ORIG.RUSSIAN: NEUTRON SLOWING DOWN IN HYDROGENEOUS MEDIA

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100110004-5
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 18
• Document Creation Date: December 22, 2016
• Document Release Date: August 26, 2009
• Sequence Number: 4
• Publication Date: May 1, 1964
• Content Type: STUDY

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the studying of physioal parameter. limited according to the a .ze
of multiplying media placed in the critical systmn.
A mathematical method published in the paper was used for
a theoretical argument of using the experimental method and for
the choice of the system size. / 3 /. As it was expected the
results of the calculations proved that in the conditions of the
cyli;drical geometry of the investigated medium placed into the
infinite "reflector" the diameter of the cylinder must be not
lose than four lengths of slowing down. (4 /,s ).
Cylindrical geometry with 41 cm. in diameter and 110 cm. high
placed into the infinite graphite "reflector" was used for all
experimental investigations of the neutron slowing down in non-
multiplying media. In order to confirm the given geometry
experimentally apace distribution measurements of neutron (Po +
Be) source were made in the following media: diphenyl + graphite
"reflector" and diphenyl + diphenyl "reflector". The measured
density distributions of slowing down neutrons up to indium
resonance in this conditions appear to be identical within
experimental errors. The values of the square length of slowing
down calculated according to this distributions are correspond-
ingly equal to: (102,3 ? 3,5) cm2 - for the diphenyl + graphite
medium and (I02,5 ? 4,1) cm2 - for the diphenyl + diphenyl
medium.
Investigating fast - neutron slowing down in metal-hydro-
geneous media the experimental systems consisted of a moderator
with evenly distributed metal rods. Two groups of media were
studied: quaaihomogeneoue media in which metal rods were of 10 mm
diameter and heterogeneous media with 40 mm rods.
Measurements were made for neutrons of fission spectrum U-235
and for neutrons of ( Po + Be ) source. Neutron fissi< a source
was a convertor made of metallic highly enriched uranium placed
into a thermalizing column of a heavy water reactor of the
Academy of Sciences of the USSR.
The space distributions were measured by 90 mg/cm2 thick in-
dium foil, the sizes of which were chosen in order to preserve
the "point" sizes of the source and detectors. Corrections were
introduced into the calculated values of the foil activities.
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These corrections conserned: I. the contribution of the neutrons
with energies above the first resonance level of indium, and 2,
the corrections concerning the thickness of the neutron fission
source. All the measured distributions were calculated to 093 mm
/5/ thickness of the source. Square length of slowing down were
calculated from the following eq motion ti/ a
K s - "/a Z t c/z
6' (r
0 ~o
where q(,&) - indium foil activity;
k, - cons tants measured in the experimental neutron
distribution for an region distant of the source
where a linear law is present eh (, a)= /4)
The results of the square length of slowing down values are
given in Tables I, II and Figures I, 2.
The experimental study, di;of the Neutron
slowinx down in a critical system
In the experimental study of neutron slowing down in a critical
system was studied in the water-uranium and uranium - isopropyl
diphenyl media. Due to neutron leakage measurements, corresponding
to various geometries of the core, it was possible to determine
neutron migration areas /6/. The periods of the doubled power sys-
tem were measured in the experiment with the change of the core
critical height. According to these periods the values of the
reactivity were calculated using the formula of inhour. /7/.
The contribution of delayed neutrons of various energetic groups
into measured values of reactivity were taken into account.
V~e values were used in the "inhour" formula instead of the
constant outputs of the delayed neutrons. These valves were
determined as follows: 2 2Pti
/9(Ll ~ ypZ t f KCAL Z yQ/~
./td? Nr
2
2P ti c
where I, s - square length of slowing down of prompt neutron
2 de, fission;
square length of slowing down of the delayed neutron
"i" group ;
buckling
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2
From - the given values of the reactivity system the
relations were determined according to the following equation:
a,P 2rr2M
Rh H3Kdo
where H - critical height;
(3)
h - the exceeding of the Brit {cal height;
Km,,- neutron multiplication coefficient for the
infinite media.
The necessary buckling values for Y2 calculations were obtained
from the critical experiments from the measurements of the axial
and radial density neutron distributions in the core. These dis-
tributions were measured with copper foils.
The experimental plant was a zero power reactor, the core of
which was located in a hexagonal tank male of stainless steel,
its side being 50 cm. The core was surrounded by an infinite
side reflector made of the moderator; there was no upper buttend
reflector, the bottom of the tank 15 mm being the lower butt-
end reflector. Fuel elements were hollow cylinders of stainless
steel filled with U. Od (the size of the inner tube being 9,0 x
0,4 mm, of the outer tube - 13,4 x 0.2 mm). The fuel elements
were located in alluminium spacing lattices. Due to lattice
pitch variations it was possible to investigate the neutron
slowing down in the media with different relationship of fuel
and liquid moderator volumes.
In this experiment square neutron migration areas values were
obtained. This values did not differ from the within the
accuracy of the experiment, the diffusion length values of
neutrons being negligible small in given multiplying media.
The value 4s (thermal) is given in Table I
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If one adds Fourier transformation to this system (1) and
then make expansion "P-",we shall obtain a system of relative
equations for the square length of slowing down determination:
j
d
Z,C
d 'oo
i,
,f e
7 7"0o dU/ 00 ~Gr. 00
I e e 11
It ,3 00 i w .
i
~
d-4 e* j
rnd
i z~0 e CUT, 2 (, +do Toz
cp d-~ + )CiEVL' CP02
e~
DU o2
z~
L
(6)
In the expression C3) the are space angular moments of the
neutron distribution function of " it group in the infinite me-
dia with the plane isotropic source.
A program of numerical calculation Gs is made for a com-
putor /8/. The calculated values of square length of the slowing-
down in hydroteneous media are given in Tables I,II and Fig.1.
Measurement Results
"Quasi-homogeneous media". The results of the measurements
and calculations Gsz for pure moderators and quasi-homogeneous
metal-water media are given in Table I.There is good agreement
between experimental and calculated data Z,s which proves the
valuability of the calculation method of the neutron slowing do-
wn as well as multigroup constant systems used in calculations
for the discription of the neutron slowing down process in hyd-
rogeneous media.
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Heterogeneous Media. The results of the neutron moderation
measurements are given in Table II and Fig. I and 2. There is
great difference in values ~.f with the same concdntration of
metal in water. In all cases the measuremented values 4.z for
heterogeneous media exceeded the corresponding values for quasi -
hoyaogeneous media. The same is true for diphenyl metal media
for which the measured values 4~ are much greater than the cal-
culated ones, obtained by the method applied to homogeneous media.
This difference can be explained by a sharply expressed anisotropy
of neutron diffusion in heterogeneous media.
In the previous papers dealing with fast neutron slowing down
in metal-water media was not observed such sharp anisotropy, as
the investigated media were, actually, quasi-homogeneous /9/.
The results obtained are evidently of interest for physical
calculations of reactors, the core of which is sharply heterogene-
ous.
II. THERMAL NEUTRON DIFFUSION
Experimental Methods
Neutron diffusion in hydrocarbons (cyclic and non-cyclic com-
pounds) has been studied in the medium with a wide range of tempe-
ratures (from melting to boiling). For investigation purposes the
method of pulsed neutron source /II/ has been used.
Thermal neutron distribution in the medium may be described
by means of a one-group diffusion equation in which diffusion con-
stants averaged by the thermal neutrons spectrum are used:
_D(trJ an-Z?zr-n = )n
(7)
where Iff : - diffusion coefficient in the infinite
3 medium;
Ga tl - neutron absorption rate in the infinite
medium.
For a finite medium the changing of thermal neutron density
in the course of time may be described as a sum of exponentially
attenuating harmonics. A sufficient period of time having passed,
all harmonics attenuate, except the main one, and neutron
distribution is described by the law e- oft , where decay constant
56 ml_ Y t3(iri. - lCD - fir> ~2 (c1
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,Jt, - geometrical buckling;
Co - diffusion cooling coefficient;
Cr - non-diffusion correction.
Description of Experiment
Measurements were made with the cyclotron of the Academy of
Science of the USSR.The unit consisted of a cylindrical tank 30 cm
in diameter, shielded with a B4C layer of 10 mm thickness and with
a 0,5 mm cadimium layer. Into the tank there was inserted a cadmium
"piston" by means of which the geometrical dimensions of the me-
dium under investigation could be changed quickly and easily.Under
the tank bottom a block of counters BF3 was placed separated and
shielded from the tank bottom with the help of a cadmium "mask" the
shape of which can be determined by the function t J. (2,yor A).
This "mask" decreased the influence of high harmonics of the
neutron density for high geometrical buckling.For heating the me-
dium an electric furnace was placed on the side surface of the tank.
For temperature control a thermocouple was placed inside the tank,
the accuracy of measuring the temperature being +2?C.
The calculation of the unit and the control tests were carried
out with water at the temperature of 21 ?C.For determining the effect
of mutual arrangement of the cyclotron target and the unit,measure-
ments were at different distances from and different angles to the
target.The results remained the same within the experimental error.
As water shielding and other scalterers were close to the unit,
but the target was rather far from it,the fast neutron source
was practically volumetric.
The liquid was heated to high temperatures and therefore the
minimum distance between a block of counters and the tank bottom
could be 2 cm, In connection with this all possible distortions of
the decay constant were measured because neutrons of various ener-
gies covered the distance from the tank bottom to the conters in
different time intervals.
The results of the experiment showing the effect of the covered
distance on the decay constant shows that this effect in negligible
from JL =0, 240 cm 2. The measurements were for ~. which
were not larger than this quantity.
The cyclotron had a pulse-repetition rate of 500 cycles and
the pulse duration of 6-8,Msec.
Time analysis of the decay of thermal neutron flux was made
with the 60-channel time analyzer,the triggering of which
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was synchronous with the cyclotron start-un. The delay of the
time-analyzer trigE ering relative t-o the fast neutron pulse
varied with-in 100-300 sec. The time channel width was 2-8.* sec.
The vibration of the base was not more than 0, 25 /u sec.
The method of treatment the results
The values off, , (CD Cr) were calculated
by the method of least square s. The dependance of the diffusion
coefficient from the temperature of the medium for all the inves-
tigated materials is well discribed by the law:
Z .DlIr) T z (9)
where ._ - is the diffusion coefficient, averaged by the
spectre of thermal neutrons at the temperature
of medium T;
v ,f - is the density of the medium at given tempe-
ratures T,To;
Q - is the parameter,depending upon the molecule
structure of the material.
The results of the treatment of experimental data are given
in table III.
It is natural to suppose,that the established neutron spect-
rum in an infinite medium oveys to the Maxwell distribution:
V/ (7f) chr: A, e YVr,: u2 01 V
where ^J : k -is the most probable velocity of the
eutrons.
n
Strickly speaking,the spectre of the thermal neutrons obeys
to the Maxwell distribution only in nonabsorbing media.But
as the experiment shows one can consider the spectre as a
Maxwell one if the absorption is weak. This allows to define the
value '213 within a small mistake. In this case one uses the
medium temperature as a parameter.
Then the equation /9/ may be written as follows:
VP = (U) T 8 Z'r T (10)
'Pe The diffusion coefficient averaged by the Maxwell spectre can
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From the equation (10) and (11) one can get the ratio (11)
for defining the differential value of the diffusion coeffi-
cient of neutrons with the velocity 1r by the values of the
diffusion coefficients of neutrons for the most probable veloci-
ty 1fo
(13)
where to (Q) - is the coefficient of the averaged function,
depending upon the kind of neutron spectrum
and of the index Q
The averaged diffusion coefficient of neutrons by the Maxwell
spectrum can be defined by the differential value of the diffu-
sion coefficient of neutrons for the most probable velocity.
J e'~~Yt~t r o
-,Tlv) r -D6j-e) 0 - zrt~~ 2
(a) -D(z)
From the equation (13) one can get the dependance
transport length uron the neutron velocity
yh(ac) ~l ?!a ~r Q
J~
(14)
h 5)
It follows from the abovementioned, that the value of the depen-
dance of the integral value .!7(7Lr upon the medium tempera-
ture and the knowledge of the kind of the spectrum of the
thermal neutrons allows to get the differential value _i)~ILro)
'~~ft (IL (18)
r) If
from the equation (14) .
And the differential value ^ ^~~ (t!`o) from the equation
(V.o) 3 DAr)
(a) . Lra
From the equations /16/ and /161/ it follows
~
~~?ll = _D~Yo) ~~ 4 (12)
v
we finally have
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Therefore it is necessary to note in references (e.g.11,13)
an in accurate ratio of the diffusion coefficient is used
7 1 7 y > _ \1 ?) Ir
.. 1~
3
19 )
Got from the equation (19) has no definite _physical sense.
This concerns also to the definition of !yf received
from the experiments with stationary diffusion.In this case 4, C~J
is an average of the spectrum of thermal neutrons:
=(?, _ 72(u): T 2W = h i ( a ) T = T? m(a) atrCuJ'~` (20)
Then in order to get an information of the transport length
value, it is necessary to find the value of Ih(q) . This can be
done :;_f one defines L 2(v) at different temperatures of the
medium and the results are treated according the abovementioned
method.
From the values of the transport length one can calculate
the transport cross section of the neutron scattering by the
molecules of the medium, averaged by the neutron spectrum; it is
also possible to obtain the differential value of the transport
cross section of moleculs neutrons of the medimm in the case of
the Maxwell distribution.The latter makes it possible to cal-
culate the transport cross section of one hydrogen atom,consi-
dering the atoms of carbon being free.
Thus it is possible to determine both the integral value
of the transport cross section of the neutron scattering by the
bound hydrogen and the differential cross section.The latter
values must correspond to the values of the transport cross sec-
tion obtained from the differential experiments.
In order to verify the methods of treatment of the experimen-
tal results,a comparison of the values of transport cross section
of neutron scattering by the medium molecules was made.These
values were obtained both from integral and differential expe-
riments.The comparison was made for water.The results of the in-
tegral experiment for water /11/ were treated according to the
abovementioned method /equation 17/.
From differential experiments on the scattering of neutrons
with different energies with water COS 9 was taken from /12/
and 6f - from /13/,and was calculated. G was
also obtained from /11/ using the empreEatnn (17).The results
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agreed perfectly.Besides, from /11(3)/ 9'/V. were obtained
using (19) . These values of G differ greatly from the re-
sults of the differential experiment. The difference is of about
40% (fig-3).
Table III gives the values of the parameter of a and 6tG
by bound hydrogen for the investigated matter at the medium tem-
perature 18?C, including the data of water and dowtherm /11,14/
treated accorai_iL. to he aboveiaentioned method.
Transport cross section of the bound hydrogen Gto changes
from 33 barns for 0 N 1 to 100 barns for a " 3. There is a
whole spectrum of intermediate values (fig.4) depending on the
structures of compounds.
Transport cross section of the neutron scattering by the bound
hydrogen strongly depends on the medium temperature in the case
of non-cyclic compounds.
Acknowledgements the authors express their gratitude to S.A.
Gavrilov,I.G.Moro sov,E.I.Injutin,G.I.Sidorov,B.M.Stasevetch,
V.V.Okorokov,V.V.Dolganov,V.A.Fedorovitch for their help,as
well as V.P.Kotchergin,A.F.Zagirko for making calculations on
the computor.
References
1./ H.GOLDSTEIN, P.F. ZWEIFEL, D.O. FOSTER, Jr.
The second United Nations international conference on the peace-
ful uses of atomic energy. Report 2375.
2./ H. KOUTS, R.SHER, S.R. BROWN, D.KLEIN, S.STEIN, R.L.HELLENS,
H.ARNOLD, R.M.BALL, P.W.DAVISON
The second United Nations international conference on the peace-
ful uses of atomic energy. Report 1841.
3./ A.W.MoREYNOLDS, M.S.NELKIN, M.N.ROSENBLUTH, W.L.WHITTEMORE.
The second United Nations international conference on the peace-
ful uses of atomic energy. Report 1540.
4./ C.D.J0INOU, A.J.000DJOHN, N.F.WIKNER.
"Nuclear Sci. and Eng.B., 171-189/1962/.
/2/ G. A. STOLYAROV, Z. B. KOMISSAROV, V. P. KATKOV, U. V. NIKOLSKY.
The meeting of the Academy of Science of the USSR
on the peaceful use of atomic energy 1955.A of Be.
of the USSR /1955/.
/3/ A. E.GLAUBERMAN,T,1.TALJANSKY.
"Atomic energy" N 3 /july 1957 /.
/4/ L.N.Jurova,A.A.POLJAKOV,S.B.STEPANOV,V.B.FROJANSKY.
356 12
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"Neutron physics" Gosatom isdat /19603.
/5/ 1./ L.N. JUROVA,A.A.POLJAKOV,A. A. IGNATOV.
"Atomic Ener-y" v.12 part 2 /1962/.
2./ L.H.JUROVA,A.A.POLJAKOV,A.A.IGIIATOV.
"Some questions of engineer:in~ physics" Gosatornisdai;
/1963/.
/6/ S.KRASIK, A.RADKOWSKY
International conference on peaceful u,.. ! o_' atomic
energy.Report F/601 /1955/.
/7/ P. GLASSTONE and M.EDLUND.
The principals of the theory of nuclear reactors.
Foreign literature publishing house.III.1954.
/8/ 1./ G. I. MARCHUK.
"Methods of calculation of the r}uclear reactors state
publish house of atomic science and technique .1.MI.1961.
2./ V. P. KOCHERGIN, A. F. ZAGIRKO.
"The program of the calculation of the square of the
neutron slowing doem length in homogeneous media in
multigrouped approximation.
The phys. energ.Inst. of the State Comittee of the Sov.
of Minist of the USSR Report N / 557
/9/ 1./ A.MUNN,A.B.PONTECORVO.
"Car.J.Res,".A.25 157-167 /1947/.
2./ M.REIER, F.OBENSHAINE and R.L.HELLENS.
"Nuclear Sci.a.Eng.4 ,1-11 /1958/.
/10/ C.D.JOANOU, A.J.000DJOHN, N.F.WIKNER.
"Nuclear Sci.and Eng.13,171-189,/1962/.
/11/ 1. / A. V. ANTONOV etal.
The first international conference on peaceful use
of atomic energy.Report P/661.
2./ Ct.F.von DARDTEL.
Frans. Royal Inst.Techn.N75 STOKHOLM /1954/
3.1 A. V. ANTONOV et. a1.
"Atomic Energy" v.12 part 1 /1962/
4./ G. F.von Dardel and N. G. SJOSTRAND
Phys.Rev. 96, 1245/1954/.
/12/ V.I.MOSTOVOY et.al.Report for the Geneva conference,
1964.
/13/ Donald J. HUGHES and ROBERT B. SCHWARTZ .
"Neutron cross section" BR001HAVEN national laboratory
356 .Tan.1 /1957/.
/14/ NI. KUCHLE "Nucleonic" 2 131 /1960/. 13
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TAB.1
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TAB. II
Media
(H20)
H20+Fe
H2O+A1
(C12H10)
C12H10+Fe
C12H10+A1
Neutron
source
Vmet/Vmod
L2s(1,46ev)/cm2
exper.
calcul.
56,7?0,9
58,5?1 ,5
/10
1:3
quisi. gom.
media
55,6+1,0
get. media
63,1?1,2
quisi gom.
media
53,1?1,4
2:3
get. media
69,1?1,7
quisi gom.
media
62,6?1 ,7
1,42
77,7?1,8
1:3
qui s i gom.
media
72,1+1,6
get, media
7926+2,1
102,3+3,5
99,1
1:3 1
get. media
75,0+4,4
68,5
1:4
87,8?2,3
79,9
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TAB.III
Name Index
Benzene
C6Rr
t'c
14
27
34
38
52
71
D~plenp~
Do.4en1Le/any
Dowf/fpzm ~I4f
Wofez 1l1I
DrpAen/eflie
GQSOI f
Ctya
123
/50
/75
207
243
34
!!0
f60
230
97
/10
/as
24
,~G4
T t4aa~aco~e
0,920
09M
0845
0,816
4442
48/3
4762
ran
4,s.o
a.
0,852
482/
00-10
(35t1105
1,61V4
f9f002
33,/10,7
32,5?0,3
49,016?
4?5?15
440;Z
2/6?Q4
2~~rQc'
6i3~f
258
'f!2
assn
4935
Q865
Q742
Q7x
sm
J.16 0
?JgfJ4
80
154
v?!Di
sec
42801004!
0252!002t
4248140/9
49248:!W7
1283?O$2
03X)11051
028Oi 011
Q2f7 taA'4
VW.!d r2
42S3tQO/6
Q2361QO/O
cm`sec'
cm~ sac''
5,37145/
0,86 t ?5/
5,24 1021
Off taV
466 tQ36
,126 te38
427=04/
R&-t0/
40920,
342= /X
4/3tQ33
234 t 483
,770=008
820t QSa
424208
897t 0&
4?ytgjW
:ss 01o
04014/1
401'1121
5,35+121
4&0V30
4,951033
0885
Q871
0863
0859
0,845
0824
0.955
0930
,4t,,8 0,910
rzat q8 ow
i 9 t as 0850
fl2tQ36 Q994
2~2t482 0,936
49 t f2 0897
Z' !,7 0842
4161148
~9 t!3
Q24314Oi9
.07:Q6/
76120
Q230t40Y7
,~!B1Q84
861 (9
4Wt4000
45211f4
!49 t z9
44dttQ7l17
423tgp/
z2tQ6
4MS*4tW
4ZI07
2.9tQ5
Q 3O2A
.621442
40 t3
GWtQW
-14-09
AV-44M
tIe
1t *w
SWIM
Vlt4W
4a*QQ
jWtM
41Yt4H
4/1t40
4W *4w
4099
z3' Q
QJ3tt4X/
=5144
47t l1
Qh#t 40
?s7 4w
_
W-#406
:QN
JAW
48t4w
~s4~G
T.tt_
5,3t02y
' f0
? W?4w
16
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{
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