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Tic ЛГЬ. 94 ? K F K I - 7 5 - 2 1

L . K O B L I N G E R J . P Á L F A L V I

MONTE CARLO CALCULATED SPECTRA OF NEUTRONS TRA N SM ITTED THROUGH AND REFLECTED FROM

HOMOGENEOUS POLYETHYLENE SLABS

cj

H u n g a ria n A c a d e m y o f S c ie n c e s

C E N T R A L R E S E A R C H

I N S T I T U T E F O R P H Y S I C S

B U D A P E S T

(2)

2017

(3)

K F K I - 7 5 - 2 1

MONTE CARLO CALCULATED SPECTRA OF NEUTRONS TRANSMITTED THROUGH AND REFLECTED FROM

HOMOGENEOUS POLYETHYLENE SLABS

L. Koblinger, J. Pálfalvi Health Physics Department

Central Research Institute for Physics, Budapest, Hungary February 1975

Work supported by the

International Atomic Energy Agency under Research Contract No. 1115/RB and Research Agreement No. 889/Rl/CF

ISBN 963 371 020 О

(4)

Transmission and reflection of 14.5 MeV and fission neutrons are calculated for polyethylene shields of thicknesses from 5 to 40 cm. The 48 group spectra are calculated by the Monte Carlo code 05R5S and plotted by the code TRESSPASS. Characteristic quantities of the spectra, average ener­

gies, thermal and fast fractions, as well as the transmission or reflection probabilities are also given.

АННОТАЦИЯ

Даются спектры нейтронов, прошедших через однородные слои полиэти­

лена или отраженных от них. 48-групповые спектры были вычислены с помощью программы 05RS5S Monte Carlo и вычерчены с помощью программы TRESPASS.Для каждого спектра приведены вероятности и прохождения или отражения, средняя энергия, а также доля тепловых и быстрых нейтронов.

KIVONAT

Homogén polietilén rétegeken áthaladt, illetve azokról visszavert neutronok spektrumát közöljük. A 48 csopotos spektrumokat az 05R5S Monte Carlo programmal számoltuk és a TRESPASS programmal rajzoltattuk fel. Minden spekt­

rumra megadjuk az áthaladási vagy visszaverődési valószinüséget, az átlagener­

giát és a gyors, illetve termikus hányadokat.

(5)

1. Introduction

In neutron dosimeter evaluation one of the most critical points is the knowledge of the spectrum of the neutrons. As a measurement of the spectrum in every case is practically impossible a compendium of spectra calcu­

lated for and/or measured in typical situations (typioal shield materials, thicknesses, input spectra and geome­

tries} could well be used.

The International Atomic Energy Agency (IAEA) sup­

ports this work in which our Institute participates, on the basis of Research Contract No. III

5

/RB and Research Agreement No.

8 8 9

/Rl/CF.

We have developed a special version of the

0 5

R pro­

gram for the calculation of the speotra of neutrons trans­

mitted through or reflected from different homogeneous

slab shields. This code, the 05R5S (Koblinger, 197^) prints and punches out the speotra.

Two other codes, the TRESPASS (Pálfalvi, 197^0 and SPECTRANS-2 (Pálfalvi, 1973 ) plot the computed spectra and calculate some of their characteristic quantities.

Some speotra calculated for water shields were pub­

lished earlier (pálfalvi, Koblinger, 197^)» in the present report results obtained for polyethylene shields are

given.

Although for dosimeter evaluation only the shape of a spectrum is interesting and not the attenuation, all the quantities calculated are presented here as it is hoped that our results can be used in other fields.

2. Comments on the calculations

The 05R5S calculates the spectra by Monte Carlo technique using the collision density method, i.e. the transmission and reflection probabilities are determined after each scattering, regarding the incidence of a

neutron as the scattering. This method results in

(6)

better statistics in comparison with the analysis of the really escaping neutrons.

The 05R5S prints and punches out the number of the transmitted or reflected neutrons in 49 energy groups.

The energy limits and the mean energies for 48 groups are given in Table 1, the 0 th contains the thermal neu­

trons. The coefficients of variation are also calculated and edited for every group.

Details of the calculation method are given in the description of the 05R5S code (Koblinger, 1974).

The calculations were performed using the following parameters:

a/ for cross section handling, the energy super­

groups of the

0 5

R code were divided into 128

subgroups (for details: see Lux, Koblinger, 1973) b/ the cutoff energy under which the neutrons are

considered as thermal, was

0 . 5

e V ;

с/ for thermal neutrons the non-absorption proba­

bility was set to 0.99437, the mean free path length was chosen to be 0.2494 cm. These values were calculated by the code

T H E R M O S

(Gadö, 1973).

d/ the scattering angular distribution for the

hydrogen was assumed to be isotropic, whereas for the carbon the distribution was approximated by a Legendre expansion of

6

terms. The Legendre coefficients are given for 64 subgroups in every supergroup.

З. Comments on plotting

From the 05R5S results code TRESPASS determines the

^ ( u ) = E * ф (

e

) spectra (neutrons per unit lethargy

interval) normalized to unit incident neutron.

(7)

3

Table 1

standard energy

EV 1

2

.

17010

E

-01 2 3

.

5356

ПЕ

-01 3 7

.

0715

ПЕ

-01 4

1 .

4663

О E 00

5 3

.

161

О

0

Е On 6 6.

8191

ПЕ

00 7 1

. A6630E

01

8

3

.1

619

0 E 01

9

6.В

1

о 1 OE

01

iO

1

.

466

ЗОЕ О?

,1

3

,1

619

ОЕ О?

6

.

810

ЮЕ

02 13 1

6630

Е

03 : а з.

1610

ое 0.3 15

6.Я1

9

1ОЕ

03 16 1

.

12200

Е ОА

17 1

.A

1

Z

50

E ОА

18 1

.

78160

Е ОА

19 2

.

23850

Е ОА

20 2.81820

Е ОА

21 3

.

5

А

780

Е ОА

22 А.А6630Ё ОА 23 5

.

62260

Е ОА

2

А

7.07820

Е ОА

25 8

.

911

70Ё ОА

26 1

.

12200

Е

05 27

Í

*412506 05 28 1

.

781

6ОЕ

05 29 2

.

23

R

50

E

08 30 2

.

81820

Е

05 31 3

.

5

А

730

Е

05 32

А.А

6630

Е

05 33 5

.

62260

Е

05

ЗА

7

.

07820

Е

05 35

Я.

911?0

Е

05 36 1.122

О О Е Об

37 1

1250

С G6 ЗЯ

1

.

7

8

1

6ОЕ

06 39 2.23850Е 06

АО

2

.

31

8

2

ОЕ

06

А1

3

.

5

А

7

ЯОЕ

06 42 А.А663ПЕ Об 43 5.62260

t

06 44 7

.

07

Я

2

ОЕ

06 45 8

.

911

70Е

06 46 1 112?0ОЕ 07 47 1 . А125ОЕ 07

А Я

1

.

7

8

1

6 О Е

07

limits

от

the е F9

1 f l ö 4 5 0 t - 0 1 2 . 5 0 0 0 0 5 - 0 1 5 . 0 V 0 0 0 5 - 0 1 1 0 0 0 0 0 5 00 2 . 1 5 0 0 0 5 00 4 . 6 5 0 0 0 5 00 1 . 0 0 0 0 0 5 01 2 . 1 5 0 0 0 5 01 4 . 6 5 0 0 0 t 01 1 . 0 0 0 0 0 5 02 г .1 50005 02

4 . 6 5 0 0 0 5 02 1 . OOOöOt 03 2 . 1 5 0 0 0 5 03 А . 6 50 0 0 5 03 1 . 0 0 0 0 0 5 ОА 1 2 58 0 0 5 ОА 1 . 5 9 4 8 0 5 04 1 9 9 5 1 0 5 04 2 . 5 1 1 7 0 5 ОА 3 . 1 6 2 0 0 Ь ОА 3 . 9 Я 0 5 0 5 ОА 5 . 0 1 1 2 0 5 ОА 6 308 60 5 оА 7.941805 с,С 1 . 090 00 5 05 1 . 2 5 8 9 0 5 05 1 . 584805 05 1 . 9 9 5 1 0 5 05 2 . 5 H 7 0 f c 05 3 . 1 6 2 0 0 5 05 3 . 9 8 0 6 0 5 05 5 . 0 1 1 2 0 ь 0 5 6 . 3 9 8 6 0 5 05 7 . 9 4 1 3 0 5 ;j5 1 . 0 9 0 0 0 5 0 6 1 . 2 5 8 9 0 5 г,6 1 584 30 5 об 1 8 9 5 1 0 5 об 7 . 5 1 1 7 0 5 06

3.162005 Об

3.9 Я 0 6 0 5 06 5 . 0 1 1 2 0 5 об 6 308 60 5 об 7.941805 Об 1 . 0 9 0 0 0 5 0/7 1 . ? 58 п о6 07 1.584305 07

ЕЦFRGY OKnijRS Е Е V

2 . 5 0 9 9 0 P - Ü 1 5 . 0 0 0 U O E - 0 1 1 . O OO 9 0 F Оо 2 . 1 5 9 9 0 E Оо A . 6 5 9 9 0 F 00

1 . 0 0 9 0 0 E O v 2 . 1 5 O Ü 0 E Ü1

A . 6 5 0 0 Q E 01 1,00у00? О?

2 . 1 5 0 9 0 Е О?

A . 6 5 9 O 0 F 02

1 . 0 0 ° 9 0 Е Os 2 . 1 5 9 0 0 F От А. 6 5 ОО0 Р 03 1 . 0 0 9 O 0 F 04 1.2 589О Е 04 1.5ЯА00Е 04 1.99510F 04 2.511 б О F 04 3.162U0P 04 3.98O50F 04 5.01 1 б о F 04 6.30Ö60F 04 7,9418ОF ОД 1.OOUOOE Os 1.?5ÖV0E 05 1.58<*80Е 0S 1.9981ОЕ 05 2.511бОЕ 05 3.16^О0е О5 3.9Я060Е 05 5 ,01120Е 05 6.30Ö60F 05 7 , 9 41®ОЕ 05 1.00UÜOF 06 1 .2 5 89 О F 0Л 1.5Я“в0р Об 1 ,99 91 ОF Об 2.51160F Об 3.16«:О0Е Об 3.9806о F Об 5.0112 О F Об

6.3 0 86 о f r Об

7.94180F Об 1,009О о F 07 1.258V0F 07 1. 5 Я ^8о F 07 1.99 э 1 ОЕ 07

IFTHARGT INTERVALS

9 . 2 8 3 0 9 . 6 9 3 0 9 . 6 9 3 0 9 . 7 6 6 0 9 . 7 71 О 9 . 7 6 6 0 9 . 7 6 6 0 9 . 7 7 1 0 9 , 7 6 6 0 1 = ^ 9 . 7 6 6 0 9 , 7 7 1 О 9 . 7 6 6 0 9 . 7 6 6 0 9 . 7 7 1 0 9 . 7 6 6 0 9 . 2 3 0 0 9 . 2 7 0 0 9 . 2 3 0 0 9 . 2 3 0 0 9 . 2 3 9 0 9 . 2 3 0 0 о . 2 3 0 0 9 . 2 3 0 0 о , 2 7 0 0 9 . 2 3 0 0 9 . 2 7 0 0 о , 2 7 9 0 9 . 2 7 0 0 о . 2 7 9 0

о.гзоо

9 . 2 7 0 0 9 . 2 3 9 0 9 . 2 3 0 0 9 . 2 3 0 0 о . 2 3 0 0 9 . 2 3 0 0 о . 2 3 0 0 о . 2 3 0 0 о . 2 3 0 0 9 . 2 3 0 0 9 . 2 3 Ü Q 9 . 2 3 0 0 9 . 2 3 0 0 о , 2 3 0 0 9 . 2 3 0 0 9 . 2 3 0 0 9 . 2 3 9 0 9 . 2 3 9 0

(8)

It should b e n o t e d that by this n o r m a l i z a t i o n only

U„ u.

jif>Íu.)du. c

1

= du.

u ...

is satisfied but for a given group ^'(u^) may exceed

1

. Before plotting the spectra the following two trans­

formations are carried out, if necessaryC

a/ If monoenergetic incident neutrons are considered the upper limit of the last energy interval is replaced by the source energy as there are no neutrons with ener­

gies higher than this value. If the new last energy in­

terval obtained by this method is shorter than one tenth of the original interval the last and penultimate inter­

vals are united.

b/ In the case of plotting of thermal neutrons, their distribution is assumed to be Maxwellian. The peak of the t|>(u) distribution is at E=1.5 kT (=0.0379 ev) and the differential fluence at this point is

3

ills'

tK = O.hGb

times the f l u e n c e of the t h e r m a l group.

(The r e a l d i s t r i b u t i o n sl i g h t l y d i f f e r s f r o m the

M a x w e l l i a n but g e n e r a l l y n e i t h e r the lo c a t i o n n o r the h e i g h t of the p e a k is shi f t e d by m o r e than ^-5 p er o e n t ,

t h e r e f o r e if this m i n o r e f f e c t had b e e n taken into a c c o u n t the p l o t t i n g p r o c e d u r e w o u l d h a v e be e n u n n e c e s ­ sarily c o m p l i c a t e d .)

T h e code plots the s p e c t r a as s t e p f u n c t i o n s m a r k ­ ing the s t a n d a r d d e v i a t i o n also. T he thermal p e a k is r e p r e s e n t e d by an "X".

(9)

■I. R e s u l t s and C o n c l u s i o n s

R u n s h a v e been c a r r i e d out Г о г three inc i d e n t sources a/ m o n o e n e r g e t i c sour c e of l't.5 MeV, cosi n e a n g u l a r

d i s tr ibut i o n ,

b/ m o n o e n e r g e t i c sour c e of 1^.5 MeV, p e r p e n d i c u l a r i n c i d e n c e ,

с/ f i s s i o n source: the e n e r g y d i s t r i b u t i o n is given by the Watt, f o r m u l a (cosine a n g u l a r distribution) . F or a l l the three c a s e s s h i e l d t h i c k n e s s e s of 5» 10, 20 and 2o c m are considered. T h e r m a l n e u t r o n s ar e treated only f o r 5 and 10 cm thick slabs to save r u n n i n g time, w h i c h i n c r e a s e s by a f a c t o r of two even in the c a s e of

thickness of 10 cm and g rows r a p i d l y w i t h i n c r e a s i n g t h i c k n e s s .

The spectra are g i v e n in Fi g s 1 - 2 U.

T he s t a t i s t i c s f o r the t r a n s m i t t e d n e u t r o n s w o r s e n if the t h i c k n e s s i n c r eases or the i n cident ener g y d e ­

creases. F o r instance, the time spent in c o m p u t i n g of the t r a n s m i s s i o n of f i s s i o n n e u t r o n s through 2o cm w a s more than h times h i g h e r than that spent f o r c o m p u t i n g n e u t r o n s of l 2 .5 M e V b ut the s t a t i s t i c s are p o o r e r f or the f i s s i o n n e u t r o n s (see Fig. 2')). It m u s t be m e n t i o n e d h e r e that the u n c e r t a i n t y d e c reases if f e w e r energy g r o u p s are used.

This effect is i l l u s t r a t e d in Fig. 22a, w h e r e the mean of 2 f l u x v a l u e s is taken.

T h e f o l l o w i n g c h a r a c t e r i s t i c data a re c a l c u l a t e d by code S P E C T R A N S - 2:

a / t r a n s m i t t e d or r e f l e c t e d f r a c t i o n : N,j,/N or N / N , where N is the n u m b e r of i n cident ne u t r o n s , N,^

and N are the n u m b e r s of n e u t r o n s t r a n s m i t t e d a nd r e f l e c t e d , respeo t i v e l y ;

I)/ a v e r a g e energy:

(10)

w h e r e N, is the n u m b e r of n e u t r o n s and E, is the

к ^ к

s t a n d a r d (mean) e n e r g y f o r the к g r o u p (for the r m a l n e u trons, the a v e r a g e e n e r g y is

E = 0 . 0 ^ 0 2 eV - c a l c u l a t e d f r o m the r e s u l t s of о

the code T H E RMOS);

с/ f a s t n e u t r o n f r a c t i o n of the t r a n s m i t t e d or r e f l e c t e d n e u t r o n s : N p / N ^ or ( Np, is the n u m b e r of n e u t r o n s w i t h e n e r g i e s h i g h e r than

2.5 M e V ; c o n s i d e r e d a s fast n e u t r o n s ) ;

d/ t h e r m a l f r a c t i o n of the t r a n s m i t t e d or r e f l e c t e d

F or 5 a n d 10 c m oases w h e r e also t h e r m a l n e u t r o n s are c a l c u l a t e d these d a t a are c o m p u t e d b o t h i n c l u d i n g and

e x c l u d i n g the the r m a l n e u t r o n s . The l a t t e r set of v a lues can be u s e d f o r c o m p a r i s o n w i t h data of other t h i c k n e s s e s w h e r e t h e r m a l n e u t r o n s were n o t c a l culated.

T he c h a r a c t e r i s t i c data a l o n g w i t h the n u m b e r of i n ­ cide n t n e u t r o n s N (whi c h has n o p h y s i c a l m e a n i n g b ut is i n t e r e s t i n g f r o m the point of v i e w of c o m p u t a t i o n ) are g i v e n in e a c h f i g u r e (figs 1-2^). Some of the c h a r a c t e r ­ istic da t a are p l o t t e d vs s l a b t h i c k n e s s in F i g s 25-28.

n e u t r o n s :

NTH/NT or

n t h

/N

r

>

of the t h e r m a l n e u t r o n s ) .

the n u m b e r

(11)

7

Figs 1-2^

The Monte Carlo calculated spectra

I

(12)

E«PHI(E)

10

í

о

10

10-1

-2 10

- 3

10

- 4

10

-5

10

T 1—7— 1---1 1 1---1 1 1---1 1 1 » 1 ' 1 I 1 r -y —! 1 1 1 r—1—1 г

I i l l i l l i l l I _I _I __

1

_

1

. _I _I __ I -

1

-

1

--

1

-

1

-

1

--

1

-

1

-

1

-2 -1 0

10 10 10 10 102 103 104 10s 106 107 108

ENERGY(EV) TRRNS. 5.0 CM PE E I N = 1 4 . 5 MEV, R N G L E : 90

F. 1

(13)

E-PHI(E)

- 9 - 10-1

10-2

10

10

10- 5

-6

10

-7 10

7---1---1--- Г ---1---1---1---1---1---1---1---1---1---1---1---1---1---1--- I---1---1---1---1---1--- T---1---1---1--- Г

I i l l I I___I____ I___ I___ I____ I___ 1___ I____ I___ I___I____ I___ 1___ 1____ I___I___ I____ 1___ I___ I____J___ !--- 1---L

10 10-1

10

°

101 10

z

103 104 10

s

ENERGY(EV) 5.0 CM PE EIN=14.5 MEV, ANGLE:90

1 0 6 1 0 7 10®

REFL.

(14)

1---- T--- Т---- I— Т--- Т— I---1---1---1---1---1---1---1--- Г — I---1---1— у — Г---1---11---1---1--- г

т__

ind. excl.

therm al

Ё . . . Nr/N,

NTH/NT N...

6 9 .8 % 11.5 MeV 90.1 %

1.9 7 % 3125

6 8 .4 %

11.7 MeV

9 1 . 9 ° / ,

_j I I

1

. J I x L_i x— I — I _i — L— i—

l

_ .

1

. t .i .I. . .

j

i I

10 10 10 10 10 10 10' 10 10

ENERGY(EV) TRANS. 10.0 CM PE EIN=14.5 MEV. ANGLE:90

(15)

ЕвРНПЕ)

-11 -

-1

E N E R G Y (EV) REEL. 10.0 CM PE E I N = 14.5 MEV. A NGLE:90

F. 4

(16)

Е.РНИЕ)

1 10

10

о

10

-t

10

10

10

10- 5

т---1— I— I---1— I— I---1— I— I---1— I— I---1— I— I---1— I— I---1— I— I---1— (— I---1— I— I---г

Nf/ N t : 8 7 .5 % N . . . : 5 0 0 0

I i l l i l l i l l I I _I __I _I _I __I _I _

1

--

1

-

1

-

1

--

1

-

1

-

1

--

1

-

1

-

1

--L

10-2

10

c - l

10 101

io

2 103

io

4 105

io

6 107 10

ENERGY(EV) PE E I N = 1 4 . 5 MEV. A N G L E : 90 TRANS. 20.0 CM

(17)

E.PHI(Е)

- 1 3-

ENERGY(EV) REFL. 2 0 .0 CM PE E I N = 1 4 . 5 MEV. R N G L E : 90

* F. 6

(18)

ЕшРНИЕ)

о

10

10-1

102

10

10

- 5

10

10

Т--- 1--- 1---1---1--- 1---1--- 1— 1— 1--- 1---1--- 1--- 1--- 1---1---1---(---1--- 1--- 1---1--- 1— 1---1---1---1--- 1---г

N T / N : 9 .9 2 % Ё . . . : 9 .5 9 MeV Nf / NT : 8 4 .4 % N . . . : 8 1 2 5

J___I__I__I i l l I I I___1 J__I__ i I 1---- 1 1--- 1---1--- 1--- L--- 1— 1 1--- 1 1 1----l

10 10 10 10 102 103 104 10

s

106 107 10s

ENERGY(EV) TRANS. 4 0 . 0 CM PE E I N = 1 4 . 5 MEV. A N G L E : 90

(19)

ЕшРНПЕ)

- 1 5-

10

-i

-2

10

10

10

-4

10-s

-6

10

10

-7

Т---1--- 1---1--- 1--- 1--- 1--- 1---1---1--- 1--- 1---1---1--- j---1--- 1--- 1---1--- 1--- 1--- 1---1---1--- 1--- 1--- 1---1---г

Nr/ N : 4 .1 2 % E . . . : 2.24 MeV NF / Nr : 2 8 .6 %

N : 8 1 2 5

J-- 1-1-1-- I-1-1-- 1-1-L--1-1_I__ I_I_l__1_I_I__ i l l i l l i l l I

10.-2

10 10 10 10 10' 10 10' 10 10 10

ENERGY(EV) REFL. 40.0 CM PE EIN=14.5 MEV. ANGLE:90

F. 8

(20)

E«PHI(Е)

E N ERGY(EV) TRflNS. 5.0 CM P E E I N = 14.5 MEV. C0S.0IST.

F. 9

(21)

E.PHI(E)

- 1 7-

10

-2 10

- 3

10

10

-4

- 7

10

- 5

-

10

- ind. excl.

e • therm al

- Nr / N 1 0 . 6 °/o 9 . 6 7 %

-6 Ё . . . 3.81 MeV 4 .1 5 MeV

10

Nf / N r 4 4 .0 % 4 8 . 0 %

- Nt h/ N r 8 .3 4 %

N... 3 7 5 0

i l i I _l__i__

l

_—1 _i __ I _I _I __ I _1 _I __I J — I -1 — I — I — _i— I — I -- 1 — I — I -- u io

"2

lo

1 10

° io

1

io

2

io

3

io

4 105 106 107

ENERGY(EV) REFL. 5.0 CM PE E1 N= 1 4 . 5 MEV. C0S.DI3T.

F.

10

10

(22)

E*PHI(E)

I 10

10о

10

-I

-2 10

10

-3

10

-5 10

-

2 - 1 0

I

10 10 10 10

io

2 103 104 1 0 5 1 0 6 1 0 7 1 0 8

ENERGY(EV) TRflNS. 10.0 CM PE E 1 N = 14.5 MEV. COS.DIST.

F. 11

(23)

E.PHIíE)

-19 -

10

10

-7 10 10

- ind. excl.

therm al Nr / N : 12.9 % 11.0 °/o

10-6 E . . . : 3 .4 8 MeV 4 .1 0 MeV

Nf/ Nr : 4 0 .4 ° lo 4 7 .6 % Nth/Nr : 15.1 %

N...

I I___ I___l____ I___ I___ 1 , I___I___ I____ L__ I___I____ I___ I___ L

2 5 0 0

J ____ I___I___ I____ 1___I___I____ L

’U

-2

lo

'1 10

°

101

io

2

io

3 104 ENERGY(EV) REFL. 10.0 CM PE E I N = 1 4 . 5 MEV. COS.OIST.

io

5

io

6 107 10

®

F. 12

(24)

E*PHI(E)

o

ENERGY(EV) TRANS. 20.0 CM PE EIN=14.5 MEV. C0S.DIS7.

F. 13

(25)

E«PHI(El

- 2 1 -

10-2 10-1

10 10 10 10' 10

io

5 106 10 10

ENERGY(EV) REFL. ZO.O CM PE E I N = 1 4 . 5 MEV. C0S.D1ST.

F. 14

(26)

E.PH1(El

10о

10-1

-2

10

-3

10

-4

10

10-s

-6 10

---1---1---1---1---1---1----1---1---1---1---1---1----1---1---1---1---1---1----1---1---1---1---1---1---1---1---1---- г

j

:

Ш

~

j H i ir h K -

lr ‘

I #

гя

III

N T / N : 4 . 4 5 % E . . . : 8 .8 4 MeV

NF / N T : 8 0 . 7 % N . . . : 11250 I

I I__L_l___i l l I I__L__L_I__I___L_I__L__ I__I__I___1__I--- 1---1--- 1---1---1--- 1--- L---- L

-2 -1 0

10 10 10 10 102 103 104 105 106 10 10

ENERGY(EV) TRANS. 40.0 CM PE E I N = 1 4 . 5 MEV. COS.OIST.

F. 15

(27)

E«PHI(EJ

- 2 3 -

ENERGY(EV) REFL. 4 0 . 0 CM PE E I N = 1 4 . 5 MEV, COS.DIST.

F. 16

(28)

E.PHI(E)

10

о

ю

'1

-2 10

10-8

10

-4

10-s

-6 10

1

-

1--|— 1

--

1

(

1

--

1 1 1

--

1 1 1

--

1 1 1

--

1 1 1

--

1 1 1

--

1 1 1

--

1 1 1

--r

incl. excl.

th e rm a l NT / N : 4 7 .9 % 4 1 .2 % E . . . : 1.21 MeV 1.41 MeV

_ Nf/ Nt : 17.5 % 2 0 .4 %

NTH/N T : 1 4 .0 % N . . . : 3 7 5 0

I l i t i l l I I _

1

__I _I _I __ I _I _

1

--

1

-

1

-

1

--

1

-

1

-

1

--

1

-

1

-

1

--

1

-

1

-

1

-- L

10 10* ’ 10 10 10 10 10 10' 10 10 10

ENERGY(EV) TRRNS. 5.0 CM PE FISSION. C O S. D I S T

F. 17

(29)

ЕшРНПЕ)

- 2 5 -

-1

E N E R G Y (EV) REFL. 5 .0 CM PE FISSION. COS.DIST

F. 18

(30)

ЕшРНКЕ)

1

Ö

-2 10

Ч

10 10 10 10 10 10

'

10 10 10

ENERGY(EV) TRANS. 10.0 CM PE FISSION. C O S. D I S T

F. 19

(31)

E*PHI(Ei

- 27 -

j

I

10 10 10 10 10 10 io4 io5 10

ENERGY(EV1 REFL. 10.0 CM PE FISSION. COS.DIST

10 10

F. 20

(32)

E«PHI(E)

- 2 8 - 10-2

-3

10

10

-5

10

-6 10

-7

10

-8 10

10 10 10 10 10 10 10 10' 10 10 10

ENERGY(EV) TRANS. 20.0 CM PE FISSION. C O S.OIST

F. 21

(33)

E.PHIIE)

- 2 9 - 10

-1

10

10 -з

10

10

-5

10

-6

10

-7

т--1— I— Г— т— I-1--т— I-1--1— I-1--1— I-1--1— I— г— т-1--1--1— I— »-- г I-1-- г

Nr /N : 3 4 . 9 %

Ё : 0 .4 9 3 MeV Nf/Nr : 4 .2 9 °/о N . . . : 1 2 5 0 0

J___ I__ I__ I___-L__I__ I___ i __ I__ I___ 1__ I__ I___ 1__ 1__ I___ I__ L__I___ I__ I__ I___ I__ I---- 1___ I__ I----L

10"2 10~l 10° 1 0 1 1 0 2 103 1 0 4 10s i o 6 i o 7 108

ENERGY(EV) REFL. 20.0 CM PE FISSION. C0 S. D 1 S T

F. 22

(34)

ЕжРНКЕ)

- зо- -з

E N E R G Y (EV) IRANS. 4 0 . 0 CM PE FISSION. CO S. D I S T

F. 23

(35)

ЕяРН!(Е)

- 31 -

10 1 10° ю 1 ю 2 ю 3

ENERGY(EV) TRANS. 40.0 СМ РЕ FISSION. COS.DI SI

F. 2 3 а

10в

(36)

ЕяРНКЕ)

10

-2

io"1 REFL.

10° 10 ’ i o2 i o3 i o4

ENERGY(EV) 40.0 CM PE FISSION. C0S.01ST

F. 24

io5 ío6 107 10®

(37)

33

Figs 25-28

C h a r a c t e r i s t i c q u a n t i t i e s of the s p e c t r a

(38)

TRANSMISSIONPROBABILITY(•/•)

T H I C K N E S S ( c m )

F. 25.

T he p r o b a b i l i t y of t r a n s m i s s i o n w i t h o u t t h e r m a l i s a t i o n vs slab thickness.

F. 26.

The a v e r a g e energy of the t r a n s m i t t e d n o n - t h e r m a l neutrons.

(39)

35

F . 27.

T h e p r o b a b i l i t y of r e f l e c t i o n without t h e r m a l i s a t i o n vs - slab thickness.

10

>

5

>- О

ос

ш z ш

о ÜJ

<

ос

Ul >

«

0 .5

0.2

-

0.1

1 4 .5 M e V , C O S .

J - - - -

*--4-

\

1 4 .5 M e V , PERP.

- ~o~

~*\ 0

FI SS IO N , COS.

J__ L _L

0 5 10 2 0 4 0

THI CKNESS ( c m )

F. 28.

T h e a v é r a g e energy of the r e f l e c t e d n o n - t h e r m a l neutrons.

(40)

36

A c k n o w l e d g e m e n t s

T h e a u t h o r s thank Dr. S. M a k r a a n d Mr. A. K o n d o r f o r their v a l u a b l e c o m m e n t s as well as Mr. J. G a d 6 f o r the u s e of the T H E R M O S i n structions.

(41)

37

Ref ere n o e s 5

G a d á , J ., 1973 , KFKl-73-*+7;

K o b l i n g e r , L. , 197*+, k f k i-7*+-*+7;

Lux, I., Koblinger, L. , 1973» KFKI-73-2;

P á l f a l v i , J. , 1973, K F K I - 73-57;

Pálf a l v i , J. , 197*+, KFKI-7*+-*+8;

P á l f alvi, J. , K o b l i n g e r , L. , 197*+, KFKI-7*+-63

(42)
(43)
(44)

Ú Z 45

Kiadja a Központi Fizikai Kutató Intézet Felelős kiadó: Szabó Ferenc tud. igazgató Szakmai lektor: Kondor András

Nyelvi lektor: H. Shenker

Példányszám: 210 Törzsszám: 75-441 Készült a KFKI házi sokszorosító üzemében Budapest, 1975. március hó

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