SOVIET ATOMIC ENERGY VOLUME 19, NUMBER 5
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Volume 19, Number 5
SOVIET.
TRANSLATED FROM "RU.SSIAN
'November, 1965
ATOMIC
ENERGY
ATOMHAR 3HEPrI4R
(ATOMNAYA ENERGIYA)
CONSULTANTS BUREAU
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ATOMNAYA ENERGIYA
EDITORIAL BOARD
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov
I. N. Golovin
V. F. Kalinin
N. A. Kolokol'tsov
(Assistant Editor)
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M. D. Millionshchikov
(Editor-in-Chief)
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SOVIET ATOMIC
ENERGY
A translation of ATOMNAYA ENERGIYA,
a publication of the Academy of Sciences of the USSR
? 1966 CONSULTANTS BUREAU, A DIVISION OF PLENUM PUBLISHING
CORPORATION, 227 West 17th Street, New York, N. Y. 10011
Volume 19, Number 5
CONTENTS
Plasma Stability in a Mirror Machine with Stabilizing Rods-B. A. Trubnikov ........
Magnetic Mirror Trap with a Field increasing inr All Directions-A. I. Morozov
and L. S. Solov'ev ......................................... .
Self-Consistent Distribution of Particles and Limiting Current in a Linear Accelerator
-B. I. Bondarev and A. D. Vlasov ............................... .
Use of Time Integration to Calculate the Differential Scattering Cross Sections of Slow
Neutrons-V. F. Turchin ........ .............. ..... ........ .
The Hydration of Cations in Heavy Water-V. M. Vdovenko, Yu. V. Gurikov,
and E. K. Legin ......................... ............... .
The Binary System UF4-UC14-L. A. Khripin, Yu. V. Gagarinskii, G. M. Zadneprovskii,
and L. A. Luk'yanova ....................................... .
NOTES ON ARTICLES RECEIVED
Construction of a Sectored 300 keV Cyclotron with External Injection-V. A. Gladyshev,
L. N. Katsaurov, A. N. Kuznetsov, E. M. Moroz, and L. P. Nechaeva ..........
Magnetic Field of a 300-keV Sector Cyclotron with External Injection-V. A. Gladyshev,
L. N. Katsaurov, A. N. Kuznetsov, E. M. Moroz, and L. P. Nechaeva ......... .
Improvement of the Sensitivity of Alpha-Scintillation Chambers-L. V. Gorbushina
and V. G. Tyminskii ........ ............................. .
Certain Methods for Reducing the Fluxes of Penetrating Secondary y -Radiation
-D. L. Broder, A. P. Kondrashov, and A. V. Kudryavtseva ............... .
LETTERS TO THE EDITOR
Measurement of the Pressure Distribution behind the Front of a Strong Shock Wave
-V. I. Fedulov and V. D. Borman ............................... .
Use of Surface-Barrier Silicon Detectors for Measuring Fast-Particle Spectra
-G. F. Bogdanov and B. P. Maksimenko ........................... .
Dependence of the Energy Loss Averaged with Respect to the Electron Spectrum
on the End-Point Energy of the 6 -Spectrum, the Atomic Number of the
5 -Radiator, and the Transition Type-V. F. Baranov ................... .
Coefficients of Secondary y -Radiation for Aluminum, Copper, and Tungsten
-S. P. Belov, V. P. Demin, Yu. A. Kazanskii, A. P. Lobakov,and V. I. Popov ... .
Annual Subscription: $95
Single Issue: $30
November, 1965
RUSS.
PAGE PAGE
1369 415
1376 420
1381 423
1387 428
1393 433
1398 437
1403 442
1404 443
1406 443
1408 444
Single Article: $15
All rights reserved. No article contained herein may be reproduced for any purpose whatsoever
without permission of the publisher. Permission may be obtained from Consultants Bureau, A
Division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011, U.S.A.
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CONTENTS (continued)
RUSS.
PAGE PAGE
Viscosity Coefficient of Hydrogen (H2, D2), Neon (NeZO, Ne22) and Helium (He3 )
Isotopes in the Temperature. Range -195 to +25? C-N. E. Menabde .......... 1421 453
Determination of the Spectral Characteristics of Isotopic Neutron Sources by Paired
Scintillation Crystals of the LiI(Eu) Type-P. L. Gruzin, A. Z. Kichev,
V. M. Minaev, V. T. Samosadnyi, and Su Ch'ang -sung .................. 1423 454
Cross Sections for the Inelastic Interaction of Neutrons with Nuclei of Li7, C12, N14,
Al21, Fels, Cu, Pb, U23s, U2s8, and Pu239-Yu. G. Degtyarev ............... 1426 456
Cross Sections for the Radiative Capture of Fast Neutrons in Rhenium and Tantalum
-V. N. Kononov and Yu. Ya. Stavisskii ........................... 1428 457
Producing Stable Isotopes of Krypton and Xenon by Irradiating Aluminum Halides
in a Reactor-A. N. Murin, L. K. Levskii, and A. E. Zakharova ............ 1430 458
Measurement of Gd156 Absorption Cross Section-E. I. Grishanin, G. M. Kukavadze,
V. I. Lependin, L. Ya. Mamelova, I. G. Morozov, V. V. Orlov,
and D. T. Pilipets ......................................... 1432 459
Changes in Fast-Neutron Spectra After Penetrating Aluminum, Paraffin, and Water
-G. G. Doroshenko, V. A. Fedorov, and E. S. Leonov .................. 1434 460
An Estimate of the Accuracy of the Variational Method-E. N. Erykalov .......... 1437 462
Comparison of Calculated and Experimental Parameters of Homogeneous
Uranium-Water Critical Assemblies-A. S. Dochenov, N. Ya. Lyashchenko..... 1439 463
Tangential Channels and Thermal Column Reconstruction at the VVR-M Reactor
-G. Ya. Vasil'ev, E. A. Konovalov, V. G. Pankov, and D. A. Yashin ........ 1441 465
The Effect of Core Configuration on Neutron Spectrum from a Horizontal Channel
of the VVR-M Reactor-V. P. Vertebnyi, M. F. Vlasov, and A. L. Kirilyuk ..... 1445 467
New Data on Atmospheric Radioactivity and Fallout Intensity in the Black Sea Basin
-V. P. Kotel'nikov, V. N. Markelov, and B. A. Nelepo ................. 1447 469
The Relative Levels of Stratospheric Fission Fragment Fallout-P. I. Chalov
and M. A. Tsevelev ........................................ 1450 470
Atmospheric Radioactivity above the Atlantic Ocean During May July, 1964
-L. I. Gedeonov, V. N. Dmitriev, B. A. Nelepo, A. V. Stepanov,
and G. V. Yakovleva ....................................... 1452 472
Features of the Equilibrium Shift in the Uranium-Radium Series in Uranium Deposits
with Hard Bitumens-G. N. Kotel'nikov ........................... 1455 474
SCIENCE AND ENGINEERING NEWS
[Scientific Meeting of the Nuclear Physics Division of the Academy of Sciences
of the USSR .................................................. 476]
[The Detroit Fast Reactor Conference-O. D. Kazachkovskii ....................... 477]
CHRONICLES, COMMUNICATIONS
[Reprocessing and Disposal of Radioactive Wastes in the USA-B. S. Kolychev . . . . . . . . . . . . 481]
[Radiation Chemistry and Nuclear Chemistry at Canada's Research Centers
- V. Gromov .. ............................................. 484]
A Glove Box Train-G. I. Lukishov, K. D. Rodionov, and N. I. Noskov ................. 1457 486
New German Whole Body Counter-Yu. V. Sivintsev ............................ 1460 488
Erratum ...... ............................... .. .. .. . .... .... . 1462
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CONTENTS (continued)
RUSS.
PAGE PAGE
The Table of Contents lists all material that appears in Atomnaya $nergiya, Items originally published
in English or generally available in the West are not included in the translation and are shown in
brackets. Whenever possible, the English-language source containing the omitted items is given,
The Russian press date (podpisano k pechati) of this issue was 11/10/1965.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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PLASMA STABILITY IN A MIRROR MACHINE WITH STABILIZING RODS
(UDC 533.9)
B. A. Trubnikov
Translated from Atomnaya gnergiya, Vol 19, No. 5,
pp: 415-420, November, 1965
Original article submitted March 10, 1965
The well-known criterion for plasma stability 6 f dl/B < 0 is general'iz'ed to the case of an anisotropic
plasma (psi ;,-, pi) in an axially nonsymmetric field. Stability conditions are found for a mirror machine
with stabilizing rods. The theoretical results are in satisfactory agreement with experimental data ob-
tained on the PR=5 deVice.
A stability criterion was obtained in [1] for a plasma with an anisotropic pressure and an axially symmetric
field:
S P11 B21 dl>0,
where r is the distance of a line of force from the axis; R is the radius of curvature (R > 0 for a concave line and
R < 0 for a convex line); B is the magnetic field intensity; p II and pl are the components of the plasma pressure
parallel and perpendicular to the field; the integral is taken along the line of force. This criterion can be general-
ized to the case of axially nonsymmetric fields. For this purpose we write it in the form
Ba (p 11 + p1) dl> 0,
where 8 B is the increment in field to the next (outer) line of force. If all plasma ions have the same v 2 (v is the
velocity) and the same value of J1 = ui/ B, the adiabatic invariant (Jl is conserved during a displacement), crite-
rion (2) is equivalent to
SB vl dl
B CU z I I + 2 V1 1>0 ,
j0,
which can be obtained from the conservation of the adiabatic. invariant J11 = fv11dl = const and the fact that the in-
crement in the energy of a particle when it undergoes a convective transition from one line of force to the next(outer)
must be positive.
We shall apply criteria (2) and (3) to the study of plasma stability in a mirror machine with stabilizing rods.
When there are 2n rods with a current J in each (the current flows in opposite directions in adjacent rods), the scalar
potential of the field B = V 0 near the axis has the form:.
Bo (z) dz - 1 Bo (z) r2 +4 c a )n cos ntp,
where B0 (z) is the field on the axis itself, and a is the radius of the circle within which the rods are situated. Further
A
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Br = _ 42 Bor-{can. rn-1 cos ncp; I B = _ 4nJ r-1 I
sin ncp;
can
BZ Bo 4 B?r2.
Taking Br and B. as quantities of the first order of smallness and 6 Bz 1/4Bo r2 as a second-order quantity, we
find for the modulus of the field:
B - Bo + 2B0 (- BOB0 Bog) r2
2 2n-2l
-B,
can rn cos ncp + ( can) r
In order to determine the quantity 6 B = s V B appearing in criteria (2) and (3) (s is the vector with coordinates
S r, r6 (p , S z), we must know the vector V B:
V B 2Bo C C -Bo B? + 2 B?2 r2
- B. 4nJ nrn-1 cos ncp
a,
+ 4nJ 2 (2n - 2) r 2n-3
( can J 1 ;
1 4nJ n-1
VNB = 2I3o Bo ca,, nr sin ny.
Second-order corrections can be neglected in the term V zB = B. On integrating the equations of the lines of
force, we find
r r0 /sin nrp0\i/n
= /I
V0 ` sin n~
dq)
sin nnip
(Po
a (sin n(po)
2 z/1
1-n C dt
Pn/2
'
0
n 2
where 3 (z) = Bo BO (z)
(0) ca ; a = canBfllro(0) _ ; 1 is the typical length over which the axial field BO (z) varies. In the
simplest case the field on the axis of a mirror machine can be approximated by the parabola Bo (z) = Bo (1 + z2 / l 2).
Then B = 1 + t2, where t = z/l. Expressions (8) are correct to within terms of the second order of smallness in the
parameter e = ro /i 0, (15)
R2 (t) (x)-P (t)
-x
where x = zref / 1 is the point at which particles are reflected; 8 (x) = v 2/ J 1Bo (0). Criterion (2) takes the form:
+x
Aa (1) (P 11 + P1) dl > 0, (16)
P3 (t)
-x
where x = zmax / 1 is the plasma boundary. Here we have utilized the fact that terms of order e 2 can be dropped
in the remaining factors under the integral signs, thus allowing integration to be carried out directly along the axis .
The above criteria contain only the parameter a. We must now determine the critical value of a, above
which the plasma becomes stable.
In the particular case of n = 2, to does not appear in a and so the plasma will be stable for a > acrit at all
values of the radius (near the axis). If, however, n >_ 3, the critical value of acrit will determine a radius
t
crit r canBo (0) n-2
ro _ L- 4nJl acritl
beyond which (for r > rocrtt) the plasma becomes stable.
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Let us examine the case n = 2 more closely. For the field on the axis we shall apply the parabolic approxima-
tion (3 = 1 + t2. We then have from (8)
-2a arc tan t. sin (Po -a arc tan t
tgY=tg(Poe Q j~~sincpe
A(1) = [(a2-1 +2t2) ch Ta-4at sh Ta]
(19)
1 [(a2 -1+2t2) sh Ta - 4at ch Ta ] cos 2
'~ 13 ~0+
where Tot = 2a arctaiTt. The second term, being an odd function of t, drops out the criteria (15) and (16), and con-
sequently they will not contain the angle cpo. If we write
Aa (t) = (0-1+2t2) ch Ta - 4at sh Tai
(x) 1-f- 2x2-t2 alt
1 a lea (t)
(1-1-t2)3 ]~x2-t2 >
0
For a = 0 (no current in rods) A0(t) = 2t 2- 1, and it can be seen on working out the integral Io (x) = - Tr / 8 [ 13
+ (3/(3 16 )], that stability cannot be attained at any value of x (we recall that this pertains to the parabolic approxi-
mation for the field on the axis). Stability results only if a > 1; this is clear from the expression:
Ia(x)Ix'o= 2 (a2-1)>0 for a>1.
0 for J1 C 1 ,
As a is increased small values of x first begin to be stabilized, and then larger values. The function xcrit = f (a),
found by integration from the condition Ia (xcrit), is shown in Fig. 1 (curve 1) for a system consisting of four rods
(n = 2). It is clear that x = 1 (and so also x < 1) is stabilized for a = 8J l / can Bo Pz~ 3.
Criterion (20) refers to the case when the plasma contains ions with identical values of v2 and J.L. The above
results remain qualitatively the same, however, even if the plasma contains particles with different values of v2. .We
consider the case of a Jl "cutoff" Maxwell distribution:
f (v) =
l coast exp Mv2
(- 2T )
V2 B (zmax
for J > 1
V2 B (zmax )
Here M is the ion mass, T the ion temperature, and zmax the plasma boundary. For this case we readily find
(x = ?max / 1 ):
PII +P1=M (UI -f 2 ) f dv
=coi-st [4R (x)-R (I)]'V R (x)-R (t),
and in particular we find for the parabolic approximation
Pu +P1 ^' (3+4x2-t2) 1/x2-t2. (24)
If we insert this expression in formula (16), we obtain the following condition in place of criterion (20):
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ja (x) !1a (t) 3 (1+t2)tz x"-t dt > 0.
= J
Fig. 1. Length of stable region z as a function
of the parameter a = 811 / ca2Bo for a system
with four rods (n = 2); 1) for given v 2 and J
= v i / B (identical particles); 2) for "cutoff"
Maxwell distribution.
70(x)= - 16 RYp(9R 3-2P2).
This expression is negative for 0 < x < 1, as is I0(x) [see (20)].
In real devices the mirror ratio rarely exceed 2, and so there is
not much point in considering x > 1; also, the parabolic approxi-
mation for the field on the axis breaks down in this case. In par-
ticular, we shall not discuss the "stability" appearing in formula
(26) when 95 - 3 - 2,32 < 0, which corresponds to 8 > 4.14 or
x > 1.77. Stability appears only when a > 1, which follows from
the expression [for comparison see (21)]:
ja(x)x+o=(a2-1)x2>0 for a>1. (27)
J"
crit
r
Fig. 2. Relative value of modulus of magnetic
field I B I in the plane z = 0; 1) four rods; 2)
six rods; dotted line shows stable pressure dis-
tribution p(r) in the system with six rods.
As a is further increased, more remove values of x will be
stabilized. Figure 1 (curve 2) shows the relationship xcrit = f (a),
found from condition (25) by numerical integration. In particular,
x = 1 (zmax = 1 ) is stabilized at a 2.4.
We now consider the case n> 3. In this case Eqs. (8) for
the lines of force cannot be integrated in a closed form. Only the
"moment" at which the stability appears for limitingly small x
can be fairly easily determined. Putting t = 0 in formula (14) for
A(n) (t) (with p = 1, cp = V0), we find that for s = 1 + t2 the
quantity Aan) (0) = (n- 1) a2- 1. From expressions (15) and (16)
we find that for x 0 the plasma becomes stable when:
a > acrit- }fin-1
crit a ca2B$
r? In_3 _ 12 j/2 Jl '
crit a `ca2Bo
r0 In-4 _ a ~7 /l
41 3
crtt
to the plasma will be unstable if its pressure decreases with radius.
Criterion (28) has a very simple physical interpretation, and can be obtained from the following considerations.
Since v 0 the particles will not deviate much from the plane z = 0. Formula (6) and the parabolic approxima-
tion yield the following expression for the modulus of the field in this plane:
2 4n 2 2n-2
B(r)=Bo +2[-l2+CcaJ r If
The curve B(r) / Bo = f (r) is shown in Fig. 2. The field decreases with r for small values of the latter but begins to
increase at larger r, when the last term in (30) becomes important. The critical distance rcrit corresponding: to the
minimum field is found from the relationship 8B/ 8r = 0, which yields
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x" I // 1 11
Va,
0.5 j 1.0 1.5 d
Fig. 3. Length of stable region z as a function
of the parameter a = 12J1 ro/ ca3Bo for a sys-
tem with six rods (n = 3); 1) for given v 2 and
Jy = v 2 /B; 2) for "cutoff" Maxwell dis-
tribution.
zit
dt
= a B~a~tl '
4n J1 rn_2 _ 1
ca'lB8 crit yr1_1 ,
the same result as formula (28).
For r > rcrit we have aB/ar > 0, which also leads to stabil-
ity since the field increases from the plasma boundary towards the
periphery. The particular case n = 2, when it is possible to have
everywhere aB/ or > 0 (see Fig. 2), was considered above. It is
clear that for n = 2 the plasma will be located near the axis of the
system. When, however, n equals 3, 4, 5 . . . and so on, the plas-
ma must flow into the "hole" corresponding to the minimum in
the field (see Fig. 2), so that the stable configuration takes the
form of a plasma cylinder around rcrit; the plasma pressure p(r)
decreases both outwards from rcrit and also inwards from rcrit to-
wards the axis (see the dotted curve in Fig. 2).
We now consider x Pt 0. Restricting ourselves to the case
t >> 1 and neglecting terms of order t2, we find from Eqs. (8)
cp -cpo = -a sin nqo (1- a cos npo),
will be considered a small quantity of order t = z/ 1. Further, we have
Yo[1+acosncpo-~ a2 (n-cosncpo)~.
Since a ro -2, we find from (32) that
-8ro (n - 2) a sin ncpo (1- 2a cos n(po).
Inserting these expressions into formula (14), we find, to the same accuracy (.t2),
("`)
(t)= (n-1) a2-1-;-3t2
22a2 (n-1) [1-4(n+1)-1-a2n (2n-3)]
a4122(n-1)(n-2)(2n-3) cos2ncpo.
Here we have dropped terms that are proportional to t since, being odd functions, they will drop out of integrals (15)
and (16). The last term in (35) depends on go, and consequently, the stable plasma shape for n ? 3 will no longer
be axially symmetrical.
For simplicity we shall restrict ourselves to a system consisting of six rods (n = 3):
131 (t) = 2a2-1
3t2 [1-i- 2a2 (3a2-5) + 4a4 cost 3cpo]. (36)
Since t is taken to be small, this means that a will be close to the value a = 1/,r2, corresponding to t = 0. Conse-
quently, in the term with t2 in Eq. (36), we may put a = 1 / -r2, which gives
Aa ( 1 ) C 1- 5 cos2 3cpo) (37)
Criterion (15) takes the following form, correct to within x2
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2a2 -1- 4x2 5 cost 3Wo) > 0.
This gives
4 2a2-1
X Clltlx?i
15 (1-',0,2 3TO
The other criterion (16) with the pressure pl, + pl given by formula (24) leads to a result which is the same as (39)
except for a factor i2:
(2)Ix 2xcv
xcrit 0. After denoting
b(ro) by bo, we obtain the following expression for B2(ro, z):
B2=bo--b 2b
0 Yoo
z2 + (13)
Hence, it is obvious that if 82B2/ az2 is to be positive, it is necessary that the curvature of b = b(r) at the minimum
be sufficiently small (Fig. 1). In the best case (bo = 0), we find:
J32 = b2 1 + 2 -:- .
ro
Thus, the faster the field along z increases, the closer the field minimum to the axis. However, for small curvature
of the [b = b (r)] curve, rather large distances b (rl)/b (ro) are required in order to secure a sufficiently large internal
radial mirror ratio (ro- rl). Therefore, the radial dimensions will be comparatively larger, and the field increment
along z smaller, in the case of traps with a larger radial mirror ratio. In order to secure the largest possible rise of
the field along z, it is necessary to assign a NO function that diminishes rapidly along the axis, such, however, that
32B2/ 8z2 is everywhere positive.
As an illustration of the existing possibilities, we shall consider a field which, for z = 0, is assigned by the
expression:
b (r) = c1r-m + c2r"` (m, n > 0). (15)
The presence of the field minimum for r = ro provides a relationship between cl and C2:
M
C2 = - clro m_n.
n
a2B2
2 Zm-2 2
az2 = 2clro 1 -~ (2-mn).
n
Hence follows the condition for the existence of the field minimum with respect to z:
Calculation of a2B2/ az2 at an arbitrary point r yields
1 aZ - 2cir -211-2 (1- m) + 2c2r2"-2 (1 + n)
c1c2r"-1,4-2. [4 - 2 (m - n) - (m ? n)21
=cir-'m-z?{2(1-m)? n [4-2(m-n)
-(m+n)'1 ( r r ) m+n +
2M2 ) Cr ) 2 (m+fl)l
0
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r 2n+n
The latter expression, which is quadratic with respect to -) , in-
ro
Fig. I. Graph of the field in the median
plane (z = 0).
dicates that 022B2 2 vanishes at the points rs, which are determined
by the expression:
r8 (/ 111+11 n 4-2(m-n)-(n+n)2
ro rn {_- 4(1+n)
4-2 (m-n)-(m+n)2 2 1-MI
t [ 4.(1+n) ] - 1+n } .
Here, the expression under the radical sign will be negative if the follow-
ing value is positive:
D-4-4(m-n)-(m+n)2>0.
Thus, the requirement for the positive determinacy of the quadratic form (19) leads to the condition:
m 4MD 2 1/2
~cr (oa)+ h it + 4 I
T2 /
Here M is the mass of the atom, D the self-diffusion coefficient of the liquid, and the function ycrit(t) is found from
(4) and (5), where gl (w) must be understood as the spectrum of vibracy motion of atoms in the liquid.
To calculate the spectra of slow neutrons, we must know the differential w.r.t. energy of the scattering cross
section,
(Eo -> E) = dd 2a dQ
and the first angular moment,
(Eo ---> E) = ddszaE cos 6 dQ.
In calculating the cross section by integration with respect to time, the integration with respect to dl can be per-
formed analytically. From (1) and (3) we find:
(?-I-1)2 e-ay (t)-e-b' (t),
a (E0 --> E) = ao 4n?E0 eE12T X 'e-
Y (t) ) cos et dt;
0
a
(Eo-->E)= E'o+E o (Eo-->E)-6o (?+1)
2 }1E0E satEo 1 fEOE
0 r
X Y (t) { L a+ Y fit) i e-ay (t) b
0
e-by (t) } cos st dt. (14)
y(t). JJ
Consequently the evaluation of these cross sections, like that of the second-differential cross section, reduces to
evaluation of a Fourier integral, which can be performed by introducing a "cutoff factor."
Brief Description of the Algorithm
z
For calculating 5dE a (E0 --> E) and at (E0 -> E) by the above method, an algorithm has been
devised and is known as Program for Calculating Cross Section by integration with Respect to Time [Russian acronym
"PRASSIV""]: it begins with calculation and storage of the function y(t) and its derivative y1(t) at Nt reference
points with constant spacing ht. In calculating y(t), provision is made for possible approximate allowance for Einstein
vibrations with high frequency w o, which are not excited during scattering. The influence of these vibrations on
y(t) is eliminated firstly by adding a term (variation of thermal factor) which is constant for a crystal and varies
smoothly for a liquid; and secondly by adding a small-amplitude "flicker" with frequency w0 which leads to a tran-
sition with an energy change which is a multiple of hw 0. If T
we can integrate by Simpson's rule with interval t1 / H (H can be varied). If (18) does not hold, the integral is eva-
luated as a sum of integrals of half-wave cosine curve, each of which is calculated from Gauss's formula with n = 6.
To shorten the calculations, a (which is of order unity) can be varied.
For economy in the use of subroutines, the cutoff factor and cos & t are calculated from values of the trigon-
ometrical and exponential functions at the preceding point.
Integration with respect to t is terminated when the cutoff factor becomes less than a given value e or when t
reaches its maximum value tmax = Nt * ht. The limitation imposed on the length of the main part which stores the
function y(t), i.e., on Nt, imposes a limitation from below on 6 (it assumed that the cutoff factor continues to
operate to the end of the main part).
For a crystal (D = 0, for which y(t) tends to its ultimate limit as t -> oo, we subtract from the integrand its
limiting value and thus calculate only the cross section for inelastic scattering. The cross section for elastic scat-
tering is found separately. For a liquid (D > 0) all scattering is inelastic.
This algorithm was used as a basis for the "PRASSIV-1" computer program for calculating a (Ea->E) and
a 1 (Eo --). E), and for the "PRASSIV-2" program for computing d2o/ d (ldE.
Changes in Scattering Cross Section Due to Melting of a Crystal
The author of [6] measured the total cross section for scattering of neutrons by water as a function of the tem-
perature and state of aggregation. He found that when ice undergoes transition to water at 0?C, there is a disconti-
nuous change in the total cross section for very slow neutrons; on further increase of temperature this cross section
increases nonlinearly, rising very rapidly by comparison with the weak linear dependence of the total scattering cross
section for ice.
When ice melts, its temperature remains constant, and thus the motions of its atoms (which can be typified as
"rapid" or "crystalline") should not change very much. The essential changes are the disappearance of long-range
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order in the positions of the molecules and the appearance
of diffusion motion leads to an abrupt change in the total
to transition from elastic to quasi-elastic scattering, since,
in the first place, the integral is unaffected by replacing
the 0 runction Dy the Lorentz runction, ana, in the second
place, the magnitude of the discontinuity in the total cross
(approximately as 1/v), showing that it is due to inelastic
so scattering.
N By means of our model of diffusion motion of atoms
Ice
1000 1?DOt, eV 1 in in a liquid (as used in the PRASSIV algorithm), we can
study the effect of diffusion on inelastic neutron scattering
Fig. I. y(t) for motion. of hydrogen atom in water at
without the interference of other factors. For this purpose
?C in the solid and liquid states.
O IC
need onlyallate the diffeential and total scatter
ccur-
ing cross sections at a given temperature T and either with
D ;.4 0 (liquid) or D = 0 (crystal). Such calculations were
made for water-ice at 0?C by means of the PRASSIV-1
program. The vibration spectrum of the -hydrogen atom
J00 was taken from [7], and the coefficient of self-diffusion
for water was taken, following [8], as 2 ? 10-5 cm2/sec.
Figure 1 plots y(t) for ice and water. To make it
easier to assess the effect of scattering times on the scat-
tering law, the times are plotted in reciprocal electron
volts. It is seen that for t < 50 eV-1 diffusion has practi-
cally no effect on the form of y(t), and consequently with
6 >` 0.02 there will be no detectable effect of diffusion.
For a crystal, y(t) tends to a constant limit at large t, while
proportional to t.
for a liquid it is rou
hl
g
y
for ice and water. The scale is of velocities v = in-
stead of the more usual energies, so as to cover a wide
energy range on the same graph. For the initial energy
002 0.04 0,06 0.08 Olv, eV-72 E0 = 0.00078 eV, vo = 0.028 eVl/2. The breadth of the reso-
lution function 6 was taken as 0.0002 eV. It will be seen
Fig. 2. Differential cross sections for scattering of that the appearance of diffusion motion of the atoms leads,
in the first place, to shortening and broadening of the elas-
tic peak (in our case these effects are slight because we
deliberately chose a resolution comparable with the quasi-elastic broadening A), and in the second place, to the ap-
pearance of marked additional scattering with final neutron velocity 0.05-0.1 eV1/2, which corresponds to acquisi-
tion by the neutron of energy averaging about 0.005 eV. It is this additional scattering which leads to the step-wise
increase of total cross section during melting. The appearance of additional inelastic scattering with low energy
transfer is explained by the fact that in the presence of diffusion motion y(t) rises rapidly with time (see Fig. 1),
i.e., the atoms become as it were less rigidly bonded, in contrast to their firm bonding in the crystal.
We calculated that the increase on melting of the total scattering cross section should be about 18 barn: the
experimental value is about 25 barn. There is thus a qualitative agreement between theory and experiment. Con-
sidering that the vibration spectrum and autodiffusion coefficient are very approximate, we cannot expect more than
this qualitative agreement. Further experimental and theoretical work is undoubtedly needed on the scattering of
neutrons by liquids.
neutrons by water and ice.
1. L. Van Hove, Phys. Rev., 95, 249 (1954).
2. V. F. Turchin, Slow Neutrons [in Russian], Moscow, Gosatomizdat (1963).
~
1
l
Ice(D=0)
Water (D
=2.10
-5cm
i
sec Figure 2 plots the differential cross sections a (v0 -*v)
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3. M. Nelkin and D; Parks, Phys. Rev., 119, 1060 (1960).
4. P. Egelstaff and P. Schofield, Nucl. Sci. Engng, 12, 260 (1962).
5. V. F. Turchin, Inelastic Scattering of Neutrons in Solids and Liquids, Vienna (1961), p. 259.
6. K. Heinloth, Z. Phys., 163, 218 (1961).
7. P. Egelstaff et al., Inelastic Scattering of Neutrons in Solids and Liquids, Vienna (1963), V. I, p. 343.
8. D. Cribier and B. Jackrot, J. phys. et radium, 21, 69 (1960).
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THE HYDRATION OF CATIONS IN HEAVY WATER
(UDC 542.934 : 546.212.02)
V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 433-437, November, 1965
Original article submitted January 28, 1965
The authors use a molecular-kinetic description of the two-layer hydration model to analyze the iso-
topic differences of free energy and enthalpy of solution in aqueous and heavy-water solutions of al-
kali-metal halides. They discuss the lifetimes and water-molecule densities in the secondary hydra-
tion layer. They show that the ions undergo dehydration in heavy-water solutions. They show that
the differences between the free energies and enthalpies of solution in light and heavy water should
increase with the cation radius, i.e., from Li+ to Cs+. Their results agree with the experimental data.
Practical and theoretical interest attaches to the changes in the physicochemical properties of water occa-
sioned by substituting deuterium for hydrogen: so far there has been no complete explanation of the observed dif-
ferences between the thermodynamic properties of light and heavy water. Special attention is deserved by the
marked difference between the solvent capacities of light and heavy water-the solubilities of salts are lower in
heavy water, the isotope effect sometimes reaching 25-3G% [1], while the heats of solution have greater absolute
values in heavy water [2]. Ions are more easily extracted and sorbed from heavy water by ion-exchange media [3, 4].
The explanation seems to lie in the structural differences between H2O and D20. The thermodynamic prop-
erties and structure of water are well represented by Samoilov's model [5, 6], in which the arrangement and short-
range order of the molecules in water are regarded as identical with those in ice [1]. In heavy water, as compared
with light water, there is a smaller proportion of unfilled vacancies, the molecules have lower mobility, and the
deuteron bonds are stronger [7, 8]. Onthe whole, heavy water is more like ice in its structure and the nature of the
thermal motion of its molecules. In this sense we can say that it is more structured than light water.
In considering the thermodynamic equilibrium between the two states of water in a salt solution (i.e., as ionic
hydration shells or in the main residual bulk which is not disturbed by the ionic field), it is easy to see that strength-
ening of the structure will displace the equilibrium by removing water molecules from the hydration shells. The
isotope effects mentioned above can be explained by the weakened ionic hydration in heavy water.
The connection between hydration and solvent structure is easily established on the basis of Samoilov's mo-
lecular-kinetic ideas [6]. An important characteristic of hydration is the ratio between the time during which water
molecules remain as nearest neighbors of an ion (;T 1) to the lifetime around the equilibrium position (,r), in the un-
disturbed solvent:
Ei-EH
RT
_ C
where Ei is the energy barrier separating the equilibrium positions within and without the hydration shell, and EH is
the activation energy of self-diffusion in pure water. In D2O (a more structured solvent), the activation energy of
self-diffusion is greater [8], i.e.,
ED-;_EHH-bEW.
The barrier ED = EH + 6 Ei, which determines the emergence of D2O molecules from the hydration shells,
can vary for two reasons: either owing to the different interactions of H2O and D2O molecules with the ion, or
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because of the difference between their moments of inertia (the libration frequency of the D20 molecule is less
than that of the H2O molecules).
According to Rabinovich [7], the mean energy of rotational oscillations of the D20 molecule is lower than
that for H2O, while the corresponding activation energy is higher. The difference between the libration frequencies
largely determines the isotope shift in pure water [9]. In an ionic field the libration frequencies and the values of
6 Ei should be higher. However, we must remember that D20 has a lower polarizability [7]. This causes some de-
crease in 6 Ei, but on the whole 6 Ei > 0. The increased strength of the hydrate complexes on replacing H2O by
D20 confirms the results of [10] for the shift of the bands in the electron absorption spectra of Fe3+, N i2+, Co2+, and
Cr3+ in the short-wave region.
Applying (1) to a heavy-water solution, we get
oEi-oEw
(tii/'C)D = e RT (2)
(ti/T)H
If the libration frequencies were unaltered near the ion, the isotope shifts would be the same inside and outside the
hydration shell. Increase in the libration frequencies in the ionic field does not reduce 6 Ei, and therefore we al-
ways have
SEi > SEw. (3)
(Ti/'OD > I
(Ti/t)H
i.e., the relative lifetime of a D20 molecule in a hydration shell is greater both near a positively and near a nega-
tively hydrated ion.
From (4) it follows that hydration is reinforced in heavy water. However, this contradicts the experimental
data mentioned above. The dependence of the isotope effect on the nature of the ion determines the value of 6 Ei.
Clearly S Ei is greater when there is a stronger field created by the ion at the positions of its nearest-neighbor water
molecules. Since the electrostatic field of the ion in its primary hydration layer decreases with increasing ionic
radius ri, the value of SEi for alkali-metal cations must increase from Cs+ to Li+. From (2) it follows that the dif-
ference between the lifetimes of H2O and D20 molecules in a hydration shell will be greatest for Li+.
However, the experimental data indicate that the isotopic differences in the heats and free energies of solu-
tion of salts vary regularly in just the opposite sense. Figure 1 plots data from [2] for 6 L = LD - LH, the difference
between the heats of solution of alkali chlorides in heavy and light water. It is seen that the absolute value of the
effect increases from Li+ to Cs+. Figure 2 shows a similar variation in the free energy change 6 F on transfer of a
salt molecule from heavy to light water [11]. From the figure it is seen that the free energy of solution of the salt
in heavy water is greater than in light water, and increases from Li+ to Cs+.
According to Born's thermodynamic equation for the free energy of hydration
const
AF~ Eri
where e is the dielectric constant of the solvent: this equation also fails to explain the way in which the isotope
effects of hydration [12] depend on the nature of the ion. In fact, from (5) it follows that
8OF _ const / 1 I > o.
ri \ ED P-H,/
This equation gives the sign of the effect correctly. However, according to (5), the free energy of hydration ought
to decrease with increasing ionic radius from Li+ to Cs+.
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N
0
-600
._d
RbCI
sCl
a
KCL
LiCI i
0'
,A
Fig. 1. Difference between heats of solution of
alkali chlorides in heavy and light water, plotted
versus cation radius.
1.Zt,A
This particle shows how to explain the above facts on the
basis of a two-layer hydration model [13, 14]. In this model it
is supposed that, in addition to the primary hydration layer im-
mediately next to the ion in which the solvent molecules are
tightly bonded to the ion by nondipole forces, there is also a
more remote layer B (Fig. 3) in which the mobility of the water
molecule is greater than in the remaining main bulk of the
water (layer C), where they are not disturbed by ionic fields.
Vdovenko et al. [14] suggest a molecular-kinetic treatment of
the two-layer model. They introduce two barriers EA and EB
which determine the equilibrium positions of molecules in
layers A and B and the corresponding relative lifetimes,
AEA
CA_eRT
DEB
T B- = e RT
T
where AEA = EA - EW > 0 and DEB = EB - EW < 0.
Figure 4 shows the relation between the energy barriers.
It was demonstrated above that the potential barriers in layers
A and C are higher in heavy water. It is thus natural to suppose
that in D20 - the more structured liquid-the degree of struc-
tural irregularity in layer B is less than in light water. There-
fore, as a whole, the potential curve of D20 lies lower.
Since the observed relation between the isotope effect
and the nature of the ions cannot be explained by means of the
chan
es in the ba
i
i
l
y
A
d
i
i
l
g
rr
ers
n
a
ers
an
t
s natura
C,
to seek
Fig. 2. Difference between free energies of solu-
tion of alkali chlorides in heavy and light water, an explanation in the way in which the activation energy and
f
Fig. 3. Two-layer model of hydrated cation.
li
etime in layer B vary with the isotopic composition of the
water. In fact, the region B of broken structure near each ion
appears as a result of competition [15] between the orienting
effects of the ion's field and the tendency for the ice-like skele-
ton to retain its former, more economical configuration. Thus,
the mutual interrelationship between the two mechanisms of
disturbance of the water structure (i.e., electrostatic interaction
with the ion and strengthening of the skeleton on transition to
D20),should be more intense in layer B.
Let us consider the expected relationship between
A = ED B - Ell B and DEB = EB - EW < 0, the characteristic dis-
ruptive effect of the ion on layer B. We shall base our discus-
sion on Bernal and Fowler's concept of the structural tempera-
ture [16], according to which the water in a salt solution has
the properties of pure water at a higher temperature. As the structural disruption is localized in layer B, it is in
this layer that the effective structural temperature appears to be raised.
.We must bear in mind that the differences between the properties of H2O and D20 decrease with rising tem-
perature. This is seen, for instance, in the temperature dependences of the heats of evaporation (Fig. 5) AHD20/AI-1HZO,
and of the vapor pressure [1, 17]. The enthalpy characterizes the depth of the potential well in which the molecule
is located. Consequently the deepening of the potential well on transition to D20 must be less marked in layer B
than in pure water. In other words,
A < 6Ew,
Furthermore, we can assert that will be the less, the stronger is the disruption of the water structure in layer B,
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Fig. 4. Potential energy of water molecules
near an ion: I and II) equilibrium positions
in layers A and B, respectively; III) equilib-
rium position nearest to ion in layer C.
Approximate Barrier Potential of Hydration of Ions
in H2O
Barrier poten- -
tial of layers, Li+
Na+
K+
Cs+
kcal/ mole
A EA
1.19
1.07
1.14
0.99
0 TB
-0.81
-0.97
-1.27
-1.28
40 60
Fig. 5. Temperature dependence
of the ratio between the heats
of evaporation of light and heavy
water.
i.e., the greatest is the absolute value of AEB. The table
gives tentative values of AEA and DEB. It is seen that the
absolute value of AEB increases in the order Li+- Cs+.
The value of 0 should decrease in the same direction. Let
us now see how the differences in lifetimes T B in layer B
alter on going from Li+ to Cs+. For D20 we can write
(see Fig. 4):
P
TB=
Be RT _ TBe RT
A- 8EW
(TB/t)D = e RT
(TB/T)H
Consequently, since the difference A- d EW < 0 also increases in absolute value on going from Li+ to Cs+, for any
ion the ratio
(tB/T)D G 1
(TB/t)H
also increases from Cs+ to Li+, being nearer to unify for Li+ than for Cs+. Thus the isotope effect is greatest for Cs+
and decreases on going to Li+. This result can be extended to the thermodynamic properties of heavy and light water.
Since the lifetimes are connected with the thermodynamic probabilities, it follows from (7) that the density
of D20 molecules is lower in layer B, and consequently the ions are less markedly hydrated in heavy water. This is
easily demonstrated, remembering that the current of substance through the potential barrier is proportional to the
concentration of molecules and inversely proportional to the lifetime of water molecules in the equilibrium position.
Considering the transfer of molecules from layer B to layer C and back, we can write
IB-.CQBTC
IC-B QCTB
where pB and pC are the densities of molecules in layers B and C. In equilibrium, the currents through the barrier
are equal in either direction, and hence
QB TC
QC TB
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By (8) we get
QB (/QB') (tB/T)D _QC _QC ) D- H (TB/ti)H
QB) < QB)
CQCJD CQCJH
On the other hand, the molecular density of heavy water is less than that of light water [1, 17]. Thus, by (10),
D D
H H
< 1 .
QB QC
Thus D20 has a reduced density of molecules in layer B. Thus, the ions are dehydrated in heavy water.
Let us rewrite (9) in the form:
D-SEIV
D QB QC D (TB/t)D = QD RT
e
QB QC (TB/T)H QH
Since* PC /pC < 1, dehydration in heavy-water solutions must be most marked for Cs+. On going to Li+, there is
a decrease in the difference between the molecular densities of light and heavy water.
When H is replaced by D, the thermodynamic properties (e.g., free energy and enthalpy of solution) of a salt
solution can alter for two reasons: either because of displacement of the molecular energy levels in the hydration
shells, or by decrease in the coordination number (or, more generally, the density of molecules near the ion). If we
assume that the second mechanism predominates for alkali-metal cations, we can easily explain all the observed
effects-the weakened interaction of alkali-metal cations with water on going over to D20, and the increase in this
effect in the direction Li+ -- Cs+. However, in the case of strongly hydrated ions there is an increased contribution
to the isotope effect from the primary hydration layer. For multiply charged ions of small radius we can therefore
expect increased hydration in heavy water.
1. A. I. Brodskii, Isotope Chemistry [in Russian], Moscow, Izd-vo AN SSSR (1952).
2. E. Lange and W. Martin, Z. phys. Chem., A180, 233 (1937).
3. V. M. Vdovenko and E. K. Legin, Radiokhimiya, No. 3 (1966).
4. V. M. Vdovenko, E. K. Legin, and A. V. Zharkov, Radiokhimiya, No. 3 (1966).
5. Yu. V. Gurikov, Zh. strukturn. khimii, 4, 824 (1963).
6. 0. Ya. Samoilov, Structures of Aqueous Solutions of Electrolytes and Hydration of Ions [in Russian], Moscow,
Izd-vo AN SSSR (1957).
7. I. B. Rabinovich, Isotope Effects in the Physicochemical Properties of Liquid Deuterium Compounds [in Russian],
Doctorate dissertation, Gor'kii (1963).
8. Yu. V. Gurikov, Zh. strukturn. khimii (1966).
9. C. Swain and R. Bader, Tetrahedron, 10, 182 (1960).
10. J. Bigeleisen, J. Chem. Phys., 32, 1583 (1960).
11. J. Greyson, J. Phys. Chem. 66, 2218 (1962).
12. J. Hepler, Austral. J. Chem., 17, 587 (1964).
13. H. Frank and M. Evans,J.Chem.Phys., 13, 507 (1945); H.Frank andWen-Yang-Wen. Disc. Faraday Soc.,
24, 133 (1957).
14. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legiri, Radiokhimiya, No. 3 (1966).
15. Yu. V. Gurikov, Zh. strukturn. khimii, 1, 286 (1960).
16. J. Bernal and R. Fowler, J. Chem. Phys., 1, 531 (1933).
17. I. Kirshenbaum. Heavy Water [Russian translation], Moscow, Izd-vo inostr. lit., (1953).
* PC = 1/VC1 where VC is the molecular volume of water; pB has a similar meaning.
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THE BINARY SYSTEM UF4 UC14
(UDC 546.791.4)
L. A. Khripin, Yu. V. Gagarinskii, G. M. Zadneprovskii
and L. A. Luk'yanova
Translated from Atomnaya Energiya, Vol. 19, No.'5,
pp. 437-441, November, 1965
Original article submitted December 2, 1964
Resubmitted in revised form May 31, 1965
The authors study the binary system UF4-UC14 by DTA and x-ray diffraction and plot its phase
diagram. Three compounds are formed in this system: uranium dichlorodifluoride UC12F2, urani-
um monochlorotrifluoride UC1F3 and (obtained for the first time) uranium trichloromonofluoride
UC13F. These compounds melt incongruently at 460 ? 3, 530 t 6 and 444 ? 2?C, respectively.
The optimal conditions for obtaining these compounds in pure form from melts of the system have
been determined in general form.
Using the phase diagram of the system UF4- UC14, the authors explain the contradictory re-
sults obtained by other authors in the synthesis of UC12F2 and UC1F3.
Of the U(IV) halides, mixed halides have been least studied although their preparation and properties are of consider-
able interest. Of the six possible types of mixed U(IV) halides containing two different halogens, only one is examined
here, namely the chlorofluorides. Two chlorofluorides are described in the literature: UC12F2 and UC1F3 [1-3]. The
dichlorodifluoride has been obtained by two methods. In one method an equimolar mixture of UC14 and UF4 was
fused in a quartz tube at 800?C [1] or at 600?C [4] in pure helium. The composition of the solidified melt was de-
termined by chemical analysis and corresponded to the formula UC11.s5F2.05? The x-ray diffraction pattern of this
product was unintelligible and was not deciphered by the authors of [1]. In [4] the melting point of the dichlorodi-
fluoride was found to be 460?C; according to this report, the compound undergoes slow disproportionation to UC14
and UF4 when heated to 600?C. An analysis of [1, 4] does not confirm that these authors obtained UC12F2. This was
also noted in [2], where attempts to reproduce experiments described.in [4] on synthesis of UC12F2 by fusing UC14
and UF4 were unsuccessful, UC1F3 being obtained instead of the target compound.
The second method of obtaining uranium dichlorodifluoride [5] consists in reacting uranyl fluoride with CC14
vapor at 450?C:
U02F2 + 2CC1 -- UC12F2 + 200012 -f- Cll.
Analysis of the product showed that its formula was UC1y63F2, i.e., not that of the dichlorodifluoride. The authors
of [2, 3] indicate that Gates et al. [5] obtained UC1F3, not UC12F2.
The author of [2] obtained uranium monochlorotrifluoride by several methods, but only three will be discussed
here. It was apparently first obtained from uranium trifluoride by the reaction
315?
OF
-{-1/ZC12-- UC1F3i (2)
which is mentioned in [1]. The reaction product contained about 671o UC1F3, the remainder consisting of UF3 and
UF4. In [2] UC1F3 was obtained by the action of CC14 vapor on uranyl fluoride, and by fusing a 1 : 3 molar mixture
of UC14 and UF4 in a quartz tube at 600?C in argon. In the latter case the product contained 80-90% UC1F3. Dis-
cussing syntheses of UC1F3 performed in [2], the authors of [3] note that none of the methods used in [2] gave a
homogeneous product. It is clear from the above that it is very difficult to obtain pure uranium chlorofluorides.
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The aim of the present work is to study the reaction of UC14 with UF4 at high temperatures, construct the
phase diagram of the system, determine the possibility of formation of uranium chlorofluorides in the melts, estab-
lish their compositions and determine the optimal conditions for obtaining pure compounds from the melt.
The initial components were anhydrous UC14 and UF4, purified by sublimation in vacuum. The tetrachloride
contained 99.9'fo UC141 the tetra fluoride had an impurity of ti 110 U02F2.
The system was studied by DTA and x-ray diffraction analysis. The heating-cooling curves were recorded in
an FPK- 59 pyrometer. UC14 - UF4 mixtures, prepared in a dry chamber, were heated in pure helium at tempera-
tures 100-200?C higher than their melting points, held at the maximum temperature for 25-40 min, and the cooling
curves recorded. The cooling rate was 4-7 deg/min, the temperature measurement error ? 3?. The experimental
procedure and the apparatus used for DTA are described in detail in [6].
X-ray diffraction analysis of the specimens was performed in a URS-50I diffractometer with an SI-4R ioniza-
tion counter (Cu radiation, Ni filter, anode voltage 27 kV, current 10 amps). The recordings were made with counter
speed 1 deg / min and time constant of the integrating device 4 sec. All conditions and geometry were kept con-
stant throughout recording. The specimens were powders, packed tightly in transparent plastic cells (diameter of
the powder layer 20 mm, depth 0.3 mm), rotated at 30 rev/min. Preparation of the specimens was performed in the
dry chamber because these compounds are very hygroscopic. The cells were sealed at the top with a thin Teflon
film; its "background" was taken into account when the diffraction patterns were processed.
Some of the uranium tetrachloride sublimed from the melt and was deposited on the cold lid of the apparatus,
so the compositions of the specimens after DTA did not agree with those of the initial mixtures; the compositions
of the cooled fusions were therefore checked by chemical analysis. The contents of uranium and chlorine were de-
termined by quantitative analysis; the fluorine content was found by subtraction. We also determined the content
of U02, formed by partial hydrolysis of the halides by the residual moisture in the apparatus; it was less than 0.5
to 0.616. The analytical methods are described in [6]. When it was necessary for the diffraction analysis specimens
to have specific compositions (for example, containing 25, 50, or 75Q/o UF4), the mixture of the components was fused
in evacuated nickel ampoules, which were then sealed. This eliminated volatilization of UC14 and the composition
of the specimen remained unchanged.
Figure 1 gives the phase diagram of the system UC14 - UF4, constructed from DTA and x-ray diffraction data.
It has 12 fields, the phase designation of each of these being indicated in the figure. The liquidus curve has seven
sectors, corresponding to crystallization of the a- and 0- forms of uranium tetrachloride and tetrafluoride and three
mixed compounds. The individual sectors of the liquidus intersect at six invariant points. It will be seen from the
phase diagram that the following compounds are formed in the system: the trichloromonofluoride UC13F, dichloro-
fluoride UC12F2 and monochlorotrifluoride UC1F3. The trichloromonofluoride is formed from the melt at 444 t 2?C
by the peritectic reaction
0.15UC14 cr + (0 60UC14 -~- 0.25UF4) I - UC13Fcr , (3)
When the system is heated, crystalline UCL3F is formed; it melts incongruently at this temperature, decomposing
by the reverse reaction to solid UC14 and a melt containing 28.0 mole o UF4.
Uranium dichlorodifluoride crystallizes from the melt at 460 f 3?, due to the peritectic reaction
0.34UC1F3 Cr (0.24:UF4 -I- 0.4:2UC14) 14--- UCI2F2 cr ? (4)
When the system is heated, the UC12F2 formed melts incongruently, leading to formation of crystalline uranium
monochlorotrifluoride and a melt containing 38.5 mole o UF4.
Finally, uranium monochlorotrifluoride is formed from the melt at 530 ? 6?C, as follows:
0.55UF4 cry- (0.20UF4 J- 0.25UC1,) I UCI F, cr
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UCZf + i
460?0
UC14 20 40 60 80 OF
UF41 mol.To
When the system is heated to 530 # 6?, UCIF3 melts
incongruently with formation of crystalline UF4 and a
melt containing 44 mole Qjo UF4.
All three uranium chlorofluorides and therefore
thermally unstable and decompose at elevated tempera-
tures; the thermal stability decreases as follows: UC1F3
-> UCl2F2 --> UC13F. The phase diagram of the system
UC14 - UF4 shows that Katz et al. [7, p. 541] did not give
the correct scheme of thermal decomposition of uranium
dichlorodifluoride, and their equation
2UCl2F2- UF4?UC14. (6)
is incorrect. In fact, this compound does not decompose
into the tetrafluoride and tetrachloride, but forms UC1F3
in accordance with (4); this equation indicates a hitherto
undetected close genetic relationship between uranium
dichlorodifluoride and the monochlorotrifluoride, these
compounds being linked by mutual transitions.
X-ray diffraction analysis showed that the solidified
melts containing 50 mole ?jo UF4 did not consist of UC12F2
alone, but also variable amounts of UC1F3 and another
phase (evidently UC13F, the content reaching as much as
25-30 wt. lo) and very small amounts of the initial com-
ponents. The reasons for this were the excessive cooling
rates (4-7 deg/ min) and incompletion of the peritectic
formation reaction (4), which was evidently slow (due to
participation of the solid phase UC1F3). In consequence,
the specimen contained unreacted UC1F3, and the liquid
phase, which was not fully converted, solidified at the
eutectic temperature. This also explains the prolonga-
tion of the eutectic into the region of compositions with
more than 50 mole ?jo UF4. In this region the eutectic
Fig. 1. Phase diagram of the system UC14 - UF4. is evidently metastable, so that in this part of the phase
diagram the eutectic line is expressed by a dashed line
(cf. Fig. 1).
By analogy, specimens with 25 mole jo UF4 contained not only UC13F but also UC14 and UCl2F2 (10-30 wt.1o).
This explains why (3) is a slow reaction and why some of the UC14 and the melt were not converted. The residual
melt solidified at the eutectic temperature. The eutectic line may therefore be prolonged into the region of com-
positions with less than 2% UF4, which is metastable for the eutectic. The composition of specimens with 75 mole jo
UF4 contained not only UCIF3 but also UF4 and UCl2F2 as impurities:
Figure 2 gives x-ray diffraction patterns of the initial salts, melts with compositions 3UC14 + UF4, UC14 + UF4,
UC14 + 3UF4, and the protective Teflon film. The figure also gives the most characteristic reflections of the com-
pounds formed in the system. The structural characteristics of the pure compounds UCl '2 and UC13F, formed in
this system, have not been fully determined; however, our data on the interplanar spacings and lattice constants of
UC1F3 agree with data in [3].
We can thus draw the following practical conclusion: to obtain pure UC13F, UCl2F2 and UC1F3 the melts must
be kept at the appropriate peritectic temperatures for a time sufficient to allow the reaction to proceed to completion.
The phase diagram of the system UC14 - UF4 enables us to explain why other authors have obtained contra-
dictory data on the preparation of UCl2F2. As already mentioned, the authors of [1, 4] discuss the preparation of
this compound by fusing equimolar amounts of UC14 and UF4. Reference [2] indicates that fusion of a 1 : 1 molar
mixture of UC14 and UF4 does not give UC12F2, but a product consisting mainly of UC1F3. It would appear that this
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WO
t
a
b
c
f
Fig. 2. X-ray diffraction patterns of UF4 (a), UC14 + 3UF4 (b); UC14 + UF4 (c); 3UC14
+ UF4 (d); UC14 (e); Teflon film (f). The arrows indicate reflections of the compounds:
1) UCIF3; 2) UC12F4; 3) UC13F.
discrepancy is due simply to the fact that these authors used different cooling rates of the melts; in one case the
rate was too high and the bulk of the previously crystallized UC1F3 was therefore not converted to UC12F2; in the
other case cooling was slower, so that UC12F2 accumulated in the specimen. Furthermore, since the process was
performed at 450?C, which is virtually the same as the temperature of incongruent melting of UC12F2, an increase
in temperature of only 10? led to decomposition of UC12F2; the principal reaction product could then be UCIF3.
The phase diagram of the system also explains why, at equal cooling rates of the melt, the dichlorodifluoride
is the only one of the three chlorofluorides obtained in the pure form. The point is that whereas UC13F and UCIF3
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are formed by a single peritectic reaction the formation of UC12F2 is more complex; when a melt containing
50 mole % UF4 is cooled the first stage is crystallization of UF4 alone (this begins at 585?C); then UC1F3 is formed
from the solid tetrafluoride and the melt, and, finally, UC12F2 is obtained from UC1F3 and the melt. The dichloro-
difluoride is thus formed by two successive peritectic reactions, neither of which proceeds to completion if the
cooling rate is too fast. Furthermore, since the region of existence of the dichlorodifluoride begins in the center of
the diagram, specimens obtained contain both trichloromonofluoride and monochlorotrifluoride, whereas specimens
of these two compounds contain only an admixture of the next nearest chlorofluoride.
1. The authors-have studied the binary system UC14 - UF4 by DTA and by chemical analysis, and have con-
structed the phase diagram.
2. Three uranium chlorofluorides are formed in this system: UCIF3, UC12F2, and UC13F (which is described
for the first time). All three chlorofluorides melt incongruently at 530 t 6, 460 f 3, and 444 # 2?, respectively.
No solid solutions were observed in this system.
3. The optimal conditions for obtaining uranium (IV) chlorofluorides from binary melts of the system
U C14 - UF4 have been basically determined.
1. J. Warf and N. Baenziger, The Chemistry of Uranium. Ed. by J. Katz, E. Rabinovitch USAEC, TID-5290 (1958),
p. 120.
2. A. Savage, J. Amer. Chem. Soc., 78, (12), 2700 (1956).
3. E. Staritzky and R. Douglas, Analyt. Chem., 28, (7), 1210 (1956).
4. N. Gregory, Report RL-4.6.905 (1945). Quoted in [7].
5. J. Gates et al., Report CD-460 (1944). Quoted in [1].
6. L. A. Khripin, Yu. V. Gagarinskii, and L. A. Luk'yanova, Izv. SO AN SSSR, Ser. khim. n., No. 3, 14 (1965).
7. J. Katz and E. Rabinovitch, The Chemistry of Uranium, National Nuclear Energy Series. Division VIII, Vol. 5,
McGraw-Hill Book Co., Inc., (1951).
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NOTES ON ARTICLES RECEIVED
CONSTRUCTION OF A SECTORED 300 key CYCLOTRON
WITH EXTERNAL INJECTION
(UDC 621.384.611)
V. A. Gladyshev, L. N. Katsaurov, A. N. Kuznetsov,
E. M. Moroz, and L. P. Nechaeva
Translated from Atomnaya Energiya, Vol. 19, No. 5,
p. 442, November, 1965
Original article submitted February 9, 1965
The efficiency of utilization of accelerated particles with a thin target can be improved by using additional
acceleration after passage through the target [1]. To test the feasibility of additional acceleration, a small sectored
cyclotron with deuteron energy -300 keV has been constructed at the Physics Institute of the USSR Academy of
Sciences. It is proposed to perform a number of investigations with this cyclotron: in particular, it has been fitted
with external ion injection in its median plane [2]. The magnet is made of three separate C-shaped magnets. This
ensures appreciable depth of azimuthal variation of the magnetic field without the need for additional windings be-
tween the sectors, and permits easy access to the chamber. The magnet diameter is 70 cm. Each pole piece is a
sector with straight edges and angle 66?. The magnet current is stabilized to within 3 ? 10-6. In addition, the field
of each of the three magnets is stabilized by an independent proton stabilization system.
The pole pieces form part of the lid of the vacuum chamber, while the chamber itself consists of several
sections. The main section consists of three triangular chambers made of brass, each of which is bolted to the side
walls of the pole-piece sectors of two neighboring magnets. The vacuum seal is of lead wire which is attached to
the slits between the individual components of the chamber and squeezed against them by special fastenings. The
oil vapor diffusion pump of type N-5T yields a vacuum of '' 2 ? 10-6 mm Hg.
Observation of the beam is by movable probes which can be positioned in any part of the accelerator chamber
at the required angle to the beam by means of a spherical vacuum joint with Teflon packing and a movable arm,
also with Teflon packing of the Wilson type.
The source and accelerator tube can be moved in the median plane of the magnet, so that the point of injec-
tion of the beam into the chamber can be varied.
To get the accelerating voltage to the dees, voltage from a generator is fed to a quarter-wave spiral line
made of copper tubing wound on a cylindrical glass frame. The accelerating voltage on the dees is up to 20 kV.
In addition to its constructional features (divided magnet, sectional vacuum chamber, spiral quarter-wave
line), the cyclotron is distinguished by external ion injection, which opens up new possibilities for the use of sources
of polarized particles and other complex sources.
1. L. N. Katsaurov and V. G. Latysh, Trudy HAN SSSR, XXXIII, 235 (1965).
2. V. A. Gladyshev et al., Proc. of International Conference on Accelerators, Dubna (1963), [in Russian], Moscow
Atomizdat (1964), p. 658.
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WITH EXTERNAL INJECTION -
(UDC 621.384.611)
V. A. Gladyshev, L. N. Katsaurov, A. N. Kuznetsov,
E. M. Moroz, and L. P. Nechaeva
Translated from Atomnaya i`nergiya, Vol. 19, No. 5,
p. 443, November, 1965
Original article submitted May 29, 1965
This article provides data on the magnetic field of a sector cyclotron with a split magnet, calculated for the
acceleration of deuterons to an energy of 300 keV. The cyclotron sectors are shifted away from the magnet's cen-
ter along the radius, while the center contains cylindrical core. The required field was secured by experimentally
determining the magnet parameters.
The field was measured by means of a coil, which was moved in steps. The coil was connected to the circuit
of a ballistic galvanometer. Passing through the check points in the sectors, the coil was moved in steps of 20 along
the azimuth and steps of 1 cm along the radius. The field at the check points was measured by means of the nu-
clear resonance method.
The focusing properties of the field of an isochronous cyclotron depend on the azimuthal variation depth. and
are determined by the frequencies of betatron oscillations. The azimuthal variation depth is characterized by the
"flutter," defined as F - t/32) _ (B)z
~13~2
In this cyclotron, the flutter smoothly increases from 0.2 to 0.45 as the radius changes from 10 to 30 cm. The
amplitudes of the field's first and second harmonics, which characterize the departure of the magnetic field from
symmetry, are smaller than the amplitudes causing radial instability by approximately one order of magnitude.
The equations of motion were integrated by means of an electronic computer, while the measured field was
assigned in the form of tables. This made it possible to obtain complete information on the behavior of particles
and the orbit parameters in the actual field.
We plotted the equilibrium orbits for different energies and calculated the mean magnetic field along the
equilibrium orbits. The thus obtained field differed only slightly from an isochronous field, while the phase shift
in acceleration from 40 to 300 keV was equal to 6? for an energy increment of 10 keV per revolution. The proper-
ties of the orbits are especially clearly revealed in the so-called phase ellipses, which close after N revolutions.
The number N is related to the frequencies Qr and Qz of betatron oscillations by the following expressions:
By plotting the ellipses for different energies and betatron oscillation amplitudes, it was found that the maxi-
mum allowable amplitude of radial oscillations, which was equal to 3 cm at 50 keV, increased with an increase in
the energy and attained 5-6 cm at energies above 100 keV. The frequencies of betatron oscillations calculated
with respect to the phase ellipses by means of a computer indicated that the focusing was sufficiently effective
throughout the entire energy range.
The betatron oscillation frequencies calculated by means of the computer were compared with the frequency
values calculated under the assumption of circular orbits. This comparison showed that the frequencies calculated
by means of the "smooth approximation" expression, the expression based on harmonic field analysis, and the ex-
pressions derived under the assumption of a step field differed from the results obtained by means of the computer
by 5-7a/o.
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An analysis of the magnetic field shows that the split-magnet cyclotron design makes it possible to produce
an isochronous field with great azimuthal variation depth, whereby good focusing in all orbits is secured.
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OF ALPHA-SCINTILLATION CHAMBERS
(UDC 543.52)
L. V. Gorbushina and V. G. Tyminskii
Translated from Atomnaya L`nergiya, Vol. 19, No. 5,
pp. 443-444, November, 1965
Original article submitted March 1, 1965
Original abstract submitted April 22, 1965
The standard a-scintillation chambers presently used for a-radiation measurements have a cylindrical shape
with a volume of 350-2000 cm3. Even with the maximum chamber volumes, the sensitivity of the instruments does
not exceed 3.7 ? 10-13 Ci/pulse/ min, which is insufficient for emanation measurements in dosimetry work and
emanation determinations of the percentage of radioactive elements in water.
The article provides the results obtained in experiments on improving the sensitivity of instruments with
a-scintillation chambers by increasing the utilization factor of alpha radiation and using chambers with the opti-
mum dimensions.
Figure 1 shows the dependence of the utilization factor of a-radiation (K, %) on the scintillation chamber's
volume (v, cm3). Curve 1 was plotted by using the available data obtained in experimental determinations of the
utilization factors in chambers with different volumes [1, 2], while curve 2 was plotted on the basis of the approxi-
mate expression K = ' 9- ? Ioo , which is convenient for approximate estimates of the utilization factor of
a-scintillation chambers of various sizes where the height and the diameter are approximately equal. The table
contains experimental data, from which it is seen that the utilization factor of alpha radiation has different values
in different sections of the chamber's sensing surface
i
ON
(F
g
'500 72090 V. cm3
Fig. I. Dependence of the utilization
factor of a-radiation on the scintillation
chamber's volume: 1) experiment; 2)
calculation.
It was found that the radiation utilization factor has
the largest value at the chamber's bottom and that it sharply
increases if a negative voltage is supplied to this section.
Fig. 2. Schematic diagram of the
chamber: 1) zone 1; 2) zone 2;
3) zone 3; ) conical cham-
ber; ---- ) standard chamber.
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Operating
Area of the
sensing surface
Measured activity, Io of
total activity
surface
cm2
percentage of
without
with electro-
over-all area
a field
static field
Bottom
88.2
21
35
56
Wall
zone 1
106.1
25
27
17
zone 2
112.0
26
22
14
zone 3
118.2
28
16
13
If a- scintillation chambers are used for measurements with respect to thoron (in through flow), the optimum
voltage value is equal to -400 V. The counting rate produced by a control specimen in this case increases from
450 to 535 pulses/ min. Thus, the factor of radiation utilization in the chamber increases by 191o.
1. V. L. Shashkin, Methods for Analyzing Natural Radioactive Elements [in Russian], Moscow, Gosatomizdat
(1961).
2. E. I. Zheleznova and A. A. Popova, Byulleten' Nauchno-Tekhnicheskoi Informatsii ONTI (Gosgeoltekhizdat),
No. 6 (50), 70 (1963).
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OF PENETRATING SECONDARY y-RADIATION
D. L. Broder, A. P. Kondrashov, and A. V. Kudryavtseva
Translated from Atomnaya L`nergiya, Vol. 19, No. 5,
pp. 444-445, November, 1965
Original article submitted October 26, 1964
Original abstract submitted August 5, 1965
Secondary y-radiation, which contributes greatly to the resulting dose rate beyond the shield, arises in the
radiative capture of neutrons in the materials of the screens, the vessel, and the biological shield of reactors. The
largest portion of capture y-quanta, which determines the radiation fluxes, is formed in the immediate vicinity of
the core.
The present article is concerned with certain experimental assemblies used for simulating the screens and the
reactor vessel, which consisted of alternating layers of steel and a hydrogenous material as well as one-piece mono-
liths. The yield of capture y-radiation from such compositions and methods for radiation suppression were in-
vestigated.
There is a very efficient method for reducing the fluxes of penetrating secondary y-radiation from screens
and reactor vessels which consists in reducing the fluxes of thermal and epithermal neutrons that return from the
light components of the biological shield. This reduction can be secured in two ways: 1) by adding to the mate-
rials of the reactor's thermal shield a substance which intensively absorbs neutrons without producing high-energy
secondary y-radiation (for instance, boron carbide); 2) by placing a layer of this material between the vessel and
the hydrogenous component of the biological shield. -
We 'calculated and measured the reduction of fluxes of y-quanta with energies E > 6 MeV that were formed
in mock-ups of four screen and reactor vessel variants, where the vessel was blocked with layers of boron carbide
.and boron steel with boron concentrations of 0.5, 0.8,~ and 2% by weight.
The fluxes of capture y-radiation can also be reduced by installing immediately beyond the vessel a layer
of a heavy substance with a small neutron radiative capture cross section, for instance, a layer of lead.
The main purpose of our experiments was to determine the variation of the reduction factor for capture y-
radiation fluxes in the case of vessel blocking in dependence on the biological shield's thickness. The blocking
factor was calculated and measured for different shield thicknesses. Good agreement between the theoretical and
experimental values was observed.
The results of calculations and measurements are given in the form of graphs and tables.
Our investigations led to the following conclusions: 1) good materials for reducing the yield of capture y-
radiation are lead (thickness, 60 mm), boron carbide, and boron steel (2'316 boron by weight); 2) the blocking fac-
tor decreases with an increase in the shield thickness up to 4 mean free path lengths, while it changes only slightly
with a further increase in thickness.
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LETTERS TO THE EDITOR
BEHIND THE FRONT OF A STRONG SHOCK WAVE
(UDC 533.9)
V. I. Fedulov and V. D. Borman
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 446-448, November, 1965
Original article submitted April 14, 1965
According to the one-dimensional theory of shock tubes, where it is assumed that the gas in the tube's chan-
nel is ideal, while the friction between the gas and the tube walls is neglected, a region of uniformly heated gas,
which is separated from the thrusting gas by a contact surface, develops behind the front of the shock wave. We
shall refer to this region as the plug of the shock wave. The experimentally measured length of the plug is smaller
than the length calculated according to the idealized theory. For relatively low velocities of the shock wave
(M < 8), this discrepancy can be explained by the effect of the boundary layer on the gas flow in the shock tube
[1-3]. Moreover, the presence of the boundary layer leads to a slight increase in the pressure, density, and temper-
ature of the gas along the plug's length. With an increase in the wave velocity, this effect diminishes. However,
the radiation losses increase, which, in turn, may be the cause of the plug's nonuniformity as a result of the differ-
ent times of deexcitation of the plasma sections located at various distances from the wave front. Therefore, it is
of interest to measure the plasma parameters along the entire length of the plug and not only at the wave front.
The pressure distribution along the length of shock wave plugs was investigated in [4]. These experiments,
which were performed with an ordinary shock tube, showed that the pressure in the plug is constant during the first
50 p sec, after which it drops, attaining a value of 80?/o of the initial value at the contact surface.
The aim of the experiment described here was to investigate the pressure distribution in the plugs of shock
waves produced in electric-discharge shock tubes. The specific feature of such tubes (Fig. 1) is the fact that the
energy of electric discharge is used for raising the temperature of the thrusting gas. In connection with this, there
arise at least two additional factors which promote nonuniformities in the plug of the shock, wave: 1) the electric
discharge time is commensurable with the diaphragm's opening time; 2) the discharge power is not constant in
time.
For pressure measurements, we prepared a data unit whose design was similar to that described in [5-8]. The
distinctive features of the piezoelectric transducer used in our experiments were the following:
1) For the sensing element, we used disks of TsTS-19 piezoelectric ceramic (lead zirconate titanate), whose
parameters were much superior to those of barium-titanate piezoelectric ceramic; the disk diameter was 7 mm,
while the thickness was 0.5 mm;
2) the piezoelectric ceramic disks were soldered by using Wood's low-temperature alloy, which made it pos-
sible to improve the quality of the mechanical joining of the disks to each other and to the end-face of the zinc
acoustic cylinder;
3) for insulation from plasma, the data unit was coated with an epoxide resin layer, which made it possible
to mold the data unit's end-face on the inside surface of the tube; the leakage resistance of the piezoelectric trans-
ducer amounted to a few thousands of megohms.
The entire measuring circuit (see Fig. 1) transmitted without distortion pulses with a duration of up to
700 p sec.
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Fig. 2. Oscillogram of the calibration experiment.
(The pulse from the piezoelectric transducer was sup-
plied to the upper beam, and the signal from the di-
aphragm data unit was supplied to the lower beam.)
The piezoelectric transducers were calibrated by
means of a diaphragm data unit [5]. The operating
principle of the diaphragm data unit consisted in the fol-
lowing: Under the action of a pressure pulse, the dia-
phragm, which is fastened along its rim, is deflected
until it comes into contact with a needle, whose end can
be positioned at a certain given distance from the dia-
phragm's center by means of a micrometric screw. In [5],
the diaphragm data unit was used under conditions where
the duration of the pressure pulse was much shorter than
the time necessary for the diaphragm to reach the needle,
while the diaphragm was considered to be unrestrained
in calculating the magnitude of the pressure pulse with
respect to the time of the diaphragm's movement.
If a constant pressure p acts for a certain time on
a diaphragm whose surface density is p , which corre-
sponds to the conditions in the shock tube, a relationship
between the needle-diaphragm gap u and the time t in
which the diaphragm covers this gas can be obtained by
taking into account the fastening of the diaphragm:
Fig. 3. Oscillograms of signals from two piezoelectric
transducers, located at different points of the tube (x is
the position of the contact surface).
It follows from this relationship that the value of pt2/ u
is constant. This was confirmed in our experiments.
The value of pt 2/ u was equal to 273 ? 7. 10-8 rnm
? sec/cm. A typical calibration oscillogram is shown in
Fig. 2. The experiments on pressure measurement were
performed in the 6-10 range of Mach numbers. Argon
plasma was investigated for an initial argon pressure of
10 mm Hg in the channel. For the propelling gas, we
used helium under a pressure of 3 atm, which was heated
by discharge from a battery of capacitors, which were
charged to 5-6 kV. The pressure in the shock wave's
plug was measured by means of two piezoelectric trans-
ducers, which were located at distances of 263 and 303 cm
from the diaphragm (see Fig. 1). Both oscilloscopes were
started simultaneously, which made it possible to measure
the shock wave's velocity in the channel section between
the two piezoelectric transducers withrespect to the time
interval between the signals from these transducers.
The oscillograms of the signals obtained from the
two piezoelectric transducers are given in Fig. 3. The
position of the contact surface relative to the shock
wave's front, calculated with an allowance for the ef-
fect of the boundary layer on the basis of data from [3], is marked on the oscillograms. It is seen that the pressure
behind the wave front drops over a distance reaching the contact surface, where it amounts to approximately 851o
of the pressure at the front, after which it remains constant until the second shock wave appears. A comparison of
the oscillograms of signals from the first and the second transducers shows that the pressure drop at the shock tube's
section where the first transducer is located is larger than the pressure drop at the location of the second transducer.
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nin Hg
600
600
400
?
I 8
9
M
19 0 1,1 1.1 Z.3 2.4 ZS 1.6 ?.7 ?. 8 2.9 3.0 ?iv-, k sec
Fig. 4. Dependence of the pressure at the front of the first shock wave on
its velocity v (the argon pressure was pt = 10 mm Hg). A) First ,piezoelec-
tric transducer; A) second piezoelectric transducer.
The smoothness of the lower-beam pulse after the second pressure rise could be explained by the fact that the os-
cilloscope beam had left the linear characteristic region.
The dependence of the pressure at the front of the first shock wave on its velocity is shown in Fig. 4. For the
sake of comparison, this figure also shows the theoretical velocity dependence of the pressure (solid curve), which
was calculated with an allowance for the ionization [9]. Good agreement was observed between the measured and
calculated pressure values not only in the region where the ionization effect on the plasma parameters can be neg-
lected (M < 8), but also in the region of considerable ionization (M > 8).
A characteristic feature of the oscillograms of signals from the piezoelectric transducers is the presence of
two pressure jumps, corresponding to two shock waves, which move it in the same direction along the channel of
the shock tube. In order to explain the causes of the development of the second wave, we performed a series of
experiments where the helium pressure p4 in the chamber was measured. In each experiment, we determined the
velocities of the first and the second shock waves and also the time interval between these waves.
On the basis of these experiments, we reach the conclusion that the distance between the first and the second
shock waves diminishes with a reduction in p4; for a pressure p4 = 1 atm, the second wave overtakes the first at the
location of the first transducer. If we know the distribution of the shock wave's velocity along the length of the
tube (which was actually measured in these experiments) and the time interval between the waves at the observa-
tion points, we can estimate their time separation at the diaphragm. This time diminished from 700 to 550 ?sec
with a reduction in the pressure p4 from 3 to 1.5 atm. The measured half-period of the discharge current was equal
to 100 ?sec. A comparison of these time values indicates that the development of the second shock wave cannot
be explained by the heating of the gas during the second and the subsequent half-periods of the discharge current.
Considering the dependence of the characteristic times on the pressure p4, it can be assumed that the second
shock wave develops in the following manner. The shock wave that had developed during the first half-period of
discharge is reflected from the diaphragm back toward the chamber. Then, after repeated reflection from the.
chamber's end-face, it appears as the second shock wave. A reduction in the pressure p4 leads to an increase in the
specific energy input in the discharge region, which increases the velocity of waves in the high-pressure chamber.
This could explain the fact that the second shock wave overtakes the first at p4 = 1 atm.
In conclusion, the authors extend their thanks to N. A. Kolokol'tsov for his interest in this project, N. V.
Filippov for his useful advice at the initial stages of the work, and D. S. Derkbukov, who performed the precision
mechanical work.
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1. A. Roshko, Phys. Fluids, 3, 835 (1960).
2. W. Hooker, Phys. Fluids, 4, 1451 (1961).
3. H. Mirels, Phys. Fluids, 6, 1201 (1963).
4. O. Laport and T. Wilkerson, J. Opt. Soc. America, 50, No. 12 (1960).
5. N. V. Filippov, In the collection: Plasma Physics and the Problem of Controlled Thermonuclear Reactions
[in Russian], Vol. 3, Moscow, Izd. AN SSSR (1958), p. 231.
6. W. Willmart, In the collection: Shock Tubes [Russian translation], Moscow, Izd. Inostr. Lit., (1962), p. 364.
7. G. Knight, in the collection: Shock Tubes [Russian translation], Moscow, Izd. Inostr. Lit., (1962), p. 374.
8. S. G. Zaitsev, Pribory i Tekhnika Eksperimenta, No. 6, 97 (1958).
9. E. Resler, S. C. Lyn, and A. Kantrowitz, In the collection: Shock Tubes [Russian translation], Moscow, Izd.
Inostr. Lit., (1962), p. 218.
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USE OF SURFACE-BARRIER SILICON DETECTORS
FOR MEASURING FAST-PARTICLE SPECTRA .
G. F. Bogdanov and B. P. Maksimenko
Translated from Atomnaya Energiya, Vol. 19, No. 11,
p. 449, November, 1965
Original article submitted April 26, 1965
Surface-barrier silicon detectors of nuclear radiation made it possible to reduce considerably the recording
threshold in the energy analysis of charged particles. A linear dependence of the amplitude of detector pulses on
the proton energy in the 18- 250 keV range was obtained in [1]. The aim of our experiments was to check the pos-
sibility of using detectors of this type for measuring the spectra
of neutral charge-exchange ions and of ions with energies of
10-200 keV emerging from the Ogra machine [2].
The counters which we used were made of n-type silicon
8 f 1 with a resistivity of 700 Ocm and a lifetime of the minority car-
riers of 2100 p sec; the operating surface area of the counters was
'o 5 . I 5 mm2, while the thickness of the gold plating was - 25 p g /cm2.
/?_~N With a bias of 50 V, the back current did not exceed 3.4 ? 10-8 A.
Z 4
The detectors were checked by means of a magnetic sepa-
rator in proton beams with energies of 28; 29.7; 49.5; 69.3 keV.
The dependence of the amplitude of detector pulses on the en-
alib
ation of the
a
linea
ithin the a
u
a
of the
E
w
s
r w
r
r
cc
cy
c
,._ ergy
10 20 30 se arator
The amplitude distribution of the detector pulses in record-
Fig. 1. Amplitude distribution of counter ing protons with an energy of 28 keV is shown in Fig. 1. The total
pulses in recording protons with an energy width at the half-maximum was equal to 11.6 keV; to a consider-
of 28 keV. able extent, it was due to the preamplifier noise.
Fig. 2. Spectrum of neutral ions reaching the walls of the Ogra chamber (the dashed
curve marks the spectrum obtained when the slit was covered with an aluminum foil).
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Figure 2 shows the spectrum of neutral molecular ions reaching the walls of the Ogra chamber. It was meas-
ured under conditions where the energy spread of atomic (E1 80 keV) and molecular (E2 160 keV) neutral ions
did not exceed 10% (according to measurements performed by means of an electrostatic analyzer with a foil). In
order to ascertain that the peak E2 corresponds to neutral molecular ions, the slit in front of the detector was cov-
ered with aluminum foil, which caused the dissociation of H2. The angular spread of the dissociation products of
a single H2 molecule precluded the possibility of their reaching the counter simultaneously. The thus obtained spec-
trum is indicated by the dashed curve without the second peak. The energy loss in the foil was equal to 9 keV.
Thus, the peak E2 in fact corresponds to neutral molecular ions.
The results obtained were in good agreement with the data given in [1]. They show that surface-barrier sili-
con detectors are suitable for measuring the spectra of particles emerging from plasma.
The authors hereby express their gratitude to Yu. S. Maksimov for his help in practical work and the useful
discussions, 9. Z. Ryndina and V. F. Kushniruk for the consultation on the, counter preparation technology, and
A. T. Vinogradova and V. V. Strulev for their help in preparing the counters.
1. R. Ewing, IRE Trans., NS-9, No. 3, 207 (1962).
2. G. F. Bogdanov, P. I. Kozlov, and B. P. Maksimenko, In the collection:
Edited by B. P. Konstantinov, Moscow, Gosatomizdat, (1963), p. 175.
Plasma Diagnostics [in Russian],
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DEPENDENCE OF THE ENERGY LOSS AVERAGED WITH RESPECT
TO THE ELECTRON SPECTRUM ON THE END-POINT ENERGY
OF THE 13-SPECTRUM, THE ATOMIC NUMBER OF THE 3-RADIATOR,
AND THE TRANSITION TYPE
Translated from Atomnaya E`nergiya, Vol. 19, No. 5,
pp. 450-451, November, 1965
Original article submitted January 28, 1965
Final version submitted April 7, 1965
D = 1.6.10-8NtS rad,
Eo
S(E, Zabs)n(E)dE
where N is the density of the flux of 13-particles (cm-2-sec-1), t is the irradiation time (sec), And 'S is the ioniza-
tion loss per single 3-particle, averaged with respect to the electron spectrum (MeV ' cm2 ? g-1). The _S value de-
pends on the absorber material, the end-point energy, and the shape of the electron spectrum; it is calculated by
means of the expression:
TABLE 1. Calculated Values of Ionization Losses
per Single B-Particle for Aluminum and Tissue (water)
:0, Me\I
Absolutely for-
bidden first-order
3 -transitions
I! 1
N 1111
II
N
0,1
13,2
14,4
16,3
16,8
17,2
8,45
9,70
11,5
0,2
7,85
8,55
9,65
9,95
10,1
5,85
6,58
7,70
0,3
5,75
6,30
7,10
7,35
7,50
4,70
5,25
6,05
0,4
4,63
5,10
5,70
5,90
(i , 00
4,03
4,45
5,15
0,6
3,42
3,73
4,20
4,35
4,/,5
3,25
3,55
4,05
0,8
2,83
1
3,05
3,41
3,55
3,65
2,79
3,05
3,43
1,0
2,48
2,65
2,95
3,05
3,15
2,50
2,73
3,03
1,5
2,02
2.13
2,30
2,38
2,44
2,08
2,25
2,42
2,0
1,80'
1,88
1,98
2,04
2,08
1,85
1,99
2,11
3,0
11621
1,661
1,70
1,73
1,77
1,69
1,75
1,82
0,1.
17,1
18,6
21,1
21,7
22,2
10,9
12,5
14,9
0,2
10,1
11,0
12,4
12,8
13,0
7,51
8,45
9,90
0,3
7,35
8,05
9,06
9,39
9,57
6,00
6,70
7,72
0,4
5,88
6,47
7,24
7,50
7,61
5,11
5;65
6,54
0,6
4,30
4,70
5,29
5,47
5,60
4,09
4,46
5,10
0,8
3,54
3,81
4,26
4,44
4,56
3,48
3,81
4,29
1,0
3,08
3,30
3,67
3,80
3,92
3,11
3,40
3,77
1,5
2,48
2,62
2,83
2,93
3,00
2,56
2,77
2,98
2,0
2,20
2,29
2,42
2,49
2,54
2,26
2,43
2,57
3,0
1,96
2,01
2,06
2,09
2,14
2,04
2,12
2,20
S=0
r
ED
1 n(E)dE
0
where n (E) dE is the number of electrons with energies in
the interval from E to E + dE; E0 is the end-point energy
of the spectrum, and S (E, Zabs) is the ionization loss of
electrons with the energy E in an absorber whose atomic
number is Zabs' In [1, 2], the Sti values for tissue were
calculated on the basis of the 13 -spectra of certain radio-
active isotopes, which were measured by means of a scin-
tillation spectrometer. Unfortunately, such analyzers dis-
tort the shape of the S-spectrum in the energy range be-
low 200-300 keV. Moreover, the dependence of S on
the spectral shape has not yet been determined in a wide
range of the spectral end-point energies E0.
We shall calculate here the energy losses of 13-radi-
ation in aluminum and tissue, averaged with respect to
the electron spectrum, for radiators with allowed transi-
tions and with absolutely forbidden first-order transitions.
The Z values for the (3-radiators were equal to 10, 20, 40,
60, and 80; the end-point energies of the spectrum were
in the range 0.1 E0 3.0 MeV. The electron energy
distribution n (E) dE was calculated in the same manner
as in [3]. In calculating S, we used the data given in [4, 6]
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9 6
ili II
I Tissue (wa er)
2
1 .11
V
Aluminurri
Fig. 1. Averaged energy losses of 5-radiation in alumi-
num and tissue (water) in dependence on the end-point
energy of the 13-spectrum: 1) Z = 10; 2) Z = 80;
allowed transitions; ----) absolutely for-
bidden first-order transitions.
TABLE 2. Accuracy of S Determinations Based
on Expression (4)
1
Allowed (3 transitions
Absolutely forbidden
first-order 13-transition
E0, MeV
I 8, %
Ea, MeV
6, %
0,1-1,0
-}-2; -18
0,2-0,4
?8
1,0-2,0
?8
0,4-1,5
0; -12
2,0-3,0
+9; -2
1,5-3,0
?5
3
i
r'
p
I
I
a10 9 9 9 8 7 6 543
6.5 6 6 5 4 3 3 2S2.5Z
I
I
it
Fig. 2. Dependence of the averaged energy losses of
1i-radiation in aluminum on the mean energy of the
(3-spectrum: 1) allowed transitions (a); 2) absolutely
forbidden first-order transitions (f).
for the ionization losses of the electron energy in alumi-
num, water, and tissue in the energy range 1:s: E5 E0 keV.
The contribution of electrons with energies of 1 - 10 keV
to the S value is considerable for small E0 values and
large Z values of the radiator; it attains 3010. In deter-
mining S on the basis of the experimentally measured
S -spectra, this energy range is usually neglected [ 1].
The results obtained in calculating 'S by means of ex-
pression (2) for aluminum and tissue (water) are given
in Table 1 and Fig. 1. The relationship between -9 ti and
S Al for the corresponding E0 and Z values in the case of
allowed transitions and absolutely forbidden first-order
transitions in the range 0.1 5 MeV
N*I NVT
G' (R, 0)/G (R, 0)
S, %
Aluminum
20
0,21
0,64
0,40
12,4
0,19
0,09
9,5
0,36
0,71
0,66
6,0
0,63
2,2
Copper
28,5
0,43
0,71
0,66
4,8
0,54
2,9
48
0,44
0,71
0,66
4,5
0,54
3,2
5
0,44
0,60
0,14
5,0
0,73
0,68
10
0,49
0,56
0,14
5,4
0,71
0,62
Tungsten
13
0,47
0,62
0,14
5,6
0,71
0,63
l
17
0,52
0,59
0,14
6,5
0,71
0,56
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Earlier, papers [1, 3] provided the experimentally determined coefficients of secondary y-radiation for iron,
nickel, and nickel with boron on the basis of the neutron spectra of a Po-a-Be-source and of the reactor of the RIZ
stand.
In our experiments, we determined the coefficient of secondary y-radiation for aluminum, copper, and tung-
sten. The measurements were performed on the RIZ stand. The RIZ stand and the experimental devices were de-
scribed in detail in [3]. A single-crystal scintillation spectrometer with sodium iodide, whose diameter and length
were equal to 40 mm, served as the y-radiation detector.
The values of the 6 coefficients and of the intermediate quantities necessary for calculating 5 are given in
the table.
The NO /NY ratio was determined with respect to the instrumental distributions of y-quanta by summing
the counts in each channel, beginning with the amplitudes corresponding to a y-quantum energy of 5 MeV. The
(Ny /Ny) ratio was thus determined for aluminum and tungsten. The shapes of the instrumental 'distributions N"y(E)
and NY (E) and, consequently, the spectral distributions for these media differ only slightly from each other, so that
this operation was justified. For copper, the above distributions differ considerably. It was shown in [4] that the
spectra of y-radiation in the case of radiative capture of neutrons whose energies exceed 50 keV differ considera-
bly from the y-radiation spectrum in the case of thermal neutron capture. Therefore, the N?/N ratios for copper
were determined with respect to the spectral distributions obtained by transforming the amplitude distributions by
means of the matrix used in [4]. It should be noted that the values of these ratios were only by 10-201o lower than
those obtained with respect to the instrumental distributions. The error in determining the S -coefficients was
10-20a/o. It was calculated as the root-mean-square value of the errors in individual factors in the expression for 0.
1. A. T. Bakov et al., Atomnaya Energiya, 13, 31 (1962).
2. L. V. Groshev et al., Atlas of Spectra of Thermal-Neutron Radiative-Capture y-Radiation [in Russian],
Moscow, Atomizdat (1958).
3. S. P. Belov et al., Atomnaya Energiya, 18, 136 (1965).
4. A. T. Bakov and Yu. A. Kazanskii, ZhETF, 46, 1163 (1964).
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
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VISCOSITY COEFFICIENT OF HYDROGEN (Hs, D2), NEON (Ne20, Ne 22)
THE -
AND HELIUM (He3) ISOTOPES IN THE TEMPERATURE RANGE -195 TO +25?C
N. E. Menabde
Translated from Atomnaya E`nergiya, Vol. 19, No. 5,
pp. 553-454, November, 1965
original article submitted February 3, 1965
In studying transfer phenomena, data on the viscosity coefficient of gaseous isotopes and isotopic compounds
are of particular interest in order to obtain additional information on the mechanism of intermolecular interactions.
It is well known that experimental values of the viscosity as a function of temperature may be used to calculate
the force parameters of the interatomic -interaction,potential function, in particular the Lennard-Jones function:
L{ Jig 6
\ r \r. /
where e is the depth of the potential well and a is the collision diameter of low-energy molecules.
At the present time the parameters of function (1) have only been determined and calculated for hydrogen
isotopes H2 and D2. Since the differences in intermolecular interaction for the isotopes of heavier gases are small,
high measuring accuracy is needed in order to detect them. The present measurements . were made on a vibrating-
disk viscosimeter at pressures of 40 to 50 mm Hg-graduated with respect to the viscosity of helium [1]. A special
cryostat made it possible to keep the experimental temperature constant to 0:01?C over the whole temperature
range measured.
TABLE 1. Viscosity Coefficient p, , 106 g/ ern ? sec
He3
?lean Ne22 1Iy D,2
-
T ?C
Tl
T, dC I
j~ T ?C
T, ?C tl T, -(:
i
tl
22,1
V1,6
21,6
311,7
23,3
327,8
26,5 90,2 25,9
125,2
21,6
171,2
18;9
309,6
19;0
324,,4
24;3 89;1 2'1,1
124,7
18,0
170;0
=10,3
288,7
20,0
325,2
20,0 88,8 20,0
123,6
17,6
169,8
-50,5
258,0
17,5
3'2:3,5
~35,6 77,U --28;1
1()9 ,8
=20,0
154,4
-80,8
233,3
=20,3
294;2
-7311 I 68,/1 1
104,8
-53;5
140,5
-90,2
225,8
-33,3
283,6
-90,9 62;7 -73,0
95,8
58,0
138,8
-102,3
215,6
=38,2
280,1
-11815 57,4 -107,1
83,3
-68,0
134,2
--110,3
208,5
-75,2
249,4
-1:396 )1,8 -11140
Om'1
-93,4
123,3
=122,2
206,8
-100,6
227,6
=162,1 45,:3 -183,0
54,1
-121,7
110,6
-130,2
190,3
-119;0
210,3
--183,0 x?1,1 =19:1,8
48,:3
-123;7
109,7
-155,0
166,2
- 146,7
182;4
- 195,8 35;2 --
--
-=147,5
98,0
=156,6
164,8
-150,0
178,7
- - -
--
-159,4
91,8
-156,8
164,5
-154,2
174,8
-160,0
91,7
-161,5
159,6
=156,0
173,0
- = --
-
-174,6
83,6
-174,3
145,3
-160,0
168,2
= - -
-
-179,1
81,2
- 179,0
140,1
-177;3
148,4
- - -
-
-195,8
71, 7
-=195,8
120,3
-181,5
14 3,6
- - -
-
_ 195;8
125,0
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TABLE 2. Viscosity Ratios of Isotopes The accuracy of measuring the relative viscosity
at Various Temperatures was around 0.03afo at room temperature and 0.02% at the
boiling point of liquid nitrogen. The deuterium was ob-
7C nU~%nl (~ ,YVc-z/n'-ceo 'tiic4 "11xe; tained by the electrolysis of heavy water, D20. The iso
topes of neon enriched in a separator (Ne20 to 99.7,91o and
Ne22 to 99.88'o) and helium isotope He3 (99.81o concentra-
O 20 1,391 392 1,047
1,(, 0 1,1/18 tion) were freed from air impurities by means of activated
~4 ~ 1, 1
-20 1,391, 1,017 1,150 charcoal cooled in liquid nitrogen.
-40 1,39(7 1,01,7 1,151
-60 1,;98 1,047 1,151 The measured viscosities of the isotopes in question
-80 1,397 1,047 1,151 are shown in Table 1. We see from Table 2 that the vis-
-1OO 1,397 1,047 1,151
-120 1.395 1. 048 1 ,1,52 cosity ratio of the isotopes, 1IH/t1L, differs from
-140 1 , 388 1,0% 1 ,152 (M / ML) 1/2, where MH and ML are the molecular weights
-160 I,38(; 1,M5 1,152 H
-180 9 , 382 1, 045 9 ,152 of the heavy and light isotopes, respectively. Moreover,
995,8 1,372 1,039 1, 15'l. starting from a particular temperature for each substance,
the ratio diminishes, except in the case of helium, for
which the ratio rises between room temperature and
TABLE 3. Force Parameters of Potential (1) - 110?C, reaching 1.152 at the latter and thereafter re-
mainin constant
Isotope
r'i+, -k
a, A
Iles
11.2
2,561
lie,
I(1,2
2,582
N,,20
34,9
2,796
Nee22
2,80'2
! I ~
36.8
2 , 928
35.4
2,960
g
The viscosity of the isotopes H2 and D2 has been
measured by many workers over a fairly wide temperature
range.
Comparison of our own results with those of others
at two temperatures shows that, at 20'C, our value for
11D / nH (equal to 1.392) is quite close to the 1.388 given
in ~1], 1?39 in [2], and 1.40 in [3]. At - 190.0?C our value
of 7ID2 /r)H2 is 1.375; that given elsewhere is 1.380 [4] and
1.37 [5].
Using the method described in [6], we calculated the force parameters of potential (1) from the temperature
dependence of the viscosity. Table 3 gives the values of these parameters.
1.
A. Rietveld and A. Van Itterbeek, Physika, 25, 205 (1959).
2.
A. Van Itterbeek and A. Claes, Physika, 5, 938
(1938).
3.
J. Kestin and W. Leidenfrost, Physika, 25, 1033
(1959).
4.
J. Coremans et al., Physika, 24, 557 (1958).
5.
A. Van Itterbeek and Van Paemel, Physika, 7., 263 (1940).
6.
J. Hirschfelder et al., Molecular Theory of Gases and Liquids [Russian translation], Moscow, IL (1961), p. 443.
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DETERMINATION OF THE SPECTRAL CHARACTERISTICS
OF ISOTOPIC NEUTRON SOURCES BY PAIRED SCINTILLATION CRYSTALS
OF THE LiI(Eu) TYPE
P. L. Gruzin, A. Z. Kichev, V. M. Minaev_, -V. T. Samosadnyi,
and Su Ch'ang-sung
Translated from Atomnaya E`nergiya, Vol. 19, No. 5,
pp. 454-456, November, 1965
Original article submitted February 25, 1965 and final form May 31, 1965
Existing methods of determining the spectral characteristics of neutron sources require expensive equipment
and considerable time. The determination of the spectral characteristics of isotopic neutron sources by scintilla-
tion crystals of the LiI(Eu) type is based on a method of nuclear reactions induced by neutrons in which only charged
particles are formed [1]. By determining the over-all energy of the charged particles, we can calculate the energy
of the neutrons [2]. The advantage of the scintillation method over-all the rest is its high sensitivity to neutrons.
Owing to the high energy of the Lis(n, a)T (Q = 4.78 MeV) reaction, the effect of y-background on the energy
spectrum of the neutrons is relatively slight.
The energy of y-quantum creating the same light scintillation as that of a thermal neutron equals 3 MeV for
LiI(Eu)-type crystals. Since the number of y-quanta with energy greater than 3 MeV may in most cases be com-
pared with the number of neutrons, the y-background must be taken into account. In this paper we consider the
method of subtracting the y-background by means of paired.scintillation crystals of the Lil(Eu) type [3].
The neutron spectrum of isotopic sources was recorded by means of two LiI(Eu)-type crystals of the same
thickness and diameter, one enriched with isotope L i6 and the other with Liz. The recording efficiency for y -radi-
ation was considered to be the same for both crystals, while that for fast neutrons was 150 times greater in the
Li6I(Eu) crystal than the Li7I(Eu), since the ratio of the number of Li6 nuclei. in these crystals was 150. This enables
us to regard the Li7 I(Eu)-type crystal as practically insensitive to the recording of fast neutrons. The difference be-
tween the numbers of pulses in the same analyzer channels corresponding to the two crystals gives the number of
neutrons recorded by the crystals. Thus the y-background is eliminated.
We used Li6 I(Eu) and Li7 I(Eu) crystals 39 mm in diameter and 16 mm thick; the Lis enrichment, f , for
Lisl(Eu) was 0.90 and the Li7 enrichment for the Li7I(Eu) 0.994.
The presence of a small amount of isotope Lis (0.6%) in the L i7 I(Eu) crystal enabled us to correct the energy
scales with respect to the thermal-neutron peaks present in the apparatus spectra of both crystals. The resolving
power of the LiI(Eu) crystals was only determined with respect to the thermal neutrons and equaled 11%.
The calibration of the crystal was effected with respect to two points, its light output being linearly depend-
ent on the kinetic energy of the neutron recorded. One reference point was the energy corresponding to thermal
neutrons and the other was 4.16 MeV. Neutrons of energy 4.16 MeV were obtained in a Van-de-Graff linear ac-
celerator.
Differential neutron spectra of Po-Be, Pu-Be, and Po- B sources were obtained by the method indicated.
These spectra are shown in the figure. The spectrum of the Po-Be source is similar to that obtained by the photo-
emulsion method [4]. The upper limit of the neutron spectra of the Po-Be and Pu-Be sources lies at approximate-
ly 11 MeV, and for the Po-B source at 6 MeV, as we should expect.
From the neutron spectra obtained, relative determinations of the neutron yields may be made; by using a
source such as Pu-Be (Tr/z= 2 . 105 years) we can also obtain the absolute neutron yields of the Po-Be and Po-B
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#(f?)
20
8 En, MeV
Differential spectra of the a) Po- Be, b) Pu-Be, and c) Po-B
neutron sources obtained by the authors.
sources. Our experimental data.on strength was in good agreement with the standard values. The experimental
data on the neutron yield for the Po-Be neutron source differed by 35?/o from the standard value, this source being
experimental; it may well be that its initial strength was determined incorrectly. For the Po-B neutron source the
difference between rated and experimental values of neutron yield was 51o.
Our neutron-yield results for the Po- Be source were supported by experiments on the y-radiation of the neu-
tron sources. By comparing the radiation intensities of Po-Be and Pu-Be 4.5-MeV neutron sources it was found that
the neutron yield of the Po-Be source was some 1.35 times smaller than the rated value; this agrees with the direct
comparison of neutron yields from the neutron spectra.
Comparison of the 0.8-MeV y-radiation intensities showed that the neutron yield of the Po-Be source was
5.5 times greater than that of the Po-B source.
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Our investigations have thus shown that the proposed method gives fairly reliable differential spectra of iso-
topic neutron sources; this gives grounds for believing that the method is quite applicable for determining certain
characteristics of isotopic neutron sources.
The authors wish to thank B. M. Gokhberg and G. W. Yan'kov for collaboration in the experiments on cali-
brating the LiI(Eu) crystals, and also I. A. Velichko and E. O. Lyalin who kindly supplied the crystals.
1. R. Murray, Nucl. Instru., 2, 237 (1958).
2. E. Segtd, Experimental Nuclear Physics [Russian translation], Vol. II, Moscow, IL (1955).
3. V. V. Matveev et al., "Pribory i tekhnika dksperimenta," No. 4 (1963).
4. B. Whitmore and W. Baker, Phys. Rev., 78, 799 (1950).
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CROSS SECTIONS FOR THE INELASTIC INTERACTION
OF NEUTRONS WITH NUCLEI OF Liz, C12, N14, A127, Fe5
Cu, Pb, U235 U238, and Pu239
Yu. G. Degtyarev
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 456-457, November, 1965
Original article submitted February 20, 1965
This article contains data additional to the results published in [1] for A127, Fe56; Cu, Pb, U235, U238, and
Pu239, and also the cross sections corresponding to the inelastic interaction of neutrons with the nuclei of Liz, C12,
and Nom.
The neutron transmission coefficients for spherical samples of the materials studied were measured in
"reciprocal geometry" [2]. This method is as follows. The intensity of the flow of neutrons from an external
monochromatic source is measured by means of a detector insensitive to inelastically-scattered neutrons, both
inside the spherical sample and in its absence. Owing to the compensation of the elastically-scattered neutrons
[2], the transmission coefficient of a sphere, T = (intensity with sample)/ (intensity without sample), is simply a
measure of the inelastic-interaction cross section.
Neutron
energy, Me
x=r2- rl ,
cm
hr1
r2
16,7
6,35
0,11
0,881?0,007
0,42?0,03
1,8
Liz
18,2
6,35
0,11
0, 867?0,010
0 47?0,04
1,6
20,7
6,35
0,11
0,016?0,008
0,30?0,03
1,4
C12
15,2
3,8
0,28
0,810?0,004
062?0,02
2,8
19,8
3,8
0,28
0,800?0,002
0:65j-0,02
2,4
N14
15,2
9,5
0,14
0,792?0,004
0,70?0,03
2,0
19,8
9,5
0,14
0,792?0,010
0,69?0,05
1,7
A127
8,1
3,0
0,4
0,830?0,012
1,02?0,08
2,3
Fe56
8,1
3,0
0,4
0,700?0,010
1,34?0,06
5,3
19,7
2,9
0,42
0,738?0,007
1,22?0,04
2,2
Cu
8,1
3,0
0,4
0,675?0,010
1,47?0,07
5,5
Pb
8,1
3,0
0,4
0,793?0,008
2,28?0,08
3,5
U235
8,1
1,82
0,5
0,760?0,012
3,11?0,20
3,6
U238
8,1
2,95
0,5
0, 633?0,008
3,10?0,10
5,2
17,5
2,95
0,5
0,679?0,020
2,71?0,21
2,5
13,4
1,5
0,7
0,851?0,011
2,72?0,20
2,3
15,4
1,5
0,7
0,853?0,011
2, 70?0,20
2,0
18,4
1,5
0,7
0,861?0,006
2,57x0,07
1,5
? rl and r2 are the internal and external radii of the spherical sample, respectively.
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Neutrons with energies of 8.1 and 13 to 21 MeV, respectively were obtained in an electrostatic accelerator,
using the Be9(c , n)C12 and T(d, n)He4 reactions. The neutron-flux intensity was measured from the edge of the
spectrum of recoil protons from a scintillation plastic detector. The height and diameter of the crystal were
14 mm, ensuring fair discrimination of y-quanta for neutron energies above 13 MeV. In order to secure discrimina-
tion of y-quanta for neutron energies of 8.1 MeV, a stilbene single crystal was used as scintillator and a pulse-shape
discrimination scheme was employed [3). The main information regarding the samples used in the measurements
is shown in the table, together with the results of the measurements. For light nuclei (from Liz to Alt) a correction
for the fall in the recording efficiency of elastically-scattered neutrons was introduced into the measured transmis-
sion coefficients. The. table shows values of T with due allowance for this correction.
The inelastic-interaction cross sections one were determined with allowance for multiple scattering from the
relation
T=To+(1-To) aet-I-'Pm
ane + aetPm
T = e-nanex
,
(2)
where x is the thickness of the spherical sample, To = e-notrx, atr is the total transport cross section, aet the
elastic-scattering transport cross section, and Pm the probability of a neutron escaping from the sphere after elastic
collision. In no case did the value of the multiple scattering M (see table) exceed 5.501o. This was due to the
strong anisotropy of the elastic scattering and to the sample dimensions chosen.
The results obtained for one are very precise and partly fill up the gap in the neutron-energy range from 8 to
21 MeV.
1. Yu. G. Degtyarev and V. G. Nadtochii, "Atomnaya 6nergiya," 11, 397 (1961).
2. H. Bethe, J. Beyster, and R. Carter, J. Nucl. Energy, 3, 207 (1956).
3. F. Brooks, Nucl. Instrum., 4, 151 (1959).
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OF FAST NEUTRONS IN RHENIUM AND TANTALUM
(UDC 539.17.02 : 539.172.4)
V. N. Kononov and Yu. Ya. Stavisskii
Translated from Atomnaya $nergiya, Vol. 19, No. 5,
pp. 457-458, November, 1965
Original article submitted May 6, 1965
The cross sections for the radiative capture of neutrons in rhenium and tantalum were measured in the energy
range 30 to 170 keV. The neutrons were provided by the T (p, n)He3 reaction on the target of a pulse accelerator
with a maximum proton energy of 1.2 MeV. For recording cases of capture with respect to prompt y-rays, a liquid
scintillation detector of dimensions 0.5 x 0.5 x 0.5 m was used. The neutron energy was measured from the time
of flight with a time resolution of 20 to 30 nsec and a base of 1.5 m.
The figure shows the energy dependence of the cross sections for the radiative capture of neutrons by rhenium
and tantalum nuclei. The cross sections were measured to an accuracy of 10 to 12% with an energy resolution of
10%. The behavior of the cross sections as a function of neutron energy was determined relative to that of the cap-
ture cross section in indium [1], and the absolute cross sections fixed by means of new data on the absolute cross
sections for the absorption of 24-keV neutrons [2]. The reference cross sections used in our calculations were l0Q/o
smaller than those used in [1]. The data of [1], however, require renormalization, all the cross sections being re-
duced 5%, in view of a change in reference cross sections [3]. Thus the difference between our reference cross sec-
tions and those of [1] is effectively 5/c.
Our cross sections agree closely with the results of [1, 4] (these results are shown partly in the figures). In the
tantalum capture cross sections there is competition with inelastic neutron scattering at levels 136 and 159 keV;
this was not observed in [1]. The considerable difference between the results of [5] and the cross sections obtained
by ourselves and in [1, 4] is evidently due to the large indeterminacy in fixing the absolute value of the cross sec-
tions by using the U235 neutron-absorption cross section as reference. This indeterminacy was due to the considera-
ble difference in the spectra and number of emitted U235 neutron-absorption cross section as reference, and this led
02, 1 i 1 1 ! i 1 1
0,02 3 4 5 6 b 7 8 9 0,1 En, MeV
0.2L
0.02
6' 7 8 90,1
a
MeV
Variation of the cross section for the radiative capture of neutrons in (a) rhenium and (b) tantalum with neutron
energy: ?) present work; A) results taken from [1].
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to a 1.7-times rise in the capture cross sections. Hence in choosing the reference cross section preference was
given to the results obtained by measuring the neutron-absorption cross sections in spherical geometry.
LITERATURE CITED
1. J. Gibbons et al., Phys. Rev., 122, 182 (1961); R. Macklin et al., Phys. Rev., 129, 2659 (1963).
2. T. S. Belanova et al., "Atomnaya dnergiya," 19, 3 (1965).
3. H. Schmitt, WASH- 1044 (1963).
4. V. A. Konks, Yu. P. Popov, and F. L. Shapiro, ZhtTF, 46, 80 (1964).
5. B. Diven et al., Phys. Rev., 120, 556 (1960).
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AND XENON BY IRRADIATING ALUMINUM HALIDES IN A REACTOR
(UDC 621.039.3)
A. N. Murin, L. K. Levskii, and A. E. Zakharova
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 458-459, November, 1965
Original article submitted March 1, 1965
Much work has been done in various fields of analytical and nuclear chemistry, geochemistry, and cosmo-
chemistry in determining small concentrations (up to 10-13 or 10-14 g) of elements or their isotopes [1]. For solv-
ing this kind of problem, mass spectrometers (extremely accurate and sensitive instruments) and isotope dilution
are used [2]. The accuracy of the method is determined mainly by the presence of a monoisotope of the element
being studied (the best case) or an isotopic mixture greatly enriched with respect to one isotope. Obtaining mono-
isotopes of inert gases by classical methods of thermodiffusion is an expensive and laborious process. A more prom-
ising method is that of producing the isotopes by means of an (n, y) reaction followed by (3-decomposition, and
also that of irradiating the corresponding halides in a reactor. * Despite the wide application of stable isotopes of
inert gases, however, there is no detailed description of the irradiation procedure and sample preparation in the
literature.
For a variety of reasons aluminum halides are convenient for irradiation. The advantages of these are:
1) insignificant radiation hazard; 2) high specific halogen content; 3) crystalline state of the substance irradiated;
4) comparatively low melting point.
Despite the simplification in the separation process, however, there are some difficulties connected with the
necessity of working with sealed ampoules previously evacuated to a low pressure, since during irradiation the melt-
ing point is 300 to 400?C, so that there may be partial degassing of the sample as a result of diffusion. Attempts
have been made to use crystalline organic halogen compounds (e.g., tetrabromomethylene, C2Br4) together with
the aluminum halides, but these proved unsuccessful. The radiolysis taking place during irradiation raised the pres-
sure in the quartz ampoules and burst them.
The aluminum halides were obtained by reducing the corresponding silver halides with aluminum according
to the reaction
3AgHa + Al = AlHa3 + 3Ag. .
The apparatus for the reaction consisted of two quartz ampoules connected by a crosspiece. The reagent mixture
was placed in one of the ampoules and the system was pumped out to a high vacuum. The ampoule containing the
Yield of Krypton and Xenon Isotopes on Irradiation
with an Integral Neutron Flux of 2.16 ? 1017
ISO-
tope
Reaction Cross Gas yield,
section, 1
mb cm3
Kr80
Br79 rt n >
10,1
,4.10-2
-130 0 -> hrO
13 min
Kr82
Br81+n-3
2,6
?--0,6.10-2
S
> K02
->Br82
35, 7h
Xe182
J127?n->
0,25
6,8.10_4
S
-j Xe128
->J128
25 in
mixture was heated to some 400?C; the AlHa3 condensed
in the second (cooled) ampoule. The whole process
lasted 10 to 15 sec. The ampoule containing the AIHa3
was sealed off and placed in a container for irradiation.
Spring shock absorbers were used in the packing; these
pressed against the ends of the ampoule, which otherwise
would be broken in removing from the irradiation zone.
When using A1Br3 and AlI3, 2 g of the material
were placed in the ampoules. The resultant yield of
krypton and xenon isotopes appears in the table. In
* When a natural mixture of bromine isotopes is irradi-
ated, a bi-isotopic krypton specimen results.
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working with a sensitive mass-spectral apparatus [3], sufficient quantities of krypton and xenon were obtained for
several thousand determinations.
After holding for three weeks, the ampoules were placed in an apparatus for separating and purifying the
inert- gases. After opening under vacuum, the ampoules were heated, and the released gases were subjected to the
purification usual for inert gases [3]. The apparatus contained liquid-nitrogen traps (solid carbon dioxide was used
for working with xenon), and traps containing KOH, CuO (t = 600?C), and Ca (t = 600?C). The purified krypton and
xenon were transferred to ampoules containing activated charcoal, which were then sealed.
The isotope analysis of krypton and xenon was effected in the MV-2302 mass spectrometer (high resolving
power), the peaks corresponding to the krypton and xenon isotopes and those corresponding to possible hydrocarbon
contamination being completely resolved. One xenon peak corresponding to Xe128 appeared on the mass spectro-
gram. The atmospheric-xenon component was less than 0.110. The krypton mass spectrum contained Kr80 and Kr 82,
the ratio Kr80/ KrBZ being 3.8; this practically agreed with computed data. The contribution from atmospheric
krypton was less than 0.0556.
The authors wish to thank D. M. Kaminker for kindly permitting the use of the reactor in the A. F. Ioffe
Physicotechnical Institute, and I. K. Kirin and Yu. A. Shukolyukov for assistance in the work. Student-Diplomat
N. S. Okunev also took active part in the work.
1. D. Barnard, Modern Mass Spectrometry [Russian translation], Moscow, IL (1956). Also D. Beinon, Mass Spec-
trometry and Its Use in Organic Chemistry [in Russian], Moscow, "Mir," (1964).
2. R. Webster, Collection "Advances in Mass Spectrometry" [Russian translation], Moscow, IL (1963).
3. Yu. A. Shukolyukov and L. K. Levskii, "Zh. analit. khim," XIX, 1099 (1964).
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
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MEASUREMENT OF Gd156 ABSORPTION CROSS SECTION
(UDC 539.172.4)
E. I. Grishanin, G. M. Kukavadze, V. I. Lependin,
L. Ya. Mamelova, I. G. Morozov, V. V. Orlov, and D. T. Pilipets
Translated from Atomnaya E`nergiya, Vol. 19, No. 5,
pp. 459-460, November, 1965
Original article submitted April 2, 1965
To use gadolinium as a heavily shielded burnable poison [1], it is necessary to know the absorption cross
section of its unburnable isotopes in order to determine the residual poisoning of a reactor. In the literature
dealing with the unburnable gadolinium isotopes, there is only data on activation cross sections with not even
that sort of information available for Gd15`land Gd156 because those isotopes do not form radioactive nuclei by
the absorption of slow neutrons.
Because of the anomalously large values of the absorption cross sections of the isotopes Gd155 and Gd157,
it is practically impossible to use the existing method of transmission measurements with samples enriched in
the pertinent isotope since, in that situation, a very high degree of freedom from the isotopes mentioned above
is necessary.
The following method was used in this paper for the determination of the Gdr56 absorption cross section.
Samples containing gadolinium oxide in the amount of several milligrams were irradiated in the VVR-M reactor
at the Institute of Physics, Ukranian SSR Academy of Science, with varying total thermal neutron fluxes. Follow-
ing this, the content of Gd157 and Gdlss isotopes was measured on a mass spectrometer. Starting with some value
of the total thermal neutron flux, the Gd157 content reached an equilibrium value deriving only from the forma-
tion of these nuclei because of neutron absorption by the isotope Gd156. In the equilibrium state, the following
relations hold
66 Q7
67 Q6
where 06, 07 are the effective absorption cross sections of Gdlss and Gd157 corresponding to the neutron spectrum
of the reactor in which the irradiation is performed; p 6 and p 7 are the equilibrium concentrations of these isotopes.
The value of 07, obtained by averaging the Gd157 absorption cross sections over the neutron spectrum of the
VVR-M reactor with a neutron temperature of 400 ? 30?K, was 150,000 ? 12,000 barns. In computing the Gd157
cross sections, the resonance parameters given in [2] were used.
Having determined the isotopic composition o f the irradiated samples, it was easy to obtain the Gd156 cross
section from relation (1). Because the cross section at equilibrium concentration is independent of the value of the
total flux, in making measurements of the latter, data on the distribution of the thermal neutron flux and on the
amount of power generated by the reactor were employed.
To increase the equilibrium concentration of Gd157, gadolinium samples enriched to 94.86% in the Gd156 iso
tope were used. The content of other isotopes in the samples was: Gd152, 0.01%; Gd754, 0.14%; Gd155, 0.83%; Gd"7,
2.93%; Gd158, 0.8910; Gdlsu, 0.34%.
The mass-spectrometric, isotopic analysis of the gadolinium samples was performed with an MI- 1311 mass
spectrometer. An ion source with surface ionization was used. A strip of tungsten foil 30 p thick acted as emitter.
The gadolinium samples under investigation were deposited on the emitter in the form of an aqueous solution of
the nitrate.
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For current values of 10-14 to 10-18 A, the ion currents were recorded with an electron multiplier, and for
GdM concentration measurements where the current values were more than 10-b1 A, a direct-current amplifier
was used. Each time, before recording the ion currents, the amplification factor of the multiplier, which equalled
(5-10) ? 103, was determined.
In carrying out this work, the resolution of the mass spectrometer at the level of 5?/o of the mass spectrum
line intensity was 550 for a chamber vacuum of 2 ? 10-7 mm Hg. Before each analysis, the emitters underwent
conditioning, outgassing, and "burnup" of impurities, and the absence of residual lines in the mass range of interest
was checked. As the result of surface ionization, the ions GdO+ and Gd+ appeared on the emitter. In the gadoli-
nium samples used, impurities consisting of isotopes of other rare-earth elements were observed. Some of them,
praesodymium in the form of the ion Pro+, with mass 157 for example, which had very high ionization efficiencies
were superimposed on the Gd+ ions with mass 157 and significantly distorted the results even for the presence of iso-
topic impurities so small they could not be observed by spectral methods. Changing the emitter temperature failed
to get rid of traces of these isotopes, and therefore the work was carried on with GdO ions because that region proved
to be "cleaner." However, in this case, it was necessary to take account of the contributions from 017 and 018lead-
ing to an increase in error because the correction for 017 turned'out to be comparable in magnitude with Gdl57 con-
centration. For a total thermal neutron flux of 1020 n/cm2, the unburned initial concentration of Gd157 was only
216 of the equilibrium concentration; the equilibrium concentration, p 71 was (0.0062 f 0.001146. According to
relation (1), such a Gd157 content corresponds to a Gd156 cross section, for the VVR-M reactor spectrum, os=(0.0062
0.0011)0/o . 150,000 + 12,000 =
(95.65 t 0.09)10 9.8 ? 2.5 barns. If it is assumed that the Gd'5 cross section obeys the 1/v
law in the thermal region, its cross section will be 13. ? 3 barns for a neutron energy of 0.025 eV. This result dif-
fers considerably from the result in [3].
In conclusion, the authors are grateful to A. A Belonozhenko and L. A. Stepanov for assistance in measuring
the isotopic composition of the samples, and also to G. I. Toshinskii for valuable advice.
1. V. V. Orlov, et al., Paper 354 presented by the USSR at the Third International Conference on the Peaceful
Use of Atomic Energy (Geneva, 1964).
2. D. Hughes and J. Harvey, Neutron Cross Sections, BNL-325 (1958).
3. R. I. Holl, ACNP-63, 003, March (1963).
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AFTER PENETRATING ALUMINUM, PARAFFIN, AND WATER
(UDC 539.125.25)
G. G. Doroshenko, V. A. Fedorov, and E. S. Leonov
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 460-462, November, 1965
Original article submitted February 6, 1965
The development of high-efficiency, fast-neutron spectrometers [1] with time-amplitude selection of y-ray
background [2], of automatic stabilization of amplification factor, as well as the development of a reliable matrix
method for computing efficiencies [4, 5] taking into account all the factors which determine the line shape of a
spectrometer [6, 7], including the actual energy resolution of the detector [8], make it possible -to carry out ex-
tended precision measurements of fast-neutron spectra at levels that are a fraction of the maximum permissible
flux; in addition, it appears possible to investigate the fine structure of the spectra.
In the present work, an attempt was made to follow the changes in fast-neutron spectra with penetration
through thick layers of aluminum, paraffin, and water. This is necessary if one is to explain the influence of the
energy dependence of the cross sections of the basic materials under investigation on the shape of the fast-neutron
spectra. A Po-Be fast-neutron source was used which was placed in a paraffin collimator with a 48? aperture an-
gle in order to reduce the contribution from scattered neutrons. The material under study (aluminum, paraffin), in
the form of sheets 70 x 70 cm in size, was located 25 cm from the source. The spectrometer detector was placed
on the surface of the material directly above the source. Experimental results for aluminum (44 cm thick) and
paraffin (45 cm thick) are shown in Figs. 1 and 2.
Data collection time was 3 h, 40 min and 9 h, respectively. For purposes of comparison, these same figures
show results of measurements of the neutron spectrum from a Po-Be source and of the energy dependence of the
total interaction cross sections for aluminum and carbon. In addition, the statistical errors of the measurements
are indicated. The dashed curve in Fig. 2a represents the theoretically calculated hard portion of the neutron spec-
trum from a Po-Be source [9]. From Figs. 1 and 2, it is clear that the fine structure of the spectrum in the case of
aluminum agrees with the fine structure of the original fast-neutron spectrum from the Po-Be source; in the case
of paraffin, the nature of the spectrum is determined by the energy dependence of the total neutron interaction
cross section for carbon.
The fast-neutron spectrum after penetration of a 40-cm water layer is shown in Fig. 3 along with the energy
dependence of the total neutron interaction cross section for oxygen. The instrumental spectrum was taken from
reference [10], in which the experimental geometry is shown. It is clear from Fig. 3 that consideration of energy
resolution in analyzing the instrumental spectrum improves the agreement of the neutron spectrum fine structure
with the features of the total neutron interaction cross section for oxygen.
The results of this work point to the broad possibilities for the application of the new techniques in fast-neu-
tron spectrometry.
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p ee ~o ~ ~ O ~ 0
.~ C O Gi O N N
uisq 'p
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100
80
60
40
70
.n 2
1 2 3 4 5 6 7 8 9 10 En, MeV
Fig. 3. Fast-neutron spectrum from a Po-Be source after penetrat-
ing 40 cm of water:' 1) without including resolution; 2) including
resolution, o 0 = 0.13 [8]; 3) total neutron interaction cross section
for oxygen.
1. G. G. Doroshenko, I. V. Filyushkin, and V. A. Fedorov, "Problems in Dosimetry and Radiation Shielding,'
No. 3, Moscow, Atomizdat (1964), p. 32.
2. G. G. Doroshenko, I. V. Filyushkin, and V. A. Fedorov, Izv. AN SSSR, ser. fiz., 27, 949 (1963).
3. G. G. Doroshenko, V. A. Fedorov, and E. S. Leonov, Problems in Dosimetry and Radiation Shielding, No. 4,
Moscow, Atomizdat (1965), p. 143.
4. G. G. Doroshenko et al., Neutron Dosimetry, V. 1, Vienna, IAEA (1963), p. 337.
5. G. G. Doroshenko et al., Izv. AN SSSR, ser. fiz., 27, 1308 (1963).
6. V. G. Zolotukhin, G. G. Doroshe-nko, and'B. A. Efimenko, Atomnaya 9nergiya, 194 (1963).
7. V. G. Zolotukhin and G. G. Doroshenko, Atomnaya Energiya, 18, 287 (1965).
8. G. G. Doroshenko, V. G. Zolotukhin, and B. A. Efimenko, Atomnaya Energiya, 19, 51 (1965).
9. H. Broek and C. Anderson, Rev. Scient. Instrum., 31, 1063 (1960).
10. G. G. Doroshenko and I. V. Filyushkin, Atomnaya Energiya, 16, 152 (1964).
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AN ESTIMATE OF THE ACCURACY OF THE VARIATIONAL METHOD
(UDC 621.039.51)
E. N. Erykalov
Translated from Atomnaya tnergiya, Vol. 19, No. 5,
pp. 462-463, November, 1965
Original article submitted February 13, 1965
For many reactor problems, the determination of critical dimensions is of interest, and a detailed knowledge
of neutron distribution is not important. In this situation, the critical dimensions are usually calculated approxi-
mately, but one does not always manage to estimate the accuracy with which they are obtained. In this paper,
attention is directed to one of the methods by which it is possible to estimate both the upper and lower limit of
the eigenvalue of a Hermitian operator. The great accuracy of the eigenvalues obtainable by simple approxima-
tions is demonstrated in two examples.
We assume that the neutron flux in a reactor is described by a one-group diffusion equation with time
constant X :
L (D = a,(D. (1)
As is well known, if 4) and DgradcI) are continuous, and 4)(R) = 0 at the reactor boundary (r = R), the system of
eigenfunctions is orthogonal, the diffusion operator L is Hermitian and has a discrete spectrum of eigenvalues. Only
the maximum eigenvalue of Eq. (1) X = X o is of interest as is,the eigenfunction 4) o associated with it. In a case
where it is difficult to solve Eq. (1), it is possible to approximate (Do (r) by a simpler function l o (r). In such case,
it is of interest to know how large the error in the computation of X. will be, and also how to choose 0 o(r) so that
the error is minimized. Following a method similar to one used previously,* we estimate this error.
We expand the trial function 0 0(r) in the complete system of eigenfunctions of Eq. (1):
where the cl are real numbers. The function 0 'must satisfy the same boundary conditions that 4) does, and also
must be continuous along with Dgradl'
Using (2), it is possible to show, on the one hand, that the functional
0 = (+Vo, Li,o) 7,0,
o, 'Po)
1 . (LVo-()*0, LiVo-0 0)
Q -a (1 o, 1Vo)
The quantity a lies between p and the eigenvalue X 1 which follows x0. It follows from (3) that the maximum
value of the functional p for various trial functions will be closest to a o and that only for 0 p = 4) o will the value
of p reach the value X o and the "error" A p go to zero.
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We shall show that even simple approximations ensure high accuracy in p . We assume that the cross sec-
tions in Eq. (1) are constant so that the first eigenfunction of a plane reactor without reflector and of dimension
2R is
mo (r) -- cos (2R r I
It is approximated by the trial function
2
'PO (r) ~' 1-( R
then, as follows from expression (4), the error A p will be such that the relative error in reactor dimension OR /R
corresponding to it will be -1%. If a more complicated function is selected, for example
Vo(r)^ [1-(R )2] [1-a(R )2],
where the factor a, selected on the basis of maximum p , turns out to be 0.21, the value of the error AR/R is
3 10-5.
Now, in contrast to the previous problem, let the absorption and fission cross sections have a cosine distribu-
tion over the reactor, and let the diffusion coefficient be constant as before. Such a situation can exist in a heavy-
water reactor with cosine fuel distribution where it is possible to neglect neutron capture by the moderator and
leakage during slowing down. If a trial function is chosen in the form:
tp,, --- cos [(2n?1) 2R r], n-0, 1, ...,
it is possible to compute p from (3) and to estimate the error Ap from (4). It turns out that the relative error in
reactor dimension does not exceed 0.3% in the critical state (p = 0). In this same problem, if an equal amount
of fuel and absorber are distributed uniformly over the reactor, it is easy to obtain the eigenvalues. In that case,
however, the maximum eigenvalue will be less than p by an amount almost 50 times greater than the error 0 p .
The author is deeply grateful to Yu. V. Petrov, G. S. Danilov, and E. A. Garusov, for valuable comments and
a discussion of the results.
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OF HOMOGENEOUS URANIUM-WATER CRITICAL ASSEMBLIES
(UDC 621.039.520.22)
A. S. Dochenov and N. Ya. Lyashchenko
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 463-464, November, 1965
Original article submitted January 15, 1965; in revised form April 19, 1965
Method of calculation. The Pi-approximation equations for neutron transport and the one-velocity equation
for the diffusion of thermal neutrons were used as the reactor equations. The slowing-down equations were reduced
to a system of multigroup equations of the diffusion type as described in [1]. For this purpose, the entire energy
range was broken down into 12 groups, including the thermal group. The method was developed for homogeneous
reactor calculations.
Experimental critical assemblies.* The core of the critical assemblies was a fuel assembly 70 x 35x 250 mm
in size and with a volume of 0.62 liter. The fuel elements were plates 250 x 70 x 2.7 mm in size pressed from a
mixture of polyethylene and uranium oxide (U3O8). The uranium enrichment was 94o. The plates were covered
on both sides by aluminum foil 0.05 mm thick. In addition to the fuel elements, plates of aluminum, copper, and
1Kh18N9T stainless steel were also used.
Experiments that were performed showed that a multiplying assembly was quasihomogenous [1] for a hydro-
PH pH
gen-U235 concentration ratio 50. When 50, the size of the water gap between the plates
pU 235 PU 235
reached -5 mm and became comparable to the range of thermal neutrons in water. Therefore, it was necessary to
PH
consider the effect of heterogeneity in the calculation of critical assemblies with >` 50. Since the method
PU235
of calculation being used was suitable only for homogeneous systems, it was possible to compare the computa-
tional results with experiment only in the region PH < 50.
P
U235
Calculation and comparison with experiment. In the calculations, the actual shape of the critical assem-
blies was replaced by a spherical one, and the thickness of the water reflector was assumed to be 50 cm. To com-
pare the results of calculation with experimental data, it is necessary to convert from a spherical geometry to the
geometry of the critical assemblies.
It is well known [2] that the various methods for conversion from a spherical geometry to a cylindrical one,
with the height of the cylinder nearly equal its diameter (on the basis of equal volumes or equal geometric param-
eters, with or without allowance for a reflector), lead to good agreement with experiment. However, conversion
on the basis of equal volumes slightly under-estimates cylinder dimensions and, on the other hand, conversion on
the basis of equal geometric parameters slightly over-estimates them.
Since the actual critical assemblies had the shape of a rectangular prism, or nearly so, it is possible to take
as the upper limit of the critical volume the prism volume which is obtained by equating the geometric param-
eters of the sphere and prism. Computational results and experimental data are shown in Figs. a, b, c, d. A series
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0
is
PN/PUras ZU
60 py/p(1235
Critical assemblies with aluminum fuel element assembly (a); with aluminum fuel
element assembly and aluminum plates with relative concentration of aluminum
PAl
?
.
a??00
0
0 0
? 0 p 0
= 5.8 (b); with aluminum fuel element assembly and copper plates with
P Cu
relative concentration of copper = 8.3 (c); and with fuel element assembly
PU235
of lKhl8N9T stainless steel (d): (V) core volume, liter; 1) calculated critical volume
of sphere; 2) calculated critical volume of prism; e) supercritical experimental
volume; 0) subcritical experimental volume.
PH
of experiments is shown in each of them. The critical assemblies with the ratio < 50 are intermediate be-
P U235
cause the thermal neutron contribution to the U235 fission density is less than 506.
A comparison of the results shows that, on the whole, the calculated and experimental critical volumes are
PH
in satisfactory agreement in the region `< 50.
P U235
The experimental values of the critical volumes for the region specified are between the upper and lower
computed limits, and the limits themselves differ from one another by 20-25 o. The complexity of the critical
assembly geometries does not allow any narrowing down of the limits shown.
The critical assembly calculations that were performed and the comparison of the computed and experi-
mental data permits one to conclude that the computing method employed gives satisfactory agreement between
calculated and experimental data, and that it can be recommended at least for calculations of the critical dimen-
sions of an intermediate-neutron, homogeneous reactor with hydrogen- containing moderator.
1. S. M. Feinberg et al., Proceedings of the Second International Conference on the Peaceful Use of Atomic
Energy, Geneva (1958) [in Russian], Dokl. sovetskikh uchenykh, Vol. 2, Moscow, Atomizdat (1959), p. 334.
2. Callihan, Morfitt, and Thomas, Proceedings of -the International Conference on the Peaceful Use of Atomic
Energy, Geneva (1955) [in Russian], Vol. 5, Moscow, Izd-vo AN SSSR(1958), p. 179.
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TANGENTIAL CHANNELS AND THERMAL COLUMN RECONSTRUCTION
AT THE VVR-M REACTOR
G. Ya. Vasil'ev, E. A. Konovalov, V. G. Pankov,
and D. A. Yashin
Translated from Atomnaya L`nergiya, Vol. 19, No. 5,
pp. 465-467, November, 1965
Original article submitted April 21, 1965
In planning the VVR-M reactor at the A. F. Ioffe Physical-Technical Institute of the USSR Academy of
Sciences, provision was made for nine horizontal channels in the concrete shielding and a tenth channel in the
thermal column. All the channels were directed along the normal to the core and had a shutter structure con-
sisting of five shielding disks which overlapped one another in the closed position of the channel aperture. The
centers of all the channels were located at .1 m from the floor of the reactor room (reference height, +1.0 mm).
The performance of experiments in channels directed along the normal to the core is hindered considerably
by the fact that radiation from the core is incident to a considerable degree on the detection equipment in addi-
tion to the radiation under investigation. Thus, in performing studies with a crystal diffraction spectrometer [3],
the necessary lead shielding against y-radiation from the core leads to a decrease in neutron flux at the sample to
2 ? 1012 n/cm2 . sec. For that reason, it is essentially impossible to use the high neutron flux of the reactor for
such experiments. However, it is possible to reduce the y-ray background at the sample significantly if the chan-
nels are directed tangentially to the surface of the core toward the beryllium reflector or toward the water outside
the reflector. In this situation, there will be at the channel exit only secondary y-radiation scattered in the re-
flector and y-radiation from activity induced. in the structural materials of the end of the channel.
In November 1961, straight-through channel 10 (Fig. 1), which passed through the recess for the thermal
column at 1390 mm from the center of the core, was drilled in the concrete shielding of the VVR-M reactor. The
center of the channel was located at the reference height +1.25 m. The orientation of the channel was chosen so
that the cast iron shielding ring was not interfered with during the drilling nor were process channels damaged.
Similarly, in September 1963, the two tangential channels 11 and 16, which opened into the thermal col-
umn recess, were drilled. Channel 11 was located at a reference height +0.75 m, and was directed toward the
beryllium reflector along a tangent to the core. With such a choice of direction, it was expected that a higher
ratio of thermal to fast-neutron flux would be achieved at the channel exit. Channel 16 was directed toward the
water along a tangent to the beryllium reflector and was located at a reference height +1.25 m. The choice of
direction for this channel resulted from the necessity for obtaining a minimal y -ray background at the channel
exit for maximum possible proximity of the channel to the core in order to assure a high neutron flux at the point
where the sample under study would be located.
The direction of the channel axes (Fig. 2) was determined, on the one hand, by the distances from the cen-
ter of the core to the channel axes (412 and 580 mm), and, on the other hand, by the distance from the channel
axes to the edge of the cast iron shield. After determining the direction of the channel axes, their centers were
marked on the outer surface of the biological shield of the reactor.
Together with the drilling of the tangential channels, there was reconstruction of the thermal column in
order to increase the number of horizontal channels available for research in solid state physics. The thermal
column (total length 3040 mm) was made up of six graphite disks enclosed in aluminum and installed next to one
another in a retractable structure in the recess on the north side of the reactor.
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3
Fig. 1. Locations of new channels in the reactor: 1) reactor vessel; 2) beryllium reflector;
3) core; 4) recess for retractable carriage; 5) concrete shielding disk; 6) physical sensors;
7) retractable cast iron shielding.
Fig. 2. Orientation of tangential channels and channels in the retractable structure on the north
side of the reactor.
In the reconstruction, the five outer graphite disks were replaced by a single concrete one of equivalent
shielding. In this disk, four horizontal channels were drilled: at reference height +1.0 m, central channel 13,
120 mm in diameter with a transition to 136 mm at its outer portion, and channels 12 and 15, 102 mm in diam-
eter, as well as channel 14, 80 mm in diameter, at the reference height +0.9 m (see Fig. 2). The concrete disk
was installed in the retractable structure so that between it and the retractable cast iron shielding an open space
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Physical Parameters of Channels
Thermal neutrons
Fast neutron
y -Ray dose
Channel
flux,
cadmium
flux
rate at chan-
s
n/cm2 ? sec
ratio
n/cm2 ? sec
el exits, x 10
n el
R / sec.
1
2.6
6.0
3.0
6.104
10
2.6.106
-
-104
3
11
6.6 ? 107
21
4.5. 105
66
16
6.6 ? 107
25
4.0 . 105
44
remained where there was located a monocrystal monochromator of Co + Fe (in the magnetic field of permanent
magnets or of electromagnets) at angles of 32? and 39? to the axes of channels 12 and 15, respectively, in order to
obtain monochromatic, polarized beams of neutrons with a 1 = 1.13 A and X 2 = 1.37 A. In this same space, equip-
ment was installed which permitted remote adjustment of the crystals in the neutron beam.
The first graphite disk was intended to shield against scattered radiation which penetrated mainly beneath
the retractable structure. During reactor operation at a power of 5 MW without the first graphite disk, the y-ray
dose rate beneath the retractable cast iron shield on the north side of the reactor was 100 times greater than the
maximum permissible level. Holes were drilled for channels 12, 14, and 15 in the retractable cast iron shield.
For channel 14, the opening penetrated parallel to the axis of channel 13, and for channels 12 and 15, at angles
of 32? and 39?, respectively.
Drilling of the channels in the concrete shield of the reactor and in the retractable cast iron shield was done
by the Leningrad composite geological expedition of the Northwest Geological Board under the control, and with
the participation, of the staff of the Division of reactor operation. In drilling the channels in concrete, several
auxiliary metallic structural elements were cut through. When the drilling equipment encountered a metallic struc-
tural element, the pressure on the drill bit was reduced and the spindle rotation was decreased. Drilling concrete
in which small cast iron shot was incorporated presented no additional difficulties.
It took a little more than three days to cut through the 6000 mm, continuous channel 10, including assembly
of the equipment and preliminary operations; to drill two channels in concrete (11 and 16) and three channels in
the cast iron shield (12, 14, and 15) took 24 working days, including preparatory, survey, and drilling operations.
The drilling of all channels was carried out with satisfactory precision. For example, the error in the distances
from the axes of channels 11 and 16 to the center of the core as compared with the specified dimensions was not
more than 10 mm.
Steel pipe was installed in allchannels cut through the concrete. To shield against radiation, an extensive
portion of the channel was closed by water-filled plugs and three cast iron plugs with a total length of 450 mm
were installed behind them. A permanent shutter arrangement for these channels is planned for each individual
case depending on the nature of the physical apparatus.
Physical parameters were measured for all the newly created channels: thermal-neutron flux, cadmium
ratio (using gold), fast-neutron flux, and y-ray dose rate. These parameters were also measured for channel 1,
which is directed along the normal to the core.
The results of the measurements are given in the table, normalized to a power of 10 MW. The data in the
table was obtained from measurements with a graphite disk having no openings for the newly created channels
installed in the retractable structure. In the absence of the graphite disk, the neutron fluxes at the exist of these
channels will be greater [2]. The thermal neutron fluxes were measured with an accuracy of 20Q16, the cadmium
ratio with an accuracy of 1556, and the fast-neutron fluxes with an accuracy of 40'/o. The y-ray dose rate was
measured with an accuracy of 20F/o.
Yu. V. Petrov, a member of the staff of the A. F. Physical-Technical Institute, advanced the suggestion for
the creation of tangential channel 10 in 1961. In 1963, I. A. Kondurov proposed drilling channels 11 and 16.
V. S. Gvozdev assumed a large part of the work on the creation of tangential channels.
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The authors take this opportunity to thank the personnel of the Division of Reactor operation for the rapid
and skilfull completion of the job of creating new channels, and also wish to thank D. M. Kaminker for his concern
and assistance.
1. V. V. Goncharov et al., in Proceedings of the Second International Conference on the Peaceful Uses of
Atomic Energy, Geneva (1958) [in Russian], Dokl. sovetskikh uchenykh, Vol. 2, Moscow, Atomizdat (1959),
p. 243.
2. D. M. Kaminker and K. A. Konoplev, Paper No. 325, presented by the USSR at the Third International Con-
ference on the Peaceful Uses of Atomic Energy, Geneva (1964) [in Russian]. .
3. O. I. Sumbaev and A. I. Smirnov, Nucl. Instrum. and Methods, 22, 125 (1963).
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FROM A HORIZONTAL CHANNEL OF THE VVR-M REACTOR
(UDC 621.039.519)
V. P. Vertebnyi, M. F. Vlasov, and A. L.' Kirilyuk
Translated from Atomnaya gnergiya, Vol. 19, No. 5,
pp. 467-468, November, 1965
Original article submitted November 30, 1964
The shape of the slow-neutron spectrum in a beam extracted from a reactor core depends to a great extent
on the core configuration close to the region from which the neutron beam is extracted. Finding the optimum
core configuration is of interest in time-of-flight studies using mechanical choppers or neutron monochromators.
This is necessary in order to obtain the maximum yield of neutrons in a definite region of the spectrum with min-
imum flux of fast neutrons, i.e., the best signal-to-noise ratio for the largest possible signal. It is well known that
the thermal neutron flux can be increased several times in comparison with the average flux in the core by creat-
ing a cavity in the moderator surrounding the fuel elements [1]. Although it is impossible to obtain a closed cavity
in experiments with beams, one can hope that the thermal neutron flux would be increased if the neutron beam is
extracted from the surface of the moderator. Since the flux of resonance neutrons is determined by the well known
expression [2]:
-P (E) = S
SEE
The replacement of a light moderator by .a heavier one may lead to some increase in the yield of resonance
neutrons and also to a shift in the ratio between the intensities of resonance and thermal neutrons. These consider-
ations also led to the setting up of the experiments described below.
With the help of a mechanical neutron chopper installed in one of the horizontal channels of the VVR-M re-
actor at the Institute of Physics, Ukranian SSR, and used to investigate the neutron cross sections of separated iso-
topes [3] a study was made of the neutron spectra for various configurations of the core near this channel (Fig. 1).
In the first case (see Fig. la), the neutron source was only fuel elements; in the second (see Fig. lb), it was fuel
Fig. 1. Core configuration near a horizontal channel of the VVR-M reactor.
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G
-711
0.004
En, eV
Fig. 2. Effect of core configuration on neutron
spectrum from a'horizontal channel: ?) fuel
elements; 0) fuel elements + water; x) fuel
elements + beryllium.
a b
Type of configuration
Fig. 3. Effect of core configuration on signal-
to-noise ratio: a) fuel elements; b) fuel ele-
ments + water; c) fuel elements + beryllium;
1) 0.0253 eV; 2) 1.0 eV; 3) 0.007 eV.
elements and a water layer 5.5 cm thick; in the third (see Fig. 1c), it was fuel elements and a beryllium
layer of the same thickness.
The neutron spectra from the horizontal channel are shown in Fig. 2 for all the core configurations men-
tioned. It is clear from Figs. 2 and 3 that the absolute gain in intensity is close to 2 in the thermal and cold re-
gion for water and beryllium. The signal-to-noise ratio in these cases is approximately twice as large as that for
extraction of the neutron beam from the surface of the fuel elements. In the resonance region, the counting rate
is approximately 1.4 times greater for beryllium than for the other configurations. This behavior is qualitatively
explained by expression M. Therefore, one can consider the arrangement with beryllium moderator as best from
the practical point of view.
The authors are grateful to D. T. Pilipets, chief engineer of the VVR-M reactor at the Institute of Physics,
Ukranian SSR Academy of Sciences, and to other members of the staff for assistance in setting up the experiments.
1. M. Osredkar and R. Stephenson, J. Nucl. Energy, 5, 210 (1957).
2.- A. Weinberg and E. Wigner, Physical Theory of Reactors [Russian translation], Moscow, Izd-vo inostr. lit.
(1961).
3. M. F. Vlasov, and A. L. Kirilyuk, Ukr. fiz. zh., 8, 947 (1963).
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AND FALLOUT INTENSITY IN THE BLACK SEA BASIN
(UDC 551.577.7:541.182.2/3)
V. P. Kotel'nikov, V. N. Markelov, and B. A. Nelepo
Translated from Atomnaya gnergiya, Vol. 19, No. 5,
pp. 469-470, November, 1965
Original article submitted March 19, 1965
During the 16th voyage of the Mikhail Lomonosov in August-September, 1964, studies were made of the at
tificial radioactivity of the atmosphere in the Black Sea basin. As a result of these studies, determinations were
made of the concentration and isotopic composition of the radioactive aerosols in the surface layer of the atmos-
phere, of the shortlived radioactive isotopes in the surface layer of the atmosphere, and of the intensity of radio-
active fallout and its isotopic composition. In addition, studies were made of the correlation between concentra-
tion of radioactive aerosols and the intensity of radioactive fallout at the surface of the sea under various meteoro-
logical conditions.
The route of the voyage made it possible to collect samples from a considerable area of the Black Sea during
a relatively short time.
The aerosol particles were collected by a filtration apparatus using an FPP- 15 filter. The capacity of the
equipment was 225 m3/h. The filter was exposed for 48 h. Analysis and measurement of sample activity was ac-
complished by standard techniques. To determine the content of short-lived decay products of radon and thoron,
measurement of filter activity was started within 1-1.2 h after removal of the filter, and was carried on continu-
0 ously for several days. The decrease in sample activity
lJ
20 22 24 26 28 30 1 3 S 7 8 10 12
August September
was investigated, and then the decay curve was analyzed.
Counts were taken with a type PP-8 (Volna) radiom-
eter employing an end-window MST-17 counter. Deter-
mination of the value of the factor for converting from
counts to sample activity had been done previously under
laboratory conditions. The error in measurement was
5-10To.
Radioactive fallout was collected in stainless steel
pots with an area of 0.64 m2. An oil-saturated filter paper
was placed in the bottom of the pot. The collection effi-
ciency was practically unity. The pots were set up on the
upper bridge of the ship at a height of 14 in above the sur-
face of the water. The length of exposure for the pots was
two days. After completion of collection, the paper was
removed, ashed, and calcined under the same conditions
as those for the FPP-15 filters. On rainy days, the moisture
which accumulated in the pot was evaporated, and the dry
residue was mixed with the ash from the oiled paper. Sam-
ples were prepared from the ash residue for measurement
14 .16 of total 6 activity, just as was done for the FPP-15 filters.
To study the isotopic composition of the samples col-
NaI(Tl) crystal and a 100-channel AI-100 (Radura) pulse
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Concentration
Fallout-rate,
Year
d/sec m3
d/ sec m2 ? day
1960
30 ? 10-4
492 ? 10-2
1964
34.4 - 104
462 ? 10-2
height analyzer was used. Energy calibration of the spectrometer
IN A Ce14 was carried out by using -sources of Ce144(134 keV), Ru103 (495 keV),
161 111 1 1 1 1 1 1 [--I active isotopes in the atmosphere and for the average daily inten-
sity of their fallout on the surface of the sea during August to
14 September, 1964, are shown in Fig. 1; the results are compared
12
within the limits (8.9-66.6) ? 104di ec ? m3, and the average was
10 34.4 ? 10-4 d/ sec ? m3. The average daily value for the fallout
intensity of long-lived radioactive aerosols on the sea surface was
8 within the limits (3.3-211) ? 10-1 d/sec ? m2, and the average dur-
n 6 ing the voyage was 46.2 ? 10-1 d/sec ? m2. The average value for
the concentration on a day when there was precipitation was 31.0
nd on
5 9 . I \ "Cs u S4 J 1v d/ - iii , a
o ay is clear ? 10-4 d/ see ? m3. From an analysis of the the data, , it t is cleathat
at
f C 11 Ny' I kA V Ma - - there is some reduction in the value of the concentration of radio-
0 /ZS 250 JIS S00 615 ISO 875 IX E, ke V
active products in the atmosphere and an increase in fallout activ-
ity on days with precipitation. This can be explained by the fact
that radioactive products are strongly washed out of the atmosphere
Fig. 2, y Ray spectrum of atmospheric fall-
and into the surface of the sea by precipitation. For example, on
out sample.
September 6, 1964, in the eastern part of the Black Sea, a heavy
rain occurred which was associated with a thunderstorm. On that
day, the fallout intensity was 211 ? 10-1 d/sec ' m2 ' day, the concentration 19.9 ? 10-4 d/sec ? m3, the effective
height of the "cleared layer" 10,500 m/day, while on a day without precipitation, the average values of these same
quantities was 18.1 ? 10-1 d/sec ? m2 ? day, 45.5 ? 10-4 d/sec ? m3, and 390 m/ day, respectively. Fallout activity
on September 6, 1964,was 11 times greater than the magnitude of the average daily fallout on days without pre-
cipitation.
Thus there is a correlation between the concentration of long-lived radioactive products present in the atmos-
phere, the average daily fallout intensity, and atmospheric precipitation. The average values for the concentrations
of the natural radioactive decay products of radon and thoron in the atmosphere above the Black Sea during August-
September, 1964,was 9.2 ? 10-1 and 17.7 ? 10-3 d/sec ? m3, respectively. From the data obtained, it follows thatthe
concentration of radon decay products in the atmosphere is three orders of magnitude greater than the concentration
of long-lived radioactive aerosols from fission products.
In the spectrum from air samples (Fig. 2), the following radioactive elements were identified: Ce1r14 (134 keV),
Ru106 + Rh106 (513 keV), Cs137 (661 keV); a y-ray line at -800 keV indicates the presence of Mn54.
The isotopic composition of the radioactive products found in the atmosphere as determined by us differs from
published data. *
An analysis of the information obtained during the 16th voyage of the Mikhail Lomonosov shows an insignifi-
cant increase in concentration and a reduction in the intensity of the average daily fallout of radioactive products
on the surface of the sea in comparison with the 9th voyage (October, 1960).
? V. P. Shvedov, et al., Radioactive Contamination of the Seas and Oceans, Moscow, Nauka (1964), p. 49.
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The isotopic composition of the radioactive products found in the atmosphere, and the rapid variations in
their fallout intensity as a function of atmospheric precipitation indicate that there still remains in the stratosphere
a considerable amount of radioactive products, produced as the result of nuclear testing, which enter the lower layers
of the atmosphere.
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THE RELATIVE LEVELS OF STRATOSPHERIC FISSION FRAGMENT FALLOUT
(UDC 551.577.7)
P. I. Chalov and M. A. Tsevelev
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 470-472, November, 1965
Original article submitted February 13, 1965
It is possible to obtain information about the arrival of nuclear test products from the stratosphere by studying
the time changes in the concentration of radioactive aerosols in the surface layer of the atmosphere, particularly
during the time when such tests are prohibited. As the result of several investigations (see, for example, [1]), it was
established that the aerosol concentration in the surface
layer of the atmosphere exhibited a seasonal variation,
0.16 CS 137 increasing in the spring-summer period and then falling
D 14 in the fall and winter. The existence of the maxima
012 mentioned is usually explained by seasonal variation in
0.10 the rate of transfer of air masses from the stratosphere to
0.08 the troposphere. A similar seasonal change in concentra-
11.06 tion in the surface layer of the atmosphere is observed
1109 for ozone and Be7 [2], which are produced in large amounts
002 in the stratosphere. During the ban on atmospheric nu-
clear testing, the spring-summer maximum in the concen-
125 tration of radioactive aerosols in the surface layer of the
A9 Ru 106 atmosphere can be uniquely associated with the arrival of
,03 fission fragments from the stratosphere.
0.2
[ 01 In this paper, a possible relative level of stratos-
3 pheric fission fragment fallout is determined by compari-
1.80 son of the fallout intensity (total fission fragments and
1.60 Ce1ff several long-lived isotopes) in 1962, when tropospheric
1.90 fallout was still possible, and in 1963, when it is possible
2 1.20 to consider the fallout as purely stratospheric as a result
',00 of the prohibition of atmospheric nuclear testing in 1962.
0 0.8
01 Fallout intensity was determined from mean month-
w ly samples whose activity was assigned as the activity of
0.4 the mean date of sampling. Fallout was collected on a
0.2- water surface by samplers with a collecting area of 0.3 m2
14 [3]. Samples were prepared for measurement by methods
12 described in the literature [4]. The total 6-activity of
10 the samples was measured with a B-2 radiometer having
8 a SI-2B counter which was calibrated with a Sr90 source.
Long-lived y -emitters were analyzed with a scintillation
4 spectrometer using an AI-100-1 analyzer (resolution for
2 the Cs 137 photopeak, about 101c). Results of observations
from October 1961 to December 1963 are shown in Fig. 1
/l lY Vl Y111 X X11 11 IV V/ Y111 X X11 in the form of a histogram. It is clear that the fallout in-
1962 1393
tensity for total fission fragments, Cs 7, Cep, and Ru106
Fig. I. Time variation in fallout intensity for total exhibits the seasonal variation ordinarily observed for the
fission fragments and for several long-lived y-emitters. concentration of radioactive aerosols in the surface layer
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of the atmosphere. The spring-summer maximum was observed both
10 in 1962 and in 1963. The seasonal variation for total fission fragment
fallout in several cases differs somewhat from the seasonal variation in
p9
individual isotope fallout. This is apparently connected with the fact
that the total 5-activity in fallout results not only from the identified
total fission fragments in 1963 was approximately 3 times greater than
E the summer maximum in 1962. The same sort of difference, but on a
c)
> phere because about six months elapsed after the atmospheric tests in
2 1962. Furthermore, the summer maximum in the fallout intensity of
o ? pheric nuclear testing occurred during this period. The 1963 maximum
was mainly caused by fission fragments which arrived from the stratos-
3 superposition of tropospheric and stratospheric fallout because atmos-
y -emitters but also from other isotopes which are contained in the mix-
[ 6 ture of fission fragments. The 1962 maximum may be caused by the
reduced scale, can be noted for the individual isotopes also.
The relatively high fallout intensity in the 1963 spring-summer
period as compared with 1962 can be associated, in principle, with a
large amount of precipitation. However, a comparison we made of the
amounts of precipitation in 1962 and 1963, particularly in the spring-
1961 1962 190
Fig. 2. Cumulative fallout intensity,
1961-1963.
summer period, showed that there was no such correlation. The considerable intensity of stratospheric fallout in the
summer of 1963 is associated with the fact that there was injected into the atmosphere during the period of nuclear
testing in 1962 an additional amount of fission fragments whose transfer in significant quantity into the troposphere
began in the spring-summer period of 1963.
Shown in Fig. 2 is the cumulative fission fragment fallout intensity, for which the concept and method of cal-
culation is given in [3]. Its rise in 1963, in comparison with 1962, is actually less marked because the calculations
took account of the decay of isotopes which were deposited during the previous period. The total dose from external
y -radiation, which was caused by deposition of fission fragments during the period under consideration was calcu-
lated by the method outlined in [5, 6]. With the indicated increase in total fission fragment fallout intensity, the
dose in 1963 rose more sharply (by approximately 10 times) because, in addition to the increase in intensity, the
1963 fallout contained a large fraction of long-lived isotopes.
Therefore, it has been established that the total S -activity of stratospheric fallout may be greater than, or
equal to, the activity of tropospheric fallout. Stratospheric fallout, which contains mainly long-lived isotopes, in
this instance is a greater radiation hazard than tropospheric fallout.
During the period of a nuclear test ban, the cumulative fallout intensity, and the resulting external y-ray
dose, are mainly determined by stratospheric fallout.
1. S. G. Malakhov, Contamination Level in the Surface Layer of the Atmosphere from Products of Nuclear
Weapons Tests: Measurements in the Moscow Area, 1955-1959 [in Russian], Moscow, AN SSSR(1960).
2. V. P. Shvedov, E. G. Gritchenko, and L. I. Gedeonov, Atomnaya Energiya, 12, 64 (1962).
3. V. P. Shvedov et al., Atomnaya Energiya, 5, 577 (1958).
4. Radioactive Contamination of the Environment, V. P. Shvedov and S. A. Shirokova, eds. [in Russian], Moscow,
Gosatomizdat (1963).
5. V. P. Shvedov, Atomnaya Energiya, 7, 544 (1959).
6. V. A. Blinov and L. I. Gedeonov, Reactor Physics and Heat Engineering [in Russian], Moscow, Gosatomizdat
(1958), p. 96.
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ATMOSPHERIC RADIOACTIVITY ABOVE THE ATLANTIC OCEAN
DURING MAY-JULY, 1964
L. I. Gedeonov, V. N. Dmitriev, B. A. Nelepo, A. V. Stepanov,
and G. V. Yakovleva.
Translated from Atomnaya Energiya, Vol. 19, No. 5,
pp. 472-474, November, 1965
Original article submitted March 1, 1965
During the 15th voyage of the Mikhail Lomonosov, atmospheric radioactivity and fallout was studied (track of
the ship is shown in Fig. 1). Samples of radioactive aerosols were collected by filtering air through an FPP- 15 filter.
Radioactive fallout was collected in a flanged pot with sticky bottom. A scintillation y-spectrometer with an
AI-100 analyzer was used for sample analysis. The atmospheric content of aerosols of artificially radioactive ma-
terials and their rate of fallout (in terms of total activity) are shown in Fig. 2, and the results of y-analysis are
shown in Fig. 3. The Sr90 concentration in the atmosphere was determined by radiochemical methods. For this pur-
pose, samples collected in the southern hemisphere (south of 80? S) were combined and analyzed together. The same
treatment was given to samples collected in the northern hemisphere (north of 8? N) and in the equatorial region
(8? N to 8?S). The results of the atmospheric sample studies are given in the table.
A comparison of the results in this paper (see table) with data obtained on the 12th voyage of the Mikhail
Lomonosov (at the end of 1962) [1] showed the specific activity of aerosols in the surface layer of the atmosphere
and the fallout rate were, in the spring of 1964, more than an order of magnitude lower than at the end of 1962 be-
cause of the ban on atmospheric nuclear testing.
--------
- --
)Z- -
--------
I/
-------------
aerosol concentration was practically independent of lati-
tude in the range 5? N to 38? N. This is explained by the
fact that the data obtained were typical of the northeast
trades zone where the lower layers of the atmosphere are
intensely mixed in the meridional direction. In addition,
it is clear from Fig. 2 that there is no direct correlation
30? between radioactive aerosol concentration and fallout rate,
on the one hand, and between radioactive aerosol concen-
tration and the mean daily values of atmospheric temperature
60, 60?
90? 60? 30? 0? 10?
Fig. 1. Track of the 15th Voyage of Mikhail
Lomonosov.
60? 30? 0? 30? It is clear from Figs. 2 and 3 that the radioactive
Average Atmospheric Concentration of Radioactive
Isotopes (x 10-15 Ci/m3)
Collection
Isotope
area
Mn54
Sr90
Ru106
I Cs137
Ce144
Southern
hemisphere
0,13
0,13
0,84
0,16
1,2
Equatorial
region
0,14
0,13
1,1
0,22
1,8
Northern
-
4
9
-
-
-
hemisphere
,
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30] p
20]
t 13 ?L~
130
20
10
n 2,7x103
P
500-
U
c4
a 40?N 30? ?0? 10? 0 10? 20? 30?S
Fig. 2. Radioactive aerosol concentration and fallout
rate for ship travel from north to south.
/91
11
iz
?
12
~
13/
1181
19)
(13)
6
31
10
p51
11
(91
1)
(21
Fig. 4. Mean latitudinal distribution of fission product
concentration in the lower layer of the atmosphere.
n.. '36
I Cs'
y
Til
Ce
I
HH
_1_
h
Total activity
r--
I ---
r-__ J
20
Jo
0
40?
3G? 20? 10?
0? S
Fig. 3. Radioactive aerosol concentration in the north-
ern hemisphere: ) outbound (22 April-15 May,
1964); - -- ) return (16-24 July, 1964).
and pressure, on the other. The high radioactive fall-
out rate in the equatorial region is explained by intense
precipitation in the form of rain which washed out the
radioactive aerosols in the lower layers of the atmosphere.
Concentration values in the equatorial region and
in the southern hemisphere were much lower than in the
northern hemisphere.
Statistical analysis of the published results of ob-
servations made during previous voyages of the Mikhail
Lomonosov [1-3] made it possible to establish an aver-
age picture of the latitudinal distribution of fission prod-
ucts in the lower layers of the atmosphere above the
Atlantic Ocean. Results of the averaging are shown in
Fig. 4 where the vertical lines indicate the mean square
deviation in the concentration of atmospheric fission
products, and the number of averaged quantities is given
in parentheses. It is clear that the maximum distribu-
tion in latitude of fission products in the northern hemi-
sphere is located between 14 and 40? N. South of 10? N,
a sharp decrease is observed in the concentration of at-
mospheric fission products. The specific activity of
aerosols in the southern hemisphere is not more than
10% of the value typical of the northern hemisphere. Some reduction in the concentration of atmospheric fission
products was observed in the range 50-60? N.
In conclusion, the authors consider it their pleasure to express their deep appreciation to V. M. Vdovenko and
A. G, Kolesnikov for making it possible to carry out this work. The authors thank I. N. Maksimov and L. N. Sysoeva
for assistance in analyzing the results.
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1. V. A. Blinov, et al., Proceedings of the Maritime Hydrophysical Institute, AN UkrSSR [in Russian], Vol. XXXI,
Kiev, Izd-vo AN USSR (1965).
2. V. N. Lavrenchik, Atomnaya gnergiya, 13, 72 (1962).
3. V. N. Lavrenchik et al., Atomnaya gnergiya, 14, 569 (1963).
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IN URANIUM DEPOSITS WITH HARD BITUMENS
(UDC 553.495)
G. N. Kotel'nikov
Translated from Atomnaya tnergiya, Vol. 19, No. 5,
pp. 474-475, November, 1965
Original article submitted February 25, 1965
The variation in the radioactive equilibrium coefficient at deposits of uraniferous hard bitumens has been
studied in three regions separated hundreds and thousands of kilometers apart. The first region, where the basic
observations were performed, features mountainous and taiga terrain, with absolute heights of 900 to 1600 m, a
15-25? (and in points as much as 40?) curvature of slope, a yearly precipitation average of 700-800 mm. The sec-
ond region is in a moderate climate zone at heights of 400 to 450 m, slope angles 10-15?, and precipitation in the
400-450 mm range. The third region is semi-arid and desert-like, bare of forest stands or grass cover; the slopes
are gentle (5-10?); the yearly precipitation average is 200-300 mm. All three regions are severely denudated. The
thickness of coeval overlying deposits ranges 1 to 5 m.
The deposits of uraniferous hard bitumens (anthraxolites) are located between paleozoic crystalline shales and
sandstones, and are represented in two of the regions by zones of rock fracture and almost-vertically dipping beds, in
the third region by gently sloped (8-10?) sheet deposits.
When radioactive anomalies due to mechanical and salt dispersion halos in a deluvial layer are uncovered by
trenching and sampling, regular variations in the radioactive equilibrium coefficient are established in both vertical
and horizontal planes depending on the distance to ore bodies bedded in bedrock formations.
The top layer, 0-0.25 m thick, is made up of wood soils, loams, is usually free of radioactive elements, and
is characterized by y-radiation in the normal background range (see diagram). The next depth interval (0.25-0.5m)
is a level showing a maximum equilibrium shift of up to 600% or more in the direction of radium. Further on the
radioactive equilibrium coefficient decreases gradually with increased depth: to 200-3001c in the 1.0-1.5 in range,
to 120- 1505r in the 1.5-2.0 m range. Equilibrium ores prevail from there on down. The lowest talus bed directly
overlying an ore body shows an abrupt depletion in radium. The equilibrium ratio is usually 40-60% in that level.
The radioactive equilibrium coefficient stays at a 80-90/0 level to greater depths in uraniferous hard bitumens
found among unaltered host rocks.
Vertical changes in the radioactive equilibrium coefficient both along the strike and athwart the strike of ore
bodies is also observed in underground mines worked in host rock around massive lenses of uraniferous anthraxolites.
The equilibrium coefficient is 70-90a/c in the central portions of the ore lenses, gradually increases to 120-2005, at a
distance of 0.2-2.0 m as the uranium content simultaneously drops to tenths or fractions of tenths. The dispersion
halos of ore bodies lying alongside run together in the plane of the ore bodies and the equilibrium coefficient does
not exceed 2005o.
Radioactive equilibrium shifts gradually toward radium in ore-bearing deposits as the distance from the ore
bodies in bedrock increases in the horizontal plane. The radioactive equilibrium is 120 to 200"/ in the first few
meters distance from the ore bodies; it rises to 300-400% as the distance stretches to the first few decameters, and
to 600-10005c in the range of tens and hundreds of meters. But this extent of change in the equilibrium coefficient
can be traced only along a minimum-shift horizon which, as mentioned, is situated in the bottom of a talus bed
bounded by bedrock. As the distance from the ore bodies increases, the horizons featuring equilibrium shift toward
uranium or featuring an equilibrium state disappear, and the minimum-shift horizon moves closer to the surface.
The most remote anomalies appear to be purely radium anomalies (shift to 1000?/c or more) and are localized in
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Depth
Radioactive equilibrium coefficient,
,
Composition of rocks
cm
SO 100 150 200 250 300 350 400 450 500 SSO 600
0-25
Forest soils, inactive bed
25-50
Fine shale detritus, buried
layer of vegetation
Greenish-gray, brownish
50-100
shale debris
100-150
Black powdery bitumens
Yellow-brown ferruginized
130-200
shale debris
>200
Bitumens in bedrock
buried beds of vegetation 0.2-0.5 m down from the surface. The size of these salt anomalies varies from 1 to 20 m2,
and the intensity can attain 600 p r/ h (after screening drifts have been stripped off).
In the lower-precipitation regions all three dispersion halos are situated in a belt 10-15 m wide, and the zone
located near ore bodies and characterized by a 120-200% equilibrium shift is a little different in size from the cor-
responding zone in the first region. A sharp reduction in size to a strip 2-4 m wide is observed for the zone of
300-400% equilibrium coefficient, while the third zone, the zone of salt dispersion halos, either disappears com-
pletely or narrows to 5-6 in.
These regularities can be used must readily in prospecting bedrock ore bodies of uraniferous hard bitumens
over an ore field with extensively developed radioactive talus deposits. They must be taken into account in deter-
mining conversion factors for appraisal of ore reserves from logging data.
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CHRONICLES, COMMUNICATIONS
G. I. Lukishov, K. D. Rodionov, and' N. I. Noskov
Translated from Atomnaya $nergiya, Vol. 19, No. 5,
pp. 486-488, November, 1965
The State All-Union Planning Institute GKIAE has developed a modularized glove box train (TsBP-1) designed
for handling a-active and 5-active materials in standard modularized junior laboratories following the three-zone
planning principle [1].
The glove boxes forming the train are equipped with process instrumentation for packing solid and liquid radio-
active materials, but the train can also be used for other work handling a variety of toxic materials when the proper
equipment is provided.
The train of glove boxes (see photographs) consisted of three airtight boxes and a vehicle carrier, fabricated
as a single unit at the point of manufacture, so that the facility can be brought into operation with little delay and
with assembly operations minimized.
The modular design of the glove boxes provides a simple solution of zoned baffling to separate the operator
zone and overhaul-inspection zone, by directly joining the boxes in line. The joints between modules are made
pressure-tight by adhesive PVC lining or by heat-sealing backing strips.
The casings of the glove boxes and the vehicle are made of stainless steel, supports for the glove boxes and
modules are made of carbon steel. Each glove box unit is equipped with a ventilation system which rarefies the air
in the interior of the boxes to not less than 20 mm Hg; the volume turnover of the ventilating system is 30 volumes
per hour.
Intake and exhaust filters [2], each presenting a filtering surface area of 0.4 square meter, are mounted above
the glove boxes. The exhaust filter is a two-stage unit: dacron fiber and FPP-15 fabric (V-04 filter). This design
lengthens the service life of the second stage. The (aerosol) clean-up factor of the filters is 99.9To. When it is time
to change replace filters, the connecting ducts to the ventilating system are valved shut.
Each work place is illuminated by luminescent panels giving off 80 W (4.tubes of 20 W power each). This
provides 350 lux illumination for the table-top surface.-
Control desks and electric switchgear panels are built into the unit. Each glove box has an access door in
back with a pressure-locked sliding mechanism for hooking up the vehicle, a pressure-tight door for inspection and
maintenance, a wash faucet and an overflow drain. Seven process piping manifolds communicate to the glove boxes
underneath the work-table (hot and cold running water, vacuum pipe, compressed air, gas duct, overflow drainage,
stand-by line).
The intake box in the train has two transfer compartments at a single work station. The left compartment is
for introducing and removing radioactive materials, with the outer hatch door opening into the inspection and main-
tenance zone. The right-hand transfer compartment is for delivering clean materials and wares, the outer door open-
ing into the operator zone. Preliminary unpacking of radioactive materials takes place in this box.
The packing box has two work stations equipped with proper tools [3] for opening isotope casks, penicillin
vials, ampules and cans, an ampule sealer, and an electrically driven mixer. This box has a set of syringes and re-
mote controls (gripping tongs), as well as clamping stands and dripping trays. Liquid, solid, and powdered mate-
rials are packed in this box.
The box for weighing packed materials is equipped with OVM- 100 balances on which the set of weights can
be positioned by remote control. The balance can handle 100 g to within 0.1 mg precision. There are also wire
cutters to cut radio active wire to calibrated lengths.
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The TsBP-1 glove box train: a) forward view; b) view from the rear. 1) Intake box; 2) packaging
box; 3) weighing box; 4) vehicle; 5) solid wastes receptacle assembly; 6) KZhO- 10 carboy for
liquid wastes.
The carrier vehicle is placed behind the glove boxes and is a pressure-tight box structure 250 mm by 250 mm
in cross section. The vehicle box frame is pinned to the glove boxes in a pressure-tight joint. A moving-platform
carriage is located inside the box frame. The carriage has a load-carrying capacity of 10 kg. The platform lift
drive is manual or by cable. The carriage control hand wheel is located in the center zone of the glove box train.
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A solids receptacle assembly is found at the left extreme of the vehicle (at the intake box) [4] - it is a long PVC
sack connected by a pressute-tight joint to the bottom of the vehicle. When wastes are discharged a part of the PVC
bag (in the wastes zone) is heat-sealed by a special sealing device and is then cut off at the seam. Solid wastes are
removed with danger of spills or contact by this procedure. The solid wastes discharge assembly may also be used
in the opposite direction for delivering materials in an air-tight connection.
The vehicle has one glove port on the side of the solid wastes discharge assembly and a window on the top of
the box frame, as well as inspection handholes. Liquid wastes are removed via traps in the glove boxes and collect
inside the vehicle. High-level wastes are drained into a KZhO-10 carboy, while low-level wastes to into a special
drainage system.
1.
Standard GSPI "GKIAE" project. Junior laboratory for handling radioactive materials. Type 1 [in Russian].
2.
V. M. Krupchatnikov,
Russian].
Ventilation in work with radioactive materials. Moscow, Atomizdat (1964) [in
3.
Shielding techniques.
V/O Izotop catalog. Moscow, Atomizdat (1964) [in Russian].
4.
E. Ya. Spitsyn, Treatment and disposal of laboratory radioactive wastes. Moscow, Atomizdat (1965)
[in Russian].
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Translated from Atomnaya b`nergiya, Vol. 19, No. 5,
pp. 488-489, November, 1965
A novel shielding technique was employed in the design of the German Democratic Republic's first whole-
body counter [1]. The designers chose y-ray NaI(Tl) crystal spectrometer as best suited to their purpose of devising
an equipment to analyze accident cases and for experimental research (they also plan. to build a new spectrometer
using several crystals of the same type).
The absence of steel melted down prior to testing a nuclear weapon led to the use of plaster for shielding
against external background radiation. Plaster has a density ranging from 1.3 to 1.8 cm3 and is better suited
for shielding structures than other nonmetallic materials (concrete, chalk, asbestos, etc.) tested by the authors of
references [2-4]. The specific activity of plaster of the brand tested is 10-14 to 10`15 Ci/g and is due to y-emitters
whose energies lie below 400 keV; no signs of K40 or Ra226 have been detected. Only water of very low specific ac-
tivity is used in mixing the plaster. The shielding is no less than 75 cm thick at any point, with a density of
1.6 g/cm3, equivalent to about 15 cm thickness of iron (120 g/cm2).
. The measuring chamber is made of a section of iron pipe (140 cm inner diameter, 200 cm in length) made in
1925. This pipe is placed between the plaster blocks (Fig. 1) whose specific activity was first verified, and the pipe
is then covered with unhardened plaster. The bent section of pipe serves as inlet duct to the measuring chamber.
The spectrometer detector consists. of a NaI(T1) crystal 100 mm in diameter and 70 mm high, series Z, fabri-
cated at the Karl Zeiss plant in Jena, and a S-12 FS-100 photomultiplier tube. The sodium iodide and the mate-
rials used in packaging it are not chosen for their specific activity, so that the crystal contains a potassium impurity
on the order of 10-4%. The detector is packaged in aluminum, while other parts in the interior of the spectrometer
chamber are made of electrolytically refined copper and brass. The inner surface of the pipe is polished and left
unpainted.
The detector is mounted on two guides so that it can be moved along the chamber length (Fig. 2). The mount-
ing design also makes it possible to vary the distance from the detector to the patient vertically or on an inclined
path.
Holes are left as air passages in the vertical panel delimiting the counting chamber (the air is not cleaned)
and also serve as outlets for electrical wiring.
This shielding turned out to be quite effective (Fig. 3). In the energy range around 1 MeV the shielding de-
presses the background count rate tenfold; it becomes even more effective at lower y -energies. In the region of
soft y-rays (100 keV), the background count rate is lowered by a factor of 23. The shielding depresses the back-
ground 14-fold on the average, the 1083 counts per minute, in the operating range (0.1 to 2 MeV). The 1083 count
is 7.8 ' 103 counts per hour per kg as converted to unit scintillator weight, for comparison. This is roughly twice the
background [5] for a crystal of the same geometry placed under a lead shield. The higher background is due in
large measure to K40 impurities in the NaI(Tl) crystal and in the glass of the phototubes. The fraction due to this
source is 280 counts per minute, i.e., about 26% of the integrated background count rate. Several measures have
been proposed to reduce this background: choice of crystal, introducing additional lead lining as shielding, filter-
ing the intake air, installing a labyrinthine entrance to the measuring chamber.
Note that the shielding built here is relatively cheap. The cost of similar shielding made of chalk and steel
blocks would be three times or six times, respectively, the cost of the new shielding.
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103
Fig. 2. Interior view of whole-body counter.
45 1,0 1,5 2,0
y-Photon energy, MeV
Fig. 3. Effect of plaster shielding on background count rate
of NaI(Tl) crystal 100 mm in diameter and 70 mm high (chan-
nel width 20 keV): 1) unshielded; 2) shielded.
Fig. 1. Laying plaster blocks in place.
1. K. Poulcheim and H. Hoesselbarth, Health Physics, 11, (1), 52 (1965).
2. Low-Level Counting Installations; Nuclear Enterprises, September (1963).
3. R. McCall, Health Physics, 2, (3), 304 (1960).
4. T. Sargent, Whole Body Counting, Proc. of Symp., IAEA, Vienna (1962), p. 449.
5. H. Mehl and J. Rundo, Health Physics, 9, (6), 607 (1963).
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In "Angular Distribution of the Intensity of Gamma-Radiation Scattered by Lead and Water,"
by L. M. Shirkin (Vol. 19, N.,. 4, p. 1388), Fig. 2 should appear as follows:
by
T' 1S
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SOVIET JOURNALS AVAILABLE IN COVER-TO-COVER TRANSLATION
This list includes all Russian journals which-to the publisher's knowledge-were available in cover-to-cover translation on June
30, 1965, or for which definite and immediate plans for cover-to-cover translation had been announced by that date. The list
reflects only current publication arrangements, but the date and issue listed for first publication refer to translations available
from any source. Thus, earlier volumes of a translation journal may have been published by an organization other than that listed
as the current publisher, and possibly under a different title (and, for Doklady Akademii Nauk SSSR, in a different arrange-
ment of sections).
Five bits of information are furnished, separated by bullets:
1. The abbreviation(s) by which the journals are most frequently referred to in Russian bibliographies (if the name of the
journal is customarily spelled out, no abbreviation is given).
2. The transliterated full name of the journal.
3. The full name of the translation journal (in bold type).
4. The year, volume (in parentheses), and issue of first publication of the translation (parentheses are empty if the Russian
journal does not use volume numbers).
5. The current publisher of the translation [AGI-American Geological Institute, AGU-American Geophysical Union, AIP-
American Institute of Physics, CB-Consultants Bureau, CH-Clearing House for Federal Scientific and Technical Informa-
tion, CS-The Chemical Society (London), FP-Faraday Press, IEEE- Institute of Electrical and Electronic Engineers, ISA
-Instrument Society of America, PP-Pergamon Press].
For convenience in locating bibliographic references the journals are listed in alphabetical order of the abbreviated titles.
AE ? Atomnaya energiya ? Soviet Journal of Atomic Energy ? 1956(1)1
? CB
Akust. zh. ? Akusticheskii zhurnal ? Soviet Physics-Acoustics
? 1955(1)1 ? AIP
Astrofiz. ? Astrofizika ? Astrophysics ? 1965(1)1 ? FP
Astr(on). zh(urn). ? Astronomicheskii zhurnal ? Soviet Astronomy-AJ
? 1957(34)1 ? AIP
Avtomat. I telemekh. ? Avtomatika I telemekhanika ? Automation and
Remote Control ? 1956(27)1 ? ISA
Avto(mat). svarka ? Avtomaticheskaya svarka ? Automatic Welding
? 1959(12)1 ? British Welding Research Association
Avtometriya ? Autometry ? 1965(1)1 ? CB
Biokhim. ? Biokhimiya ? Biochemistry ? 1956(21)1 ? CB
Byul. eksp(erim). biol. (I med.) ? Byulleten' eksperimental'noi biologii
I meditsiny ? Bulletin of Experimental Biology and Medicine
? 1959(41)1 ? CB
DAN (SSSR) ? see Doklady AN SSSR
Defektoskopiya ? Soviet Defectoscopy ? 1965(1)1 ? CB
Diff. urav. ? Differentsial'nye uravneniya ? Differential Equations
? 1965(1)1 ? FP
Doklady) AN SSSR; DAN (SSSR) ? Doklady Akademii Nauk SSSR
? The translation of Doklady is published in various journals,
according to subject matter. The sections of Doklady contained
in each of the translation journals are listed in parentheses.
Doklady Biochemistry (biochemistry) ? 1957(112)1 ? CB
Doklady Biological Sciences Sections (anatomy, cytology, ecology,
embryology, endocrinology, evolutionary morphology, parasitology,
physiology, zoology) ? 1957(112)1 ? CB
Doklady Biophysics (biophysics) ? 1957(112)1 ? CB
Doklady Botany (botany, phytopathology, plant anatomy, plant
ecology, plant embryology, plant physiology, plant morphology)
? 1957(112)1 ? CB
Doklady Chemical Technology (chemical technology) ? 1956(106)1
? CB
Doklady Chemistry (chemistry) ? 1956(106)1 ? CB
Doklady Earth Sciences Sections (geochemistry, geology, geophysics,
hydrogeology, lithology, mineralogy, paleontology, permafrost,
petrography) ? 1959(124)1 ? AGI
Doklady Physical Chemistry (physical chemistry) ? 1957(112)1 ? CB
Doklady Soil Science (soil science) ? 1964(154)1 ? Soil Science
Society of America
Soviet Mathematics-Doklady (mathematics) ? 1960(130)1 ? Amer-
ican Mathematical Society
Soviet Oceanogtaphy (oceanology) ? 1959(124)1 ? AGU
Soviet Physics-Doklady (aerodynamics, astronomy, crystallography,
cybernetics and cor..rol theory, electrical engineering, energetics,
fluid mechanics, heat engineering, hydraulics, mathematical
physics, mechanics, physics, technical physics, theory of @las-
ticity ? 1956(106)1 ? AIP
Elektrokhimiya ? Soviet Electrochemistry ? 1965(1)1 ? CB
Elektrosvyaz' ? combined with Radiotekhnika In Telecommunications
and Radio Engineering ? 1957(16)1 ? IEEE
Elektrotekh. ? Elektrotekhnika ? Soviet Electrical Engineering ? 1965
(36)1 ? FP
Entom(ol). oboz(r). ? Entomologicheskoe obozrenie ? Entomological
Review ? 1958(37)1 ? Entomological Society of America
Fiz. goreniya i vzryva ? Fizika goreniya I vzryva ? Combustion, Ex-
plosion, and Shock Waves ? 1965(1) ? FP
Fiziol(ogiya) rast. ? Fiziologiya rastenii ? Soviet Plant Physiology
1957(4)1 ? CB
Fiz.-khim. mekh(anika) mater(ialov); FKhMM ? Fizikokhimicheskaya
mekhanika materialov ? Soviet Materials Science ? 1965(1)1 ? FP
Fiz. met. i metallov.; FMM ? Fizika metallov i metallovedenie ? Physics
of Metals and Metallography ? 1957(5)1 ? Acta Metallurgica
Fiz.-tekhn. probl. razr. polezn. iskopaem. ? Fizikotekhnicheskie prob-
lemy razrabotki poleznykh iskopaemykh ? Soviet Mining Science
? 1965(1)1 ? CB
Fiz. tv(erd). tela; FIT ? Fizika tverdogo tale ? Soviet Physics-Solid
State ? 1959(1)1 ? AIP
FKhMM ? see Fiz.-khim. mekhanika materialov
FMM ? see Fiz. met. i metallov.
FTT ? see Fiz. tverd. tela
Geliotekh. ? Geliotekhnika ? Applied Solar Energy ? 1965(1)1 ? FP
Geol. nefti i gaza ? Geologiya nefti i gaza ? Petroleum Geology ? 1958
(2)1 ? Petroleum Geology, Box 171, McLean, Va.
Geomagnet. I aeronom. ? Geomagnetizm i aeronomiya ? Geomag-
netism and Aeronomy ? 1961(1)1 ? AGU
Inzh.-fiz. zh. ? Inzhenerno-fizicheskii zhurnal ? Journal of Engineering
Physics ? 1965(8)1 ? FP
Inzh. zh. ? lnzhenernyi zhurnal ? Soviet Engineering Journal ? 1965(5)1
? FP
Iskussty. sputniks Zemli ? Iskusstvennye sputniks Zemli ? Artificial
Earth Satellites ? 1958(1)1 ? CB [superseded by Kosmich. issled.]
lzmerit. tekhn(ika) ? lzmeritel'naya tekhnika ? Measurement Tech-
niques ? 1958(7)1 ? ISA
Izv. AN SSSR, o(td.) kh(im.) n(auk) (or ser. khim.) ? lzvestiya Akademii
Nauk SSSR: Otdelenie khimicheskikh nauk (or Seriya khlml-
cheskaya) ? Bulletin of the Academy of Sciences of the USSR:
Division of Chemical Science ? 1952(16)1 ? CB
Izv. AN SSSR, ser. fiz(ich). ? Izvestiya Akademii Nauk SSSR: Seriya
fizicheskaya ? Bulletin of the Academy of Sciences of the USSR:
Physical Series ? 1954(18)3 ? Columbia Technical Translations
Izv. AN SSSR, ser. fiz. atm. i okeana ? Izvestiya Akademii Nauk SSSR:
Seriya fiziki atmosfery I okeana ? Izvestiya, Atmospheric and
Oceanic Physics ? 1965( )1 ? AGU
Izv. AN SSSR, ser. fiz. zemli ? Izvestiya Akademil Nauk SSSR: Serlya
fiziki zemli ? Izvestiya, Physics of the Solid Earth ? 1965( )1
?AGU
Izv. AN SSSR, ser. geofiz. ? Izvestiya Akademii Nauk SSSR: Seriya
geofizicheskaya ? Bulletin of the Academy of Sciences of the
USSR: Geophysics Series ? 1957(7)1 ? AGU [superseded by Izv.
AN SSSR, ser. fiz. atm. i okeana and Izv. AN SSSR, ser. fiz. zemll]
Izv. AN SSSR, ser. geol. ? Izvestiya Akademil Nauk SSSR: Serlya
geologicheskaya ? Bulletin of the Academy of Sciences of the
USSR: Geologic Series ? 1958(23)1 ? AGI
Izv. AN SSSR, ser. neorgan. mat(er). ? Izvestiya Akademii Nauk SSSR:
Seriya neorganicheskie materialy ? Inorganic Materials ? 1965(1)
1?CB
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Izv. AN SSSR, tekhn. kiber(netika) ? Izvestiya Akademii Nauk SSSR:
Tekhnicheskaya kibernetika ? Engineering Cybernetics ? 1963(1)1
? IEEE
Izv. v(yssh.) u(ch.) z(av.) aviats. tekh. ? Izvestiya vysshikh uchebnykh
zavedenii. Aviatsionnaya tekhnika ? Aviation Engineering
1963(6)1 ? CH
Izv. v(yssh.) u(ch.) z(av.) fiz. ? Izvestiya vysshikh uchebnykh zaved-
enii. Fizika ? Soviet Physics Journal ? 1965(8)1 ? FP
Izv. v(yssh.) u(ch.) z(av.) geodez. i aerofot. ? Izvestiya vysshikh uche-
bnykh iavedenii. Geodeziya i aerofotos"emka ? Geodesy and
Aerophotography ? 1959(4)1 ? AGU
Izv. v(yssh.) u(ch.) z(av.) priborostr. ? Izvestiya vysshikh uchebnykh
zavedenii. Priborostroenie ? Izvestiya VUZOV. Instrument Build-
ing ? 1962(5)1 ? CH
Izv. v(yssh.) u(ch.) z(av.) radiofiz. ? Izvestiya vysshikh uchebnykh
zavedenii. Radiofizika ? Izvestiya VUZOV. Radiophysics ? 1958(1)1
.CH
Izv. v(yssh.) u(ch.) z(av.) radiotekhn(ika) ? Izvestiya vysshikh ucheb-
nykh zavedenii. Radiotekhnika ? Izvestiya VUZOV. Radio Engi-
neering ? 1959(2)1 ? CH
Izv. v(yssh.) u(ch). z(av.) tekh. teks. prom. ? Izvestiya vysshikh ucheb-
nykh zavedenii. Tekhnologiya tekstilnoi promyshlennosti ?, Tech-
nology of the Textile Industry, USSR ? 1960(4)1 ? The Textile
Institute (Manchester)
Kauch. i rez. ? Kauchuk i rezina ? Soviet Rubber Technology ? 1959
(18)3 ? Maclaren and Sons Ltd.
Khim. getero(tsik). soed. ? Khimiya geterotsiklicheskikh soedinenii
Chemistry of Heterocyclic Compounds ? 1965(1)1 ? FP
Khim. i neft. mash(inostr). ? Khimicheskoe i neftyanoe mashinostro-
enie ? Chemical and Petroleum Engineering ? 1965( )1 ? CB
Khim. i tekhnol. topliv i masel ? Khimiya i tekhnologiya topliv i masel
? Chemistry and Technology of Fuels and Oils ? 1965( )1 ? CB
Khim. prirod. soed. ? Khimiya prirodnykh soedinenii ? Chemistry of
Natural Compounds ? 1965(1)1 ? FP
Kib. ? Kibernetika ? Cybernetics ? 1965(1)1 ? FP
Kinet. I katal. ? Kinetika i kataliz ? Kinetics and Catalysis ? 1960(1)1
? CB
Koks i khim. ? Koks i khimiya ? Coke and Chemistry, USSR ? 1959( )8
? Coal Tar Research Assn. (Leeds, England)
Kolloidn. zh(urn). ? Kolloidnyi zhurnal ? Colloid Journal ? 1952(14)1
? CB
Kosmich. issled. ? Kosmicheskie issledovaniya ? Cosmic Research
1963(1)1 ? CB
Kristallog. ? Kristallografiya ? Soviet Physics-Crystallography ? 1957
(2)1 ? AIP
Liteinoe proiz(-vo). ? Liteinoe proizvodstvo ? Russian Castings Produc-
tion ? 1961(12)1 ? British Cast Iron Research Association
Mag. gidrodin. ? Magnitnaya gidrodinamika ? Magnetohydrodynamics
? 1965(1)1 ? FP
Mekh. polim. ? Mekhnika polimerov ? Polymer Mechanics ? 1965(1)1
? FP
Metalloved. i term. obrabotka metal.; MiTOM ? Metallovedenie i
termicheskaya obrabotka metallov ? Metal Science and Heat
Treatment ? 1958(6)1 ? CB
Metallurg ? Metallurgist ? 1957( )1 ? CB
Mikrobiol. ? Mikrobiologiya ? Microbiology ? 1957(26)1 ? CB
MiTOM ? see Metalloved. i term. obrabotka metal.
Ogneupory ? Refractories ? 1960(25)1 ? CB
Opt. i spektr.; OS ? Optika i spektroskopiya ? Optics and Spectroscopy
? 1959(6)1 ? AIP
Osnovan. fund. i mekh. gruntov ? Osnovaniya fundamenty i mekhanika
gruntov ? Soil Mechanics and Foundation Engineering ? 1964
)1 ? CB
Paleon. zh(urn). ? Paleontologicheskii zhurnal ? Journal of Paleontol-
ogy ? 1962( )1 ? AGI
Plast. massy ? Plasticheskie massy ? Soviet Plastics ? 1960(8)7
Rubber and Technical Press, Ltd.
PMM ? see Prikl. matem. i mekhan.
PMTF ? see Zhur. prikl. mekhan. i tekhn. fiz.
Pochvovedenie ? Soviet Soil Science ? 1958(53)1 ? Soil Science Society
of America
Poroshk. met. ? Poroshkovaya metallurgiya ? Soviet Powder Metallurgy
and Metal Ceramics ? 1962(2)1 ? CB
Priborostroenie ? Instrument Construction ? 1959(4)1 ? Taylor and
Francis, Ltd.
Pribory I tekhn. eksp(erimenta); PTE ? Pribory i tekhnika eksperi-
menta ? Instruments and Experimental Techniques ? 1958(3)1
ISA
Prikl. biokhim. i mikrobiol. ? Prikladnaya biokhimiya i mikrobiologiya
? Applied Biochemistry and Microbiology ? 1965(1)1 ? FP
Prikl. matem. i mekh(an).; PMM ? Prikladnaya matematika i mekhanika
? Applied Mathematics and Mechanics ? 1958(22)1 ? PP
Probl. pered. inform. ? Problemy peredachi informatsii,? Problems of
Information Transmission ? 1965(1)1 ? FP
Probl. severa ? Problemy severa ? Problems of the North ? 1958( )1
National Research Council of Canada
PTE ? see Pribory i tekhn. eksperimenta
Radiokhim. ? Radiokhimiya ? Soviet Radiochemistry ? 1962(4)1 ? CB
Radiotekh. ? Radiotekhnika ? combined with Elektrosvyaz' in Tele-
communications and Radio Engineering ? 1961(16)1 ? IEEE
Radiotekhn. i elektron(ika) ? Radiotekhnika i elektronika ? Radio
Engineering and Electronic Physics ? 1961(6)1 ? IEEE
Stall ? Stall in English ? 1959(19)1 ? The Iron and Steel Institute
Stanki i inst. ? Stanki i instrument ? Machines and Tooling ? 1959
(30)1 ? Production Engineering Research Association
Stek. i keram. ? Steklo i keramika ? Glass and Ceramics ? 1956(13)1
? CB
Svaroch. proiz(-vo). ? Svarochnoe proizvodstvo ? Welding Production
? 1959(5)4 ? British Welding Research Association (London)
Teor. i eksperim. khim. ? Teoreticheskaya i eksperimental'naya khim-
iya ? Theoretical and Experimental Chemistry ? 1965(1)1 ? FP
Teor. veroyat. i prim. ? Teoriya veroyatnostei i ee primenenie ? Theory
of Probability and Its Application ? 1956(1)1 ? Society for Indus-
trial and Applied Mathematics
Teploenergetika ? Thermal Engineering ? 1964(11)1 ? PP
Teplofiz. vys(ok). temp. ? Teplofizika vysokikh temperatur ? High
Temperature ? 1963(1)1 ? CB
Tsvet. metally ? Tsvetnye metally ? The Soviet Journal of Nonferrous
Metals ? 1960(33)1 ? Primary Sources
Usp. fiz. nauk; UFN ? Uspekhi fizicheskikh nauk ? Soviet Physics-
Uspekhi ? 1958(66)1 ? AIP
Usp. khim.; UKh Uspekhi khimii ? Russian Chemical Reviews
1960(29)1 ? CC
Usp. mat. nauk; UMN ? Uspekhi matematicheskaya nauk ? Russian
Mathematical Surveys ? 1960(15)1 ? Cleaver-Hume Press, Ltd.
Vest. Akad. med. nauk SSSR ? Vestnik Akademii meditsinskikh nauk
SSSR ? Vestnik of USSR Academy of Medical Sciences ? 1962(17)1
?CH
Vest. mashinostroeniya ? Vestnik mashinostroeniya ? Russian Engi-
neering Journal ? 1959(39)4 ? Production Engineering Research
Association
Vest. svyazi ? Vestnik svyazi ? Herald of Communications ? 1954(14)1
?CH
Vysoko(molek). soed(ineniya) ? Vysokomolekulyarnye soedineniya
(SSSR) ? Polymer Science (USSR) ? 1959(1)1 ? PP
Yadernaya fizika ? Soviet Journal of Nuclear Physics ? 1965(1)1 ? AIP
Zashch(ita) met(allov) ? Zashchita metallov ? Protection of Metals
1965(1)1 ? CB
Zav(odsk). lab(oratoriya); ZL ? Zavodskaya laboratoriya ? Industrial
Laboratory ? 1958(24)1 ? ISA
ZhETF pis'ma redaktsiyu ? JETP Letters ? 1965(1)1 ? AIP
Zh(ur). anal(it). khim(ii); ZhAKh ? Zhurnal analiticheskoi khimii
Journal of Analytical Chemistry ? 1952(7)1 ? CB
Zh(ur). eks(perim). i teor. fiz.; ZhETF ? Zhurnal eksperimental'noi i
teoreticheskoi fiziki ? Soviet Physics-JETP ? 1955(28)1 ? AIP
Zh(ur). fiz. khimii; ZhFKh ? Zhurnal fizicheskoi khimii ? Russian
Journal of Physical Chemistry ? 1959(33)7 ? CS
Zh(ur). neorg(an). khim.; ZhNKh ? Zhurnal neorganicheskoi khimii
Russian Journal of Inorganic Chemistry ? 1959(4)1 ? CS
Zh(ur). obshch. khim.; ZhOKh ? Zhurnal obshchei khimii ? Journal of
General Chemistry of the USSR ? 1949(19)1 ? CB
Zh(ur). org. khim.; ZhOrKh(im) ? Zhurnal organicheskoi khimii ? Journal
of Organic Chemistry of the USSR ? 1965(1)1 ? CB
Zh(ur). prikl. khim.; ZhPKh ? Zhurnal prikladnoi khimii ? Journal of
Applied Chemistry of the USSR ? 1950(23)1 ? CB
Zh(ur). prikl. mekhan. i tekhn. fiz. ? Zhurnal prikladnoi mekhaniki i
tekhnicheskoi fiziki ? Journal of Applied Mechanics and Tech-
nical Physics ? 1965( )1 ? FP
Zh(ur). prikl. spektr. ? Zhurnal prikladnoi spektroskopii ? Journal of
Applied Spdctroscopy ? 1965(2)1 ? FP
Zh(ur). strukt(urnoi) khim.; ZhSKh ? Zhurnal strukturnoi khimii
Journal of Structural Chemistry ? 1960(1)1 ? CB
Zh(ur). tekhn. fiz.; ZhTF ? Zhurnal tekhnicheskoi fiziki ? Soviet Physics
-Technical Physics ? 1956(26)1 ? AIP
Zh(ur). vses. khim. ob-va im. Mendeleeva ? Zhurnal vsesoyuznogo
khimicheskogo obshchestva im. Mendeleeva ? Mendeleev Chem-
istry Journal ? 1965(10)1 ? FP <
Zh(ur). vychis. mat. i mat. fiz. ? Zhurnal vychislitel'noi matematika i
matematicheskoi fiziki ? USSR Computational Mathematics and
Mathematical Physics ? 1962(1)1 ? PP
ZL ? see Zavodsk. laboratoriya
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MATSCI(NCE SYMPOSIA
T 'R AL.*FiyS1CS
N HEO ETIC
Alladi Ramakrishnan, Editor
A Plenum Press continuing series of proceedings of Matscience symposia
held at the Institute of Mathematical Sciences, Madras, India
Volume 1: Proceedings of the
First Anniversary Symposium
This symposium was arranged in tribute to
Prof. R. E. Marshak,.who accepted the first
Niels Bohr visiting professorship at the new
Institute of Mathematical Sciences. Prof.
Marshall contributed the paper "Group Sym-
metries with R-Invariance" included in this
proceedings. The other 12 papers also deal
mainly with complex problems of particle sym-
-metries and resonances.
CONTENTS: Introductory material, Alladi Rama-
krishnan , Symmetries and resonances, T K.
Radha, Group,, symmetries with' R`invariance,
R. E. Marshak Pion resonances, T. S. Santhanam ?
Pion-nucleon resonances, K. Venkatesan ? The influ-
ence of pion-nucleon resonance on elastic scattering
of charged p'jons by,deuterons, V Devanathan
Pion-hyperon resonances, R. K. Umerjee ? determi-
nation of spin-parity of?re'sonances, G. Ramachan-
dran ? Regge poles and resonances, T. K. Radha
On Regge-poles in perturbation theory and in weak
-,interactions, K. Raman' ? Some remarks on recent
experimental data and techniques, E. Segre ? On
the new resonances, Bogdan Maglic ? The higher
? resonances in the pion-riucleon system, G. Takeda. -
165 pages 1965 $9.50
Volume 3: Proceedings of the , -
First Matscience Summer School
In preparation
1 ,
Volume?2: Proceedings of the ..
Second Anniversary Symposium
CONTENTS: Origin of internal symmetries, E. C. G.
Sudarshan ? -Construction of the invariants of the
simple Lie groups, L. O'Raifeartaigh? ? Temperature
.cutoff in quantum field theory and mass renormaliza-
tion, S. P. Misra ? Some current trends in mathe-
matical research, M. H. Stone ? Recent mathe-
matical developments In cascade theory, S. K.
Srinivasan ? Semigroup methods in mathematical
physics, A. T. Bharucha-Reid ? On peratiietion
methods, N. R. Ranganathan ? Muon, capture by
complex nuclei, V. Devanathan -The theory of a
general quantum system interacting with a linear
dissipat)on system, R. Vasudevan ? Recent devel-
opments in the statistical mechanics of plasmas,
Hugh.beWitt ? Electrodynamics of superconductors,
B. Zumino ? Crossing relations and spin states,
M. Jacob ? Large-angle elastic scattering at high
energies, R. Hagedorn ? The multiperipheral model
for high energy processes, K. Venkatesan ? Effec-
tive-range approximation based on Regge poles,
B. M. Udgaonkar ? Regge poles in weak interactions
and form "factors, K. Raman ? Some applications of
separable potentials in elementary particle physics,
A. N. Mitra ? Introduction to quantum statistics of
degenerate Bose, systems F. Mohling? Form factors
of the_ three-nucleon systems H3 and He3, _ T. K.
Radha.
Approx. 2.60 pages
1966 $12.50
i Vnlumo d~ Proceedings of the
Third -Anniversary Symposium
In preparation
P PLENUM PRESS 227 West 17th Street, New-York, New York 10011
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