma ray5 w1th p01yethy1en~ 7he character15t1c 2.23 MeV capture 9amma peak due t0 the capture 0f therma1 neutr0n5 1n hydr09en nuc1e1 0f p01yethy1ene wa5 h1ndered 6y the c0nt1nu0u5 part 0f the 5pectrum wh1ch ~ ma1n1y due t0 C0mpt0n 5cattered ph0t0n5 (C0mpt0n ta10 1n add1t10n t0 the re1at1ve1y 10w capture cr055 5ect10n 0f hydr09en wh1ch decrea5e5 w1th 1ncrea51n9 neutr0n ener9y and the 10w f1ux den51ty 0f therma1 neutr0n5 1n the med1um. 50 the capture 9amma ray5 1n the hydr09en 0f the p01yethy1ene ~ec0ndary 9amma ray~ have a 5ma11

c0ntr16ut10n 0n the t0ta1 9amma ray f1ux 6eh1nd p01yeth~ene where the pr1mary 9amma ray5 have the mMn c0ntr16ut10n. F19ure 6 5h0w5 the mea5ured 9amma ray 5pectra 6eh1nd d1fferent th1ckne55e5 0f 9raph1te. 7he 5pectra are ~mf1ar and have the 5ame 5pectrum 5hape 0f the Pu-~-8e 50urce. 7he 9amma f1ux 1n~nf1ty decrea5e5 w1th the 1ncrea5e 0f the 9raph1te th~kne~. Fa5t neutr0n5 under90 1neM5t1c 5caaef1n9 w1th 9raph1te pr0duc1n9 4M2 MeV 1nda5f1c 9amma peak. A5 the capture cr055 5ecf10n~ a650rpt10n cr055 5ect10n5 and 5catter1n9 cr055 5ect10n5 0f 9raph1te are very 5ma11 and decrea5e w1th the 1ncrea5e 0f the neutr0n ener9y. 50 the 5ec0ndary 9amma ray 1n 9raph1te ha5 a very

7echn~a1 N0te 105 •

951

104

~ X ~ ~~ ~ - - × - -

6raph1te P01yethy1ene

t (cm) 9.5 ×,

104

~ ~ ~

•

~• ~ 103

~ 103 1 .. ~ 0

• •

..••"

1::.. ~ , *

1•

,~::~

"~ .

~ 1 .

~~

~, ~ 0~"

. 1 . e~

"•:1:1 : :

~ ; : ~

1

~ 1

•~,1 ~

a1

102 t (cm)

4Q

~ ~-.

9.5

~--

19

2x ~0~ 0

1

1

1

5

10

15

20

1

1

25

30

t (cm) 9 ~ 27 101 0

1 1

1 2

1 3

1 4

1 5

F1~ 7. Mea5urex1 1nte9ra1 fa5t neutr0n f1uxe5 f0r d1fferent th~kne55e5 0f p01yethy1eneand 9raPh1te. 1 6

ev¢~ev~ F19. 6. Mea5ured 9amma ray 5peetra 6eh1nd d1fferent th1ckne55e5 0f 9raph1~.

5ma11 c0ntr16ut10n 0n the t0tf1 9amma ray5 1n~nf1ty 6eh1nd 9raph1te 5amp1e5. 7he attenuat10n 0f fa5t neutr0n5 and 9amma ray5 0f the wh01e ener9y ran9e (f0r p01yeth~ene and 9raph1te) wa5 5h0wn 1n F195 7 and 8, re5peet1ve1y. 7he mea5ured neu~0n macr05c0p1c rem0v~ cr055 5ect10n5 f0r the wh01e neutr0n ener9y (1.4-10.6 MeV) were f0und t0 6e ~1845 cm-~ f0r p0~ethy1ene and 0.1153cm-~ f0r 9raph1t~ 7he 9amma t 0 t ~ attenuat10n c0eff1c1ent5 f0r the wh01e 9amma ener9y ran9e (0A 1-7.5 MeV) were mea5ured f0r p01yethy1ene and 9raph1~. 7he 06ta1ned va1ue5 are 0.1113 and 0.0978 9~4- t f0r p01yethy1ene and 9raph1te, re5pect~d~

F19ure5 9 and 10 5h0w the mea5ured neutr0n f1uxe5 at d1fferent ener91e5 a5 a funct10n 0f p01yethy1ene and 9raph1te th1ckne5~ re5pe~t1ve1y. 7he der1ved va1ue5 0f fa5t neutr0n macr05c0p~ t0ta1 cr055 5ect10n5 (E) f0r p01yethy1ene and 9raph1te at d1fferent ener91e5 were 06ta1ned w1th the a1d 0f the5e f19ure5 and the data were ta6u1ated 1n 7 a 6 ~ 2. 7 h ~ ta61e c0nta1n5 a150 the ca1cu1ated macr05c0p~ t0ta1 cr055 5~ct10n5 f0r water der1ved ~ 0 m the f0rmu1a: EH~0 = 60 (Num6er den51ty 0f 0xy9en) + 6u (Num6er den51ty 0f hydr09en)

(1)

whcre 60 and 6u are the m1cr05c0p1c t 0 t ~ cr055 ~ct10n5 f0r 0xY9en and hydr09e~ re5pect1vd~ and were taken ~ 0 m the E N D F 8 - 6 data 5et. 7 a 6 ~ 2 c0nta~5 ~50 the rehxaf10n ~n9th5 f0r p01yethy1en~ 9raph1~ and wate~ Mea5ured 9amma ray f1uxe5 at ~ffemnt ener91e5

952

7eehn1ca1 N0te 104 _ :

5 x 104 --

x

--e---x--

x

:,

6rap~ P~ye~y~ne 103

•

~ 104

104 ~

2

~,~ En(MeV) •

103

~,,,,

"• x2

-~"

103

• ~

~,,

~

~ 2

10 3

1 5

1 10

1 15

1 20

1 25

~

..~ ~ . ~

~

•..

•.

•

~ ...0"~~,,~

"~ "•.

1••••

1 30

t (cm) F19. 8. Mea5ured 1n~9rM 9amma ray f1uxe5 f0r d1fferent th~kne~e5 0f p0~ethy~ne and 9 r a p h ~

a5 a funct10n 0f the p01yethy1ene and 9 r a p ~ t~ckne55e5 a ~ 5h0wn ~ F195 11 and 1L ~5pect1ve1y. 7he der1ved vMue5 0f 9amma hnear at~nuaf10n c0eff1c1ent5 at ~fferent ener91e5 f0r p01y~hy~ne, 9 r a p ~ and water were t a 6 d a t e d ~ 7 a ~ e 3. 7he vMue5 f0r p ~ y e t h ~ e n e and 9raph1te were 06t~ned ff0m F195 11 and 1L re5pecf1vd~ 7he vMue5 f0r w a ~ r were taken fr0m W00d (1982). 7a61e 3 c0nt~n5 ~50 the re1axat10n ~n9th5 f0r the p01yethy1en~ 9raph1te and wa~L Fr0m 7a61e5 2 and 3 ~ ~ ef1dent that p d y e t h ~ e n e 15 6et~r than 9raph1te 0r w a ~ r ~ 0 m the 5h1dd1n9 p ~ n t 0f f1ew. 1n add1t10n R5 6 w denf1ty c0mpared w1th water make5 p ~ y e t h ~ e n e m0re p r e ~ r a ~ e than w a ~ r ~ the f1dd 0f pr0pdf10n r e a ~ 0 ~ where w~9ht 0ther than c05t 8 0f pr1me c0n~derat10n. A 8 0 p 0 ~ h y ~ n e can re~ace water f0r 0ther 5h1e1d1n9 app1~at10n5 w h e ~ the 5h1dd ~ n0t exp05ed t0 ~ 9 h ~mperature5 and M50 a5 a 5 ~ d d f0r p 0 ~ a ~ e radht10n 50urce~

101 0

1

1

1

1

1

1

5

10

15

20

25

30

t (cm) ~

9. Mea5ured ~ ne~r0n f1~e5 ~ h ~ d ~ r e ~ t ~ ne55e5 ~ pdy~h~ene ~ r ~ r e ~ ene~e5.

~ C0NCLU510N5

1. AN15N cMcu1at10n5 u~n9 the EUR L18 15/5 cr055 5ect10n5 data 5et and P3516appr0x1mat10n w1th 5pher1cM 9e0metry were ade4uate t0 m 0 d d the expedmenta1 data and hence ff appear5 that the data 5et 15 5at15fact0ry and f0r p0~ethy~ne need5 n0 m0d1f1cat10n 1n the ran9e 1~6-1A MeV neutr0n5. F0r 9raph1te there ~ 50mewhat w0r5e a9reement at 10wer ener#e5 6e10w 3.3 MeV due t0 a p05~61e de~ct 1n the data 5et 1n th15 ener9y ran9e. 2. 7he 5t116ene 5c1nt111at10n 5pectr0me~r 5y~em

7echn1ca1 N0te

953

104

104 L "X

103

103 x~.xxEn(MeV) •xx

~

~

2 ~

103

"~,~,

~~%~%%% %%%%%X

0

4

~

102

~

2

103

3

102

-6

••••x

~

•

7

6 0•• •0

101

1~ r

~.. • 5

"•x 5 101

1

1

10

100

•1

20

0

30

1 5

[ 10

t (cm)

[ 15

[ 20

1 25

t (cm)

F19. 10. Mea5ured fa5t neutr0n f1uxe5 6eh1nd d1fferent th1ckne55e5 0f 9raPh1te f0r d1fferent ener91e5.

F1~ 11. Mea5ured 9amma ray f1uxe5 6eh1nd d1fferent th~kne55e5 0f p01yethy1ene f0r d1fferent ener91e5.

7a61e 2. Fa5t neutr0n macr05c0p1c t0ta1 cr055 5ect10n5 (2) and re1axat10n 1en9th5 (k) f0r p01yethy1enc, 9raph1tc and water

E~ (MeV)

P~y~h~cn~ 2~

2 3 4 5 6 7 8

~

0.1783 0.1929 0.1860 0.1793 0.1774 0.1810 0.1860

Wa~r

6rap~tc

2~

2~

-~

5.61 5.19 5.38 5.58 5.64 5.53 5.38

0.1049 0.1245 0.1210 0.1050 0.1033 0.1078 0.1446

2~

1~

-~

2cm

9.53 8.03 8.26 9.52 9.68 9.27 6.91

0.2485 0.1939 0.1969 0.1423 0.1487 0.1157 0.1047

4.02 5.15 5.08 7.03 6.73 8.64 9.55

7echn1ca1 N0te

954

7aMe 3. 6amma ~n~r attenuat1~ c0e~dent5 (~) and ~1~at10n ~ n ~ E (MeV)

P~y~h~ene #~

1 2 3 4 5 6

~

0.1842 0.0967 0.1003 ~1255 0.1510 ~0590

6raph1~ 9~-~

2~

9~-~

5A3 10.33 9~7 797 6~22 16~5

0.0928 0.0870 0.0949 0.1452 ~0675 ~0764

1~78 11A1 10.54 6.89 14~2 13~8

-~0493 ~0396 ~0339 0~301 0,0275

A~

-2028 25.25 29.50 33.22 3~36

ha5 pr0ved t0 6e an effect1ve t001 f0r check1n9 the accuracy 0f the neutr0n cr055 5ect10n f16raf1e5 and the neutr0n tran5p0rt c0de~ 3. P01yethy1ene 15 a 6etter rad1at10n attenuat0r than 9raph1te and wate~ 7heref0re R can rep1ace water 1n m0611e react0r5 and 1n 0ther app11cat10n5 where the 5h1e1d ~ n0t exp05ed t0 h19h temperature. P01yethy1ene can a~0 6e u5ed a5 a 5h1e1df0r a p0rta61e rad1at10n 50urce.

~0

103

"~

E~(MeV)

~

"~0

•

•

~

.~.

REFERENCE5

8 e d n a ~ A. (198~ Rad1at10n 5h~1d5. Pr2e~ad 7ech~c25ny, Waj5k0wy. En#e W.W. (198~ AN15N, a 0 n ~ m e n ~ 0 n ~ d ~ c ~ 0 r d ~ e 5 9an5p0~ c0d~ U5AEC Rep0~ K-1693 (196~. AN15N We5t1n9h0u~ ver~0n (AN15N-W), 1985, fr0m NEA D ~ a 8 a n k Ethef1n~0n H. [Ed.] (1985) Nuc1ear En91neer1n9 Hand 800k. Mc6raw H1~ New Y0rk. He~en6er9er K (198~ EUR L18 15/5 c0u#ed neutr0n9amma cr0555ect10n 116rary, 7M~2821 ~ fr0m NEA D ~ a 8ank. Jae9er R. 6 . [Ed~ (197~ En#neef1n9 C0mpend1um 0n Ra• af10n 5h1e1~n~ V01.11, 5h~1d1n9 M a t e r ~ 5pf1n9eL 8er11n. K0Mvm0v Yu. 1. (196~. V0p. D0~ 2a5ck 12-Luchen~ 1~ 131. K0te9awa H. K. (199~ Japan AER1, 70ky0 131 ~ JAER1M 9017~ 0ct06er 1990. Kuchar J. (198~ Rad10150t0py Pra9ue C2ec• 30, 233. M c 8 ~ h 6 . W., W1nyard R. A. and L u t ~ n ~ E. (1971) K0chL19ht La60rat0r1e5 Ltd., C 0 ~ 6 r 0 0 ~ 8uck~ U.K. Pr1ce 8. ~ , H0~0n C. C. and 5#nney K. 2 (195~ Rad1at10n 5h~1d~9. Per9am0~ L0nd0m 5a~0r R. K (198~ C0n~rence 860, V01.1 5AND8%0098,

103

102

~

Ackn0w1ed9ement--7he auth0r5 ~ke t0 thank Dr E. Am1n, Nuc~ar 5afety Cenm~ At0m1c Ener9y Auth0f1t~ C~r0, E9ypL f0r mak1n9 av~h61e the c~cu1at10n5 uf1n9 the AN15N c0de.

~

0

~

Wa~r

2~

10 4 - -

~"

(2) f0r p~yet~1en~ ~apM~ and water

5

10 t

133 p ~

n0° 0

1

1

1

1

1

1

5

10

15

20

25

30

t (cm) F1~ 12. Mea5ured 9amma ray f1uxe5 6eh1nd d1fferent th1ckne55e5 0f 9raph1te f0r d1fferent ener91e5.

5ek1m0t0 H. (198~ £ NucL M a ~ 1331134, 88~ 5 ~ p m a K. (198~ 1NDCND5 233 6 ~ 1AEA V1enna 26~ p. 237. 71pt0n C.R. (196~ Rea~0r Hand 800k M a ~ r ~ V01.1. 1n~r~1ence, New Y0rk. 70m5 M. ~ (1971) NucL ~5trum. Meth. 9 ~ 61. W00d 2 (198~ C0mputat10na1 Meth0d5 ~ React0r 5h1e1d1n9. Per9am0~ 0 x ~ r d .