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
2017
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
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.
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 5R 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
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 5R 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 . 5e 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
6terms. 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.
3
Table 1
standard energy
EV 1
2.
17010E
-01 2 3.
5356ПЕ
-01 3 7.
0715ПЕ
-01 41 .
4663О E 00
5 3
.
161О
0Е On 6 6.
8191ПЕ
00 7 1. A6630E
018
3.1
6190 E 01
9
6.В
1о 1 OE
01iO
1.
466ЗОЕ О?
,1
3,1
619ОЕ О?
6
.
810ЮЕ
02 13 1.А
6630Е
03 : а з.1610
ое 0.3 156.Я1
91ОЕ
03 16 1.
12200Е ОА
17 1
.A
1Z
50E ОА
18 1
.
78160Е ОА
19 2
.
23850Е ОА
20 2.81820
Е ОА
21 3
.
5А
780Е ОА
22 А.А6630Ё ОА 23 5
.
62260Е ОА
2
А
7.07820Е ОА
25 8
.
91170Ё ОА
26 1
.
12200Е
05 27Í
*412506 05 28 1.
7816ОЕ
05 29 2.
23R
50E
08 30 2.
81820Е
05 31 3.
5А
730Е
05 32А.А
6630Е
05 33 5.
62260Е
05ЗА
7.
07820Е
05 35Я.
911?0Е
05 36 1.122О О Е Об
37 1
.А
1250С G6 ЗЯ
1.
78
16ОЕ
06 39 2.23850Е 06АО
2.
318
2ОЕ
06А1
3.
5А
7ЯОЕ
06 42 А.А663ПЕ Об 43 5.62260t
06 44 7.
07Я
2ОЕ
06 45 8.
91170Е
06 46 1 112?0ОЕ 07 47 1 . А125ОЕ 07А Я
1.
78
16 О Е
07limits
от
the е F91 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
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".
■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:
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
7
Figs 1-2^
The Monte Carlo calculated spectra
I
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
E-PHI(E)
- 9 - 10-1
10-2
-з
10
10
-ч
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 10z
103 104 10s
ENERGY(EV) 5.0 CM PE EIN=14.5 MEV, ANGLE:90
1 0 6 1 0 7 10®
REFL.
1---- T--- Т---- I— Т--- Т— I---1---1---1---1---1---1---1--- Г — I---1---1— у — Г---1---1—1---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. . .
ji I
10 10 10 10 10 10 10' 10 10
ENERGY(EV) TRANS. 10.0 CM PE EIN=14.5 MEV. ANGLE:90
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
Е.РНИЕ)
1 10
10
о
10
-t
10
-г
10
-з
10
-ч
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 103io
4 105io
6 107 10ENERGY(EV) PE E I N = 1 4 . 5 MEV. A N G L E : 90 TRANS. 20.0 CM
E.PHI(Е)
- 1 3-
-í
ENERGY(EV) REFL. 2 0 .0 CM PE E I N = 1 4 . 5 MEV. R N G L E : 90
* F. 6
ЕшРНИЕ)
о
10
10-1
102
10
-э
10~ч
- 5
10
10
-Б
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 10sENERGY(EV) TRANS. 4 0 . 0 CM PE E I N = 1 4 . 5 MEV. A N G L E : 90
ЕшРНПЕ)
- 1 5-
10
-i
-2
10
10
-з
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
E«PHI(Е)
E N ERGY(EV) TRflNS. 5.0 CM P E E I N = 14.5 MEV. C0S.0IST.
F. 9
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
"2lo
1 10° io
1io
2io
3io
4 105 106 107ENERGY(EV) REFL. 5.0 CM PE E1 N= 1 4 . 5 MEV. C0S.DI3T.
F.
1010
E*PHI(E)
I 10
10о
10
-I
-2 10
10
-3
-ч
10
-5 10
-
2 - 1 0I
10 10 10 10
io
2 103 104 1 0 5 1 0 6 1 0 7 1 0 8ENERGY(EV) TRflNS. 10.0 CM PE E 1 N = 14.5 MEV. COS.DIST.
F. 11
E.PHIíE)
-19 -
10
-э
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
-2lo
'1 10°
101io
2io
3 104 ENERGY(EV) REFL. 10.0 CM PE E I N = 1 4 . 5 MEV. COS.OIST.io
5io
6 107 10®
F. 12
E*PHI(E)
o
ENERGY(EV) TRANS. 20.0 CM PE EIN=14.5 MEV. C0S.DIS7.
F. 13
E«PHI(El
- 2 1 -
10-2 10-1
10 10 10 10' 10
io
5 106 10 10ENERGY(EV) REFL. ZO.O CM PE E I N = 1 4 . 5 MEV. C0S.D1ST.
F. 14
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
E«PHI(EJ
- 2 3 -
-í
ENERGY(EV) REFL. 4 0 . 0 CM PE E I N = 1 4 . 5 MEV, COS.DIST.
F. 16
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
ЕшРНПЕ)
- 2 5 -
-1
E N E R G Y (EV) REFL. 5 .0 CM PE FISSION. COS.DIST
F. 18
ЕшРНКЕ)
1
Ö
-2 10Ч
10 10 10 10 10 10'
10 10 10ENERGY(EV) TRANS. 10.0 CM PE FISSION. C O S. D I S T
F. 19
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
E«PHI(E)
- 2 8 - 10-2
-3
10
10
-ч
-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
E.PHIIE)
- 2 9 - 10
-1
10
-г10 -з
10
-ч10
-510
-610
-7т--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
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
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
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®
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
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.
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
осш z ш
о ÜJ
<
осUl >
«
0 .50.2
-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.
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.
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
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