SOVIET ATOMIC ENERGY VOL. 48, NO. 2

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• Publication Date: February 1, 1980
• Content Type: REPORT

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Russian Original Vol. 48, No. 2, February, 1980
August, 1980
,Lt
SATEAZ 48(2) 71-152 (1980)
5 - NOV 1980
SOVIET
ATOMIC
ENERGY
ATOMHAA 3HEPIIIH
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is a translation of Atomnaya Energiya, a
publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
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Russian journal.
11
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii 'a
Associate Editors: N. A. Vlasov and N. N.. Ponomarev-Stepnoi
Secretary: A. I. Artemov '
I. N. Golovin
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V. 1. l I'ichev
I. D. Morokhov
V. E. Ivanov
A. A. Naumov
V. F. Kalinin
A. S. Nikiforov
P. L. Kirillov
. i
A. S. Shtan'
Yu. 1. Koryakin
B. A. Sidorenko
A. K. Krasin
M. F. Troyanov
E. V. Kulov
B. N. Laskorin
E. I. Vorob'ev
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
August, 1980
Volume 48, Number 2 February, 1980
CONTENTS
Engl./Ross.
ARTICLES
Dependence of 232U Formation in Nuclear Fuel on Neutron Spectrum - T. S. Zaritskaya,
S. M. Zaritskii, A. K. Kruglov, L. V. Matveev, A. R. Rudik, and E. M. Tsenter
71
67
Structural Reliability of Atomic Power Plant - A. I. Kiemin and E. F. Polyakov ......
75
70
Estimating the Carrying Capacity of Zirconium Fuel-Element Shells - V. I. Solyanyi
and V. S. Yamnikov ........... ...............................
78
73
Crystal Structure of ys Phase in U-Mo, U-Re, and U-Nb Alloys - N. T. Chebotarev
and O. N. Utkina ...............................................
83
76
Polynomial Approximation of Neutron Flux in First-Collision Probability Method
- T. S. Poveshchenko and Ya. V. Shevelev .......... ......... .....
88
80
Cost Optimization in Connection with the Accumulation of Isotopes of the Transuranium
Elements - S. A. Nemirovskaya and A. P. Rudik . .......... .....
93
84
Measurement of the Cross Sections for Radiative Capture of Neutrons by 238U and 197Au
Relative to the Cross Section for the Elastic Scattering of Neutrons by Protons
- A. N. Davletshin, S. V. Tikhonov, A. O. Tipunkov, and V. A. Tolstikov ......
97
87
Solubility of Nitrogen in Water - Yu. A. Kalaida, Yu. D. Katkov, V. A. Kuznetsov,
A. Yu. Lastovtsev, A. P. Lastochkin, and V. S. Sysoev ...................
102
91
Optimization of Radiation Facilities with Electron Accelerators - V. V. Krayushkin .....
106
94
LETTERS
Mass Transfer in Single Crystals of Molybdenum and Silicon Carbide under Irradiation
with Low-Energy Glow-Discharge Ions - A. A. Babad-Zakhryapin, E. V. Borisov,
I. B. Savvatimova, and A. D. Senchukov ... ...........................
111
98
Diagnostics of State of BOR-60 Reactor by Calculation of Reactivity Balance
- V. A. Afanas'ev, V. M. Gryazev, V. N. Efimov, B. V. Kebadze,
N. V. Krasnoyarov, and V. A. Kachalin ..............................
114
100
Secondary Swelling of Graphite - Yu. S. Virgil'ev, I.. P. Kalyagina, E. I. Kurolenkin,
and V. G. Makarchenko ................................ ......
116
102
"Poleskop" Physical-Field Indicator - G. N. Aleksakov and G. P. Terekhov ..........
119
103
Radiation Stability of Phosphorus-Containing Cationites - S. B. Makarova,
A. V. Smirnov, A. S. Telegin, N. V. Bychkov, and B. S. Roginskaya ..........
122
105
Analysis of the Composition of a Mixture of 249Bk + 249Cf on the Basis of X Rays
- G. V. Buklanov and Yu. P. Kharitonov ..............................
123
106
Determination of Equilibrium Parameters of Sodium - Oxygen - Hydrogen System
- Yu. V. Privalov .............................................
127
108
Nonsteady Temperature in Nuclear-Reactor Channel - A. S. Trofimov and A. V. Sobolev
129
109
A a-Radiation Source Based on Polystyrene Containing Tritium - V. M. Gul'ko,
E. I. Knizhnik, V. K. Rudishin, and A. I. Yashchuk ......................
131
111
Comparison of the Results of Calculating Fast-Neutron Passage through Hydrogen and
Carbon Layers - E. B. Brodkin, A. N. Kozhevnikov, V. G. Madeev, V. A. Utkin,
and A. V. Khrustalev ...........................................
133
112 -
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CONTENTS
(continued)
Engl./Russ.
Analysis of Activation Method for Measuring Fast-Neutron Interaction Cross Sections
- A. N. Davletshin, A. 0. Tipunkov, S. V. Tikhonov, and V. A. Tolstikov ...... 136 113
Yield and Angular Distributions of Photoneutrons from Thick Lead Targets
- A. P. Antipenko, V. G. Batii, V. Ya. Golovnya, V. I. Kasilov, N. I. Lapin,
L. A. Makhnenko, and S. F. Shcherbak .................. ? 139 115
A New System of Group Constants for the Calculation of Fast Reactors - L. N. Abagyan,
N. 0. Bazazyants, M. N. Nikolaev, and A. M. Tsibulya ................... 141 117
Collation of Several Methods of Pulsed y-Ray Dosimetry - Yu. P. Bakulin,
V. N. Kapinos, A. P. Korotovskikh, and Yu. A. Medvedev ................. 143 118
Corrections to Neutron Flux Measurements by Gold Foil Method - G. M. Stukov
and I. A. Yaritsyna ............................................ 145 119
Determination of the Lanthanum, Cerium, Praseodymium, and Neodymium Content of
Solutions by an X-Ray Spectral Method Using the SRF-5 Instrument
- I. M. Krasil'nikov, I. D. Skorova, A. V. Sholomov, P. A. Konstantinov,
and A. P. Matyushin ......... ..................... ...... 146 120
Axial Stability of VVER-1000 Reactor with Control with Minimum Standard Deviation
- A. M. Afanas'ev and B. Z. Torlin ... .. .. ................... 148 121
Yields of "'Re, 112Mp , 182Re, 183Re, ta4mRe, 184Re, and .186Re in the Bombardment of
Tungsten by Protons and Deuterons, and Tantalum by a Particles - P. P. Dmitriev
and G. A. Molin .............................................. 150 122
The Russian press date (podpisano k pechati) of this issue was 1/23/1980.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
DEPENDENCE OF 232U FORMATION IN NUCLEAR FUEL
ON NEUTRON SPECTRUM
T. S. Zaritskaya, S. M. Zaritskii,
A. K. Kruglov, L. V. Matveev,
A. P. Rudik, and 9. M. Tsenter
UDC 621.039.516.22
In the combustion of nuclear fuel, 232U is formed, which is extremely undesirable since its presence in
regenerated uranium may lead to marked deterioration in the radiational set-up at all stages of the fuel cycle.
In fact, 232U itself is a weak y emitter, but its decay chain (Fig. 1) includes 208T1, which intensely emits high-
energy y radiation at an energy of 2.61 MeV.
The time dependence of the exposure dose rate at a distance of 1 m from a point source initially contain-
ing 1 mg of pure 232U is shown in Fig. 2. The dose rate reaches a maximal value of 12.9 mR/h after 10.3 years
(1 R = 2.58.10-q Ci/kg). The exposure dose rate from uranium with 1, 3, and 6% enrichment with 235U in the
absence of protection doubles if the uranium contains, respectively, 3 ?10-8, 5 -10-8, and 9 - 10-8 mass % 232U.
When, in working with regenerated uranium, release of the uran ium into the air is possible, the 232U
content should be established on the basis of the permitted concentrations of 232U and natural uranium in the
air of mineshafts [11: 6.1 .10-13 and 8.8. 10-5 mg/liter, respectively. The internal irradiation of personnel
doubles if in natural uranium there is 7 10-7 mass % 232U (6.1 .10-13 /8.8 -10-5) . The additional radiational
danger associated with 232TJ is due to the release of the gaseous decay product thoron (220Rn) into the air of
mine shafts .
232U 7 IS 228Th 1,91yrs zz4Ra 3,64dayszzoRn 55,3sec ~ePC 4145 _~tzPb 10,64 h zizBi 60,6 -min y MP,
a or . a a or fi, 64%
Fig. 1. Decay chain for 232U.
5 10 15
Time, years
2oen 310 mid waPb
d 646 min of 3,04.10'$ec
36%
Fig. 2. Time dependence of
exposure dose rate from a
point source containing 1 mg
of pure 232U initially.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 67-70, February, 1980. Original article
submitted May 28, 1979.
0038-531X/80/4802-0071$07.50C)1980 Plenum Publishing Corporation
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. Decay Chain Forming 232U
The decay chains forming 232U in nuclear-reactor fuel may be divided into two groups.. The first-colr-
tains chains including the reaction (n, y) p
236 U (n, V) 236U (n, ,) 237 U (F' )237Np (n, 2n236 Np (50%, ) 23OpU (a) 232U; (1 .1)
234U (a) 230 Th (n, y) 23ITh (({-) 231Pa (n, V) 232 Pa (N-) 232 .U; (1.2)
236 U (a) 231 Th (F'-) 2311 Pa (n, y) 232 Pa. (ri-)232U (1.3)
If the fuel is produced from regenerated uranium, it will contain a certain amount of 236U. Irradiation
of 2361J also leads to the formation of 232U
236 U (n,1 V) 237 U (N-) 237 Np (n, 2n) (1.4)
sss Np (50%, p-) 236 Pu (a) 232 U.
Fuel that has not been subjected to gas-diffusion enrichment always includes a.certain amount of 232Th,
230Th, and 231Pa. These nuclides at first give the following chain for the formation of 232U:
292 Th (n, 2n) 231 Th (R-) 231 Pa (n, ?)"I Pa (Y-) 232U;
232 Th (n, ?.1) 233 Th F('~-) 233 Pa (n, 2n)232Pa ({1-)232 U;
230Th (n,,?) zs1 Th (,-) 231Pa (n, y)232 Pa (P-)232U.
231 Pa (n, V)232 Pa (33R-) 232 U;
232 Th (n, V) 233 Th (P-) 233 Pa (R-) 239 U (n, 2n) 282 U.
The products of gas-diffusion plants do not include protactinium and thorium. However, in time, a certain
amount of 230Th and 231Pa may accumulate in the fuel as a result of the decay of 234U and 235U.
The second group contains processes that do not involve the reaction (n, y)
234 U (n, 3n) 232 U; (2.1)
238 U (n, 2n) 237 U (0.-) 237 Np (n, 2n) 236 Np (50%, 236pu ((X) 232 U. (2.2)
If the regenerated fuel includes neptunium as an impurity, an additional chain/that forms 232U appears
(2.3) 237 Np (n, 2n) 236 Np, (50%, P-) 236 Pu ((X)232 U. (2.3)
Rate of Formation of 232U
The reactions (n, 2n) and (n, 3n) are characterized by fairly high energy thresholds: 6-8 and - 13 MeV,
respectively. Therefore, it is assumed that the effective rate of the reactions. (n, 2n) and (n, 3n) - 4)Qeff(n, 2n) _
does not depend on the neutron spectrum in the reactor
( D o e (1)
ff(n, 2n) = o (n, 2n)F,
where 4 is the neutron flux density; a(n, 2n), microscopic cross section of the reaction (n, 2n); v, number of
neutrons in one fission act; W, specific power associated with the nuclear fuel; Ef, energy liberated in fission;
Nuclide
Reaction
a, b
1, -b
23OTh
.(n, v)
23,2
1010
8,0 -104 yr
231Th
25,52 h
231 Pa
(,y)
210
1500
3,25.104yr
232Pa
1,3day
232U
a
72 h
236U
582,2
275
103 yr
7,1 ?
(nj
98,6
144
.
2SOU
(n, V)
5,2
365
2,39.107 yr
237U
6,75=day
237Np
(, )
660
2,14.106 yr
(n, 2n)
0,82.10-2
TABLE 2. Probability of Nuclide Formation
Nuclide I chain
(1.4)
0236U (n, y) 02360 (n,?) s2
Q2S6U (f) 0235U (f) 2
0236U (n, y)
S
0236u (f)
0230Th (n, V) 0231pa (n, V) s$
0235U (f) 0236U (f) 2
a231Pa (n,
s
02360 (/)
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TABLE 3. Dependence of Cross-Sectional
Ratio on Neutron-Spectrum Hardness
a2361J (n, Y)/a235U (I)
6.,3OTh (n, Y)/a235U (I)
a23Lpa (n, Y)/a235U (I)
Q235U (n, Y) a236U (n. Y)
02350 (I) a235U (I)
a23?Th (n. Y) a231 P. (n, Y)
a2 35U (1) 0235U (I)
0,0 I 0,1 I 0,2 I 0,4 11,0 I --
0.17
0.0:189
0,0040
0,36
0.19
0.068
0.204
0.59
0.20
0,123
0,353
0.80
0.23
0.218
0.617
1.17
0.28
0.432
1.21
2.00
0.52
1.33
3.67
5,46
TABLE 4. Neutron-Spectrum Hardness in
Power Reactors
VVER
U
ontent
in nuc-
lear fue
maca _~I
1,6
2,4
3,6
1,8
0, 23-0, 33
0,36-0,50
0,56-0,73
0,035-0,11
Reac-
tion
type
BA ES
ss
_TUT
content
in nuc-
lear fue
mass,,N.
1,5
3,0
5,75
0,714
0,2
0,3
0,44
0,10-0,12
* Heavy-water power reactor with gas cooling, A -1 atomic
.e., in Eq. (2) (2) Ua (n, y) ?yIU. 'power station, Czechoslovakia.
F, a geometric factor taking into account the fuel-element disposition and the properties of the moderator
between them.
It is of interest to investigate the dependence of 232U formation on the neutron spectrum for certain given
depths of burnup and given initial compositions of the fuel. The only quantity sensitive to the neutron spectrum
is the cross section of the reaction (n, y). In power reactors of water-cooled-water-moderated (VVER) types,
the rate of the reaction (n, y) is given by the expression
dlaeff (n, Y) _ Ua (n, ?'Y) + yI U, (2)
where U is the thermal-neutron flux density; y is a factor characterizing the ratio of neutron flux densities in
the resonance and thermal parts of the spectrum (the rigidity of the spectrum) [2].
The dependence of 232U formation on y may be demonstrated for the example of the chains in Eqs. (1.1),
(1.4), (1.7), and (1.8). Analogous estimates may easily be made for other chains. The probability of 232U
formation by the chains in Eqs. (1.1) and (1.4) is determined by the probability of 237Np formation, and the
probability for Eqs. (1.7) and (1.8) by the probability of 232Pa formation. Table 1 shows the physical charac-
teristics of the nuclides appearing in these chains (a is the cross section at an energy E = 0.025 eV; I is the
resonance integral for E = 0.5 eV; T1/2 is the half life).
The probability of nuclide formation by a particular chain (Table 2) at small nuclear-fuel burnup [3] is
taken to mean the ratio between the number of nuclei formed at burnup s to the initial number of nuclei in the
first element of the chain, where s = 0'235U(f)4t. Table 3 gives the cross-sectional ratios appearing in the for-
mation of Table 2, which are determined for different hardnesses of the neutron spectrum y (the data of Table
1 are used). It follows from the data of Table 3 that the corresponding cross-sectional ratio increases practi-
cally linearly with rise in y. In [3], rough values of y for power reactors are given (Table 4).
Nuc-
Bumup
lido
Chain
v
0,5
I 1,0
I 1,5
2,0
287Np
(1.1)
0,0
1,48.10-4
4,77.10-4
8,70.10-4
1,27.10-3
0,1
1,21-10-3
3,75-10-3
6,64.10-3
9,39.10-8
0,2
2,30.10-8
6,92.10-3
1,19.10-2
1,63.10-2
00
3,63.10-2
6,18.10-2
5,97.10-2
4,59.10-2
(1.4)
0,0
4,15.10-8
7,72.10-3
1,08.10-2
1,34.10-2
0,1
3,05.10-2
5,47.10-2
7,36.10-2
8,83.10-2
0,2
5,1.0.10-2
9,17.10-2
0,119
0,138
ao
0,264
0,216
0,135
7,68.10-2
2321'a
(1.7)
0,0
1,62.10-8
6,30.10-3
1,32.10-2
2,22.10-2
0,1
1,32.10-2
4,65.10-2
9,25.10-2
0,146
0,2
2,93.10-2
9,76.10-2
.0,184
0,276
ao
0,647
0,931
0,988
0,998
(1.8)
0,0
0,165
0,303
0,418
0,514
0,1
0,256
0,446
0,588
0,693
0,2
0,330
0,551
0,699
0,798
00
0,935
0,996
1,00
1,00
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TABLE 6. Cross-Sectional Ratios for Fast
Reactors
Cross-sectional ratio
'Large' reactor
repr uction:
active f region
Reaction
with
highly
enriched
fuel
.a I b
0235U (n, 1')/?235[ (f)AR
0,19
0,31
0,37
0,19
o23dU (n, 'Y)/a235t7 (I R
0,25
0,36
0,45
0,22
)/a
?
(n
(1
55
0
0
87
1,0i
0,50
235U
,? Y
231pa
AR
,
,
Using the data of Tables 2 and 3, the dependence of 232U accumulation along the chains in Eqs. (1.1),
(1.4), (1.7), and (1.8) on y may be determined. The dependence of 232U accumulation along the chains in Eqs.
(1.1) and (1.4) is weaker than the dependence of the 237Np yield on y, since the quantity of 232U is determined by
the integral over time of the amount of 237Np. The dependence of the total 232U accumulation in the spent fuel
on the neutron spectrum is determined by the relative contribution of chains of the first group to the total
accumulation. The latter depends on the time elapsed from the moment of fuel-element manufacture to the
onset of the operating cycle, on the duration of the operating cycle, and on the storage time of the spent fuel.
At large nuclear-fuel burnup, the probability of nuclide formation is calculated by the method outlined in [3]
(Table 5).
Fast Reactors
Equation (2) for the rate of the reaction (n, y) is inapplicable for these reactors (formulas of this type
are only valid for reactors with a relatively soft neutron spectrum). Table 6 shows cross-sectional ratios
averaged over the spectra of different fast reactors with oxide fuel and sodium coolant; reactors with highly
enriched fuel and small dimensions of the active region [4], and reactors of type BN-350 but of much larger
power and dimensions - -1600 MW (electrical). The neutron spectra differ significantly in degree of hard-
ness, so that the data given in Table 6 characterize the limits within which these cross-sectional ratios may
vary in fast oxide reactors with sodium coolant. The mean radiation-capture cross section is referred to the
mean cross section for 235[ fission in the active region. For the. reproduction region of the "large" reactor,
data are given before (a) and after (b) taking account of the change in neutron-flux level in comparison with the
active region. The multigroup cross sections used in averaging correspond to the BNAB-70 system of con-
stants [5, 6]. Data on the radiational-capture cross section for 230Th have not been published.
Comparing the data of Tables 6 and 3, and taking into account the dependence of y on the type of reactor
(Table 4) and the probability of 232U formation (Table 2), it is found that, neglecting the different effective cross
sections for the reaction (n, 2n) in reactors of different type, the probability of 232U formation in fast reactors
over the given chains is approximately the same as in power reactors of water-cooled-water-moderated type
with an enrichment of 3.6% (it is assumed here that the burnup depth is the same).
Conclusions
As a result of the calculations, it has been established that for nuclear reactors of power type the amount
of 232U formed depends significantly on the neutron-spectrum hardness, while for fast reactors operating on
uranium fuel this amount is close to the quantity of 232U obtained in reactors of water-cooled-water-moderated
type with 3.6% enrichment.. The comparison is made for the same 235U.burnup depth, and the difference in
effective cross sections of the reaction (n, 2n) is disregarded.
To determine the absolute amount of 232U accumulation, it is necessary to take account of the reaction
(n, 2n).
1. NRB-76 Radiation-Safety Standards [in Russian], Atomizdat, Moscow (1978).
2. A. D. Galanin, Theory of Thermal-Neutron Nuclear Reactors [in Russian], Atomizdat, Moscow (1959).
3. A. K. Kruglov and A. P. Rudik, Artificial Isotopes and Methods of Calculating Their Formation in
Nuclear Reactors [in Russian], Atomizdat., Moscow (1977);
4. P. N. Alekseev, S. M. Zaritskii, and 0. M. Kovalevich, in: Nuclear-Reactor Physics [in Russian],
No. 6, Atomizdat, Moscow (1978).
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5. L. P. Abagyan et al., Group Constants for Nuclear-Reactor Calculations [in Russian], Atomizdat,
Moscow (1964).
6. L. P. Abagyan and V. M. Murogov, in: Bulletin of the Nuclear-Data Information Center [in Russian],
No. 5, Atomizdat, Moscow (1968).
A. I. Klemin and E. F. Polyakov UDC 621.039.5.58
In 1978 the first specialized technical manual "Technique of Calculating the Structural Reliability of an
Atomic Power, Plant and Its Systems in the Design Stage was developed." The present article contains informa-
tion about the main characteristics and capabilities of the manual.
General Propositions. This manual is intended for calculations, during the design stage, of the indices
of structural reliability of a unit of an atomic power plant, and its parts and separate systems, including the
safety system. Structural reliability is construed as the structural reliability of the system of the atomic
power plant unit, its parts or systems with given reliability indices for the component elements, known func-
tional relations between them, and a strategy adopted for routine maintenance. The manual gives recommen-
dations concerning the calculations of the reliability of such specific systems as the reactor control and safety
system (CSS), the system of instrumentation and automatic control (SIAC), and safety systems.
The manual is intended for atomic power plants with the following principal features:
maintenance of its complete capability to operate despite malfunctions of a separate piece of equipment
as the result of redundancy;
a capability to function despite malfunctions of several pieces of equipment at power levels below the
nominal value Nn;
presence of blocks of elements of one type, constituting a structure of the "m out of n" type;
the use of the atomic power plant at various power levels (this is particularly true of atomic power
plants according to a variable load schedule);
performance of regular routine maintenance during operation;
a capability of operation in a basic regimen or according to a variable load schedule.
Underlying the manual are analytic methods of the modern theory of reliability with the use of the tech-
nique of minimum cross sections of complex systems [1, 21. Calculations by the techniques of the manual
permit a quantitative evaluation of the level of structural reliability, to reveal the weak points, to choose
appropriate redundancy of the equipment, to distribute the requirements concerning the reliability of the
atomic power plant over the component elements by means of variation calculation (in particular, to deter-
mine the reliability requirements pertaining to the component equipment), to make comparative estimations
of the reliability of various variants of structural design of the atomic power plant, etc.
To take account of the internal and external factors which affect the value of the atomic plant's power,
in a reliability analysis it is necessary to introduce the concept of available and required power, Na(t) and
Nr(t), respectively. The available power is the highest value of the power, determined by the totality of states
of all elements of the equipment, which can be delivered by the atomic power plant at a given moment of time.
The required power is the value of power which is necessary at a given moment of time and is determined by
the demands of the system external to the atomic power plant.
For an atomic power plant as a complex system with more than two possible states, the manual intro-
duces the concept of efficient and inefficient states, Na(t) ? N and Na(t) < Ns, respectively, in relation to a
concrete power level. As a concrete set of discrete power levels the manual considers the nominal level Nn,
the minimum level Nm # 0 below which the power plant is not operated, as well as a number of intermediate
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 70-73, February, 1980. Original article sub-
mitted May 28, 1979.
0038-531X/80/4802-0075 $07.50 ?1980 Plenum Publishing Corporation 75
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levels lying in the interval [Nm, Na], in which the atomic power plant can either operate in the event of the
malfunction of a separate piece of equipment or should operate in accordance with a given load schedule Nr(t).
In the calculation of the reliability of atomic power plants operating in the basic regimen, Nr(t) Nn, a
distinction is made between total and partial malfunctions in relation to set power levels. In the reliability
calculation for atomic power plants operating according to a variable load schedule malfunctions are con-
sidered in relation to a set power level Ns and malfunctions caused by the -required power surpassing the
available power, Nr > Na.
To calculate the reliability indices of any engineering system it is necessary to formulate the conditions
for operational incapacity (or operational capacity). In the manual conditions of operational incapacity of
atomic power plants are formulated separately for each set power level Ns in the form of a matrix of critical
states of the atomic power plant. In this connection it is necessary that for each possible state of the plant the
value of the available power be found from the state of its elements and that the unoperational states be distin-
guished, i.e., states for which the available power is below the level considered, and it is further necessary
that critical states, i.e., those which are realized with the minimum number of malfunctioning units and ele-
ments in them, be selected from the set of unoperational states. In the case of a structure that is not made up
of blocks,* in order to obtain the complete set of critical states it is necessary to construct the appropriate
logical scheme, i.e., the "tree of malfunctions," and on the basis of an analysis of this scheme to distinguish
all the minimal sets of malfunctioning elements, critical groups of elements (CGE) for which malfunctions of
the plant occur. In this case the number of rows in the matrix corresponds to the number of CGE. The num-
ber of elements in each matrix row is equal to the number of elements in the plant. The elements in a CGE
are labeled by 1 and the other elements by 0.
In the case of a plant with a block structure the conditions for operational incapacity are more conve-
niently written by using the concept of the critical group of block states (CGBS). This concept presupposes
such a set of the minimum possible number of blocks of one-type elements (with a minimum number of mal-
functioning elements responsible for the state of the block) which corresponds to the nonoperational state of
the atomic power plant in relation to the set power level. In this case, the number of-columns in the matrix
of operational incapacity is equal to the number of blocks while the number of rows is equal to the set of
CGBS. In each matrix row the nonzero elements denote the number of malfunctioning elements in the blocks
in the concrete CGBS.
In turn, to isolate a CGBS from a CGE it is necessary to know the relation between the available power
and the state of the elements, this relation being given by the so-called state functions. The state function
fi(xj) of a block is the contribution of the j-th block (in fractions of the nominal power of the atomic power
plant) as a function of the number of malfunctioning elements in it while the remainder of the blocks are in
good working order. The most general form in which the state functions are given is tabular. For convenience
in analysis, in accordance with the functional purpose and the structure of the atomic power plant, the blocks
of one-type elements, constituting a structure of the "m out of n" type, are combined into complexes (steam-
generation loop, steam-piping complex, etc.).
The state functions of each complex are expressed in terms of the state functions of the blocks compris-
ing that complex. This relation cannot in general be written in analytic form and is given with allowance for
the recommendations in the manual, e, g., for complexes consisting of series-connected blocks,
k (~(k) (k) ~k~l?
qk (f ikI, ... + f] , ?. ? + / "~) = mm ( l , ? , f) + + !!r
Once state functions have been assigned for the blocks and complexes for the atomic power plant, the
state function of the power plant is assigned, representing the dependence of the allowable power (as a fraction
of the nominal) on the state of the complexes, -
Np (VI, Viz, ? Y'M)
The following data are necessary for calculating the reliability indices of an atomic power plant:
*If the plant does not contain blocks of single-type elements forming a system of the "m out of n" type.
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a) complete sets of CGE or CGBS are given according to the conditions of operational incapacity;
b) data on the reliability of elements can be presented in two ways: by giving the distribution (density)
laws of the time f(t) of malfunction-free operation and the settling time g(t) of the element or by giving the
operational readiness kr(t) and the parameter w(t) of the flux of malfunctions of the element. The second way
is preferable if as an element we consider some subsystem with a complex structure, e.g., CSS, SIAC, whose
malfunctions could result in a change in the available power. Recommendations concerning the calculation of
the indices for these systems are given in special sections of the manual;
c) the initial data concerning planned maintenance of the atomic power plant and its equipment are given
as the interval of time between running repairs and major overhauls of the atomic power plant and its equip-
ment, the average time lost for running and major repairs of an element, and data about the make-up of the
repair teams;
d) the manual considers two possible ways of giving the regimen for the required power: probabilistic
and deterministic. The first is characterized by an average time for maintaining the power at a given level
and a matrix of transitions from level to level. In the second method a change in the required power is given
by a determinate diagram in power - time coordinates.
Nomenclature of Calculated Reliability Indices. The manual makes it possible to calculate a wide range
of reliability indices, reflecting individually or collectively the properties of an atomic power plant being free
of malfunctions or suitable for repairs. For atomic power plants operating in the basic regimen there are two
groups of reliability indices: indices concerning an individual set power level and "integral" indices charac-
terizing the reliability of the power plant with respect to all power levels. The first group comprises the
operational readiness kr(Ns, t) and the average operational readiness kr(Ns), the parameter w(Ns, t) of the
malfunction flux and the average parameter w(Ns) in the interval under consideration, the probability R(Ns, t)
of malfunction-free operation with respect to the given level, the mean operating time T(Ns) between malfunctions
for the given level. The second group comprises the following indices: the mean available power Na(t) and
the mean available energy production E(t) in some period of time, the mean total duration of repairs in some
period [0, t) of operation, the coefficient Rt.u. of technical utilization of the atomic power plant (ratio of mean
operating time of atomic power plant on power to sum of that time and the mean duration of planned and un-
planned repairs during that time), the coefficient of utilization of the installed capacity, etc.
For atomic power plants operating according to a variable load schedule other indices taken into con-
sideration are those which characterize the reliability with allowance for the given regimen of power variation,
i.e., taking account of malfunctions due to the available power dropping below the required level or by the re-
quired level rising above the available power. As a matter of convention we shall refer to malfunctions of this
kind as regimen malfunctions. In the manual calculations are also made of reliability indices with respect to
regimen malfunctions: the operational readiness and the mean operational readiness, the parameter wr of
malfunction flux and the mean parameter of malfunction flux, the probability of malfunction-free operation, the
power deficit, the mean energy production by the atomic power plant in a time t, the coefficient of delivery of
the required energy production, etc.
In a separate chapter the manual expounds a technique for calculating the indices of an atomic power
plant operating in the basic regimen by describing its functioning by a Markovian process. This is valid for
those cases in which the elements are not restored during the given interval (the laws of the distribution of the
time to malfunction of elements can be arbitrary) and if the distribution laws for the time to malfunction and
the times in the interval under consideration are exponential.
In all other cases it is expedient to use the Markovian model for preliminary calculations of the relia-
bility of an atomic power plant or its separate systems when the number of operational and nonoperational
states, associated with restorable or nonrestorable elements, is no more than 50 in each case, respectively
(in this case the computation time on a B9SM-6 computer does not exceed 30 min, as a rule).
Calculation of the reliability indices by using the theory of Markovian processes is performed in the fol-
lowing sequence: the diagram of the states of the atomic power plant (or the individual system considered) is
constructed, the systems of differential equations for the probabilities of the realization of all states found
from the diagram are written and solved, and the reliability indices are calculated.
In the final three chapters the manual gives the reliability techniques for individual systems of an atomic
power plant. In particular, Chapter 7 presents the technique for calculating the reliability index for the per-
formance of the following functions by the CSS: maintenance of the reactor power at a given level, switching
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of the reactor from one level to another, and emergency protection.
Chapter 8 gives the technique for estimating the reliability indices of the SIAC with allowance for the
functions of monitoring and recording of the principal technological parameters, signaling their deviation
beyond the allowable limits, and protection and control of the principal technological parameters of the pro-
Chapter 9 presents the methodological problems of calculation of the indices of safety systems with
account for the time taken to perform the given functions for various conditions and the rule for carrying out
maintenance during power operation of the reactor.
In the addenda the manual presents brief data concerning the reliability of the equipment of an atomic
power plant, the technique for estimating the reliability of piping, explanations pertaining to the construction
of the "tree of malfunctions," and some other reference material.
To facilitate calculations according to the technique outlined in the manual, special programs have been
written for the BESM-6 computer. The complete sets of CGE and CGBS for several typical structural schemes
of atomic power plants are determined according to the FORONS program. The BAST-1 program realizes the
technique of the manual for specifying the conditions of operational incapacity in terms of the CGE.
1. R. Barlow and F. Proschan, Mathematical Theory of Reliability, Wiley, New York (1965).
2. . W. Vesely, Nucl. Eng. Design, 13, No. 2, 337 (1970).
FUEL-ELEMENT SHELLS
V. I. Solyanyi and V. S. Yamnikov UDC 621.039.54:539.4
In power reactors with water cooling, as a rule, fuel-element rods with shells made from zirconium-
based alloys are used. For the design of these fuel elements, analysis of operational reliability, especially
in transient conditions, and the investigation of this reliability in possible emergency situations, it is neces-
sary to know the limiting strength characteristics of the shells in complex stress states over a broad tempera-
ture range.
The anisotropy of shells made from zirconium-based alloys is due, on the one hand, to the deformational
anisotropy produced in the process of manufacture and, on the other, to the initial anisotropy of the a-zir-
conium single crystal. The usual experimental determination of the limiting stresses and strains of aniso-
tropic shells in a complex stress state, by testing to failure under internal pressure and axial load, requires
complex apparatus and is very demanding. However, the required characteristics may be obtained by a theo-
retical consideration of the carrying capacity of a cylindrical anisotropic fuel-element shell on the basis of the
concept of plastic-deformation stability loss.
Since experimental verification has not confirmed [1] the possibility of using the Swift criterion modified
for the case of anisotropic materials, it was decided to adopt the statics criterion [2], according to which
plastic-deformation stability loss begins when a maximum of any external load is reached, and is charac-
terized by infinitesimally small increments of this load being equal to zero.
Formulation of the Problem and Its Solution
Consider the short-term deformation of a very plastic shell under a simple load, assuming that Hill's
theory of plastic anisotropy is valid [3], i.e., that the shell material has plastic orthogonal anisotropy (ortho-
tropy) and isotropic strengthening. Note that, in tubes used for fuel-element manufacture, the texture is such
that the normal to the basis plane lies in the cross-sectional plane. The anisotropy of such shells may be
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 73-76, February, 1980. Original article sub-
mitted May 18, 1977.
78 0038-531X/80/4802-0078 $07.50 ?1980 Plenum Publishing Corporation
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characterized by the factors Re and Rz, defined as the ratio of the transverse strains under uniaxial extension
of standard samples along the 0 and z axes, respectively, i.e., as
Ro = ez/sr; 11, == selr?
The basic relations of plasticity theory for. an orthotropic metal with a plane stress state, when the
principal axes of the stress tensor and the strain-increment tensor coincide, are written in the following form:
a) the relation between the stress and strain
ee r=_ [(II +.G)-Km] 6e;
Aa
Ez= el - [(H-1-P)rrt-1-H)ao;
Aa
E
[G + Fm] ae,
Aa
where m = vz/a6 = const (0 '-
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The parameters cp, ytp, x(p, xp, z, z' uniquely define the pair of points r, r' and may serve as the new
variables in place of x, y, z, x', y', z'.
It is expedient to introduce the notation
%=(z-a')I(xm- )-
Then in the new variables
P = [4n (xq,-_xp)z (1 +AE)]-' exp I - V 1.-{.- A to (x,,, Xw, y,,, ()1,
where -ro is the optical ray for the projection of the ray on the (x, y) plane. If -the-outer channel boundary is a
-circular-cylinder of radius p, then
n.(r') S2' = P$-ym (17)
P Vi+X2
Calculating the -transformation Jacobian for the new variables, it is found that
-in ]
P~~n?,t.t dx;Sdxw~dyzjdkp ~4?~V,I,. exp{-.V1 1- 2 O)4ni1 + ~s)l.St (18)
t? t 0 D -~,
and when I+ = const
P En ao
4nt=1+ dxwdy, S dcp S dA exp (-V1 } to n li+~s)3/?/St, (19)
r o o --
where st is the cross-sectional area of the region t.
In calculating integrals over.x(p and x(,, it is necessary to know the boundary of the region along the ray
(ytp, (p). The dependence of these boundaries on (y,0, V) completely corresponds to the channel outline. This
dependence for a discrete set of values of yt and tp may be stored in the computer memory and recalled for
recalculations connected with change in the physical properties of the region (change in neutron energy, tem-
perature of the medium, density, etc.).
In calculating the first-collision probability, integrals over xtp, x~, and a are reduced to tabular func-
tions of a single variable [3]. This is because To is a linear function of x4p and x
aTo 0 ro
- -ar, (20)
= =6t; ax-
so that, if xtp- and xtp+ are the boundaries of zone t, while x~- and x~+ are the boundaries of zone t', then
z `
~dx; ~ dx(p exp 1
{-jl1 } +X$)atot x
t? t
X ( exp [ - ,t ? X2 T. (x(,,+, x~-, qq,o, wP] + exp [ - V 1 -f- 2,2 To (xa-, xw+, y.v, (p)
-expI-V 1-I-XEdo(xm+, xw+, TD, (p)] -expTo(xw-, xm-, y?,P)]
Therefore, integrals over x(p, x~, and A reduce to the function
Q (v) = exp { - V 1 -+x2 v) an
(22)
It remains to perform numerical integration over y(p and q,, since v is a function of these variables. The
calculation of qt is analogous. Note only that the zones t and t' along the ray (y(p, gip) may be multiply connected
because of the channel symmetry. In this case, the formulas obtained are applicable for each combination in-
cluding a connected subregion of t and a connected subregion of t'. The final result is obtained by summing
similar expressions over all the possible combinations.
For arbitrary functions ty and f, not double but quadruple numerical-integration must be performed (the
integral over a may be tabulated as a function of To). However, if 0 and f are polynomials of (x, y), then'in
contrast to the case when zy = f = 1 all that is involved is an increase in the number of tabulated functions of v.
In the general case, a function of the following form is needed [4]
n/z
Q.(v) exp(-V1+-2"V) (1+X) m/2 exp
-n/2
V 1
cosa/cos"`?ada.
(23)
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Fig. 1. Symmetry-sector zones of region with
RBMK channel: 1-4) graphite; 5) zirconium;
6-10) water; 11, 12) uranium oxide.
In fact, the polynomial in (x, y) becomes, after transforming to the variables (x, y(p), a polynomial in
xq, with coefficients depending on y(p and tp. Therefore, it is sufficient to calculate the integral
xW dxp x~ dx, exp I 1+~Q X 'to) d) = .J dx; dx x; x,Q2 (TO);
t t
xq+
x.11 dx4 exp (-V 1 +T2 T.) 11+2,213/2 = dxg xOQ3(t0).
t xm-
Integration by parts using Eq. (20) and the relation
dQ(-)ldv= -Qm-~ (v)
allows the powers of x p and x~: to be reduced and, simultaneously, the order of the function Qm to be in-
creased, for example
x@r+ xW+ xq+ x,p+
J dx.p x"Q2 (T0) _ - 5 a dQ3 (TO) Q3 (TO) I +
f Q x~- tQ3 (TO)
xW_ xq,_ xq,_ xp_
Thus, Eqs. (24) and (25) may be reduced to a combination of functions Qm(v) with different m and different
arguments.
A simplified RBMK-channel geometry is shown in Fig. 1. The simplification is that the coating attached
to the fuel element 'is not assigned to a separate region, but is included with the uranium oxide. To the chan-
nel a graphite layer of thickness 4.6 cm is added. It is assumed that beyond the limits of this layer the neutron
distribution may be described within the framework of the small-group P, approximation, using the Maxwell
spectrum for the thermal group. The channel symmetry sector is divided into 12 zones. In each zone the func-
tions 0 and f are taken in the form of linear functions of (x, y)
f0t=1, fxt=x+Al(t), fut=y+A21(t)x+A22(t);
(27)
dot = B (t), ixt = fxt ? B1 (t), yt = f ytB2 (t).
(28)
The constants Al, A21, A22, B1, B2, B are found from the condition of mutual orthonormality of the functions
ftlt and Nt. For the other symmetry sectors, the functions take the same form in a coordinate system applied
TABLE 1. Cross Sections of Materials
Material)
Total
cross
Scattering
(cross sec-
oral
. Materia ross sec-
catterin
cross sec-
cross
section
:tio min
tion. min
min
n
C I
0,03809
I0,03809
U02 10,06114
0,03659
Zr
0,03485
0,03400
H2O 0,21318
0,21243
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Fig. 2. Dependence of flux 4) on the radius in the cross
sections cp = 7x/12 (a) and cp = 0 W. The horizontal bars
correspond to the mean values of the flux over the zone.
at some angle to the initial system. On passing to the initial system, the appropriate coordinate transforma-
tion is performed.
Solutions of Eq. (1) were obtained by the scheme outlined in two approximations: by the usual first-
collision method and the'improved method with the polynomials in Eqs. (27) and (28). The cross sections and
the results of the calculations are shown in Tables 1 and 2 and Fig. 2. Comparison with the Monte Carlo
method shows that the improved method is of high accuracy (Table 2). It is also of interest to compare the
results with the usual first-collision method but with division into 16 zones (Table 2). The error of the usual
method in calculating 4' with division into 12 zones amounts to 27.3%, the corresponding figure for the im-
proved method being 3%0. The difference in computation times is a factor of 4.5, whereas the number of un-
knowns (matrix elements) is increased by a factor of 9. It is seen in Fig. 2 that the linear functions fxt and
fyt reduce the discontinuities of the flux -4' at the zone boundaries, but cannot eliminate them entirely.
It must be noted that division of the RBMK-channel symmetry sector into 12 zones with linear functions
fit is the optimum. A smaller number of layers can probably be introduced in the graphite layer. But
TABLE 2. Calculation of 4. in RBMK Channel by Different Methods
Monte Carlo method
Division into 12 zones
Division into 16 zones
Linear approximation
one
No.
Material
0.103
O. SOS
x?103
m- 'MC
mMC ?100%
.5 103 I
m-m MC
m MC ?100%
x?103
m-AMC
mMC ?100%
1
C
6,491
0,006
6,424
-1,0
6,445
-0,7
6,454
-0,6
2
C
6,059
0,008
5,971
-0,2
6,005
-0,9
5,998
-1,0
3
C
5,577
0,010
5,496
-1,4
5,542
-0,6
5,530
-0,8
4
C
5,066
0,011
4,974
-1,8
5,037
-0,6
5,023
-0,8
5
Zr
4,592
0,012
4,484
=2,4
4,566
-0,7
4,556
-0,8
6
Hs0
4,000
0,011
3,867
-3,3
3,965
-0',9
3,986
-1,4
7
H20
2,594
0,009
2,646
+2,0
2,631
+1,4
2,570
-0,9
11
UOs
2,348
0,008
.2,418
+3,0
2,395
+2,0
2,362
+1,4
8
H30
1,543
0,010
1,810
+17,3
1,593
+3,2
1,516
-1,7
12
U0,
1,328
0,009
1,633
?23,0
1,417
+6,7
1,320
-0,6
9
H2O
1,298
0,016
1,651
+27,2
1,365
+5,2
1,267
-3,6
10
Zr
1,316
0,018
1,626.
+23,6
1,368
+4,0
1,278
-2,9
92
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additional division into small zones may perhaps be worthwhile between the,series of fuel elements. On the
other hand, the addition of quadratic terms in certain zones may eliminate the need to divide them.
CONCLUSIONS
The generalized first-collision method may prove useful in calculating channels with complicated geom-
etry - e. g., RBMK channels. Then polynomials of different order may be used in different zones, taking into
account, where necessary, the curvature of the neutron distribution by means of quadratic terms.
It remains to thank Yu. P. Elagina, A. S. Il'yashenko, and V. A. Lyul'ke for generally offering the pos-
sibility of comparing the results of the present work with results obtained with their program.
1. G. I. Marchuk and V. I. Lebedev, Numerical Methods in Neutron-Transfer Theory [in Russian], Atom-
izdat, Moscow (1971).
2. T. Taxeda and T. Sekiya, J. Nucl. Sci. Technol., 8, No. 12, 663 (1971).
3. J. Askew, E. Fayers, and P. Kemshell, J. Brit. Nucl. Energy Soc., 5, No. 4, 564 (1966).
4. W. Bikley and J. Nayler, Phil. Mag., 20, 343 (1935).
COST OPTIMIZATION IN CONNECTION WITH THE
ACCUMULATION OF ISOTOPES OF THE
TRANSURANIUM ELEMENTS
S. A. Nemirovskaya and A.. P. Rudik UDC 621.039.554
A system of equations has been proposed in [1] which describes cost redistribution in connection with the
accumulation of isotopes of transuranium elements. The purpose of this article is to develop a formalism
which permits optimizing the costs in connection with the accumulation of the isotopes of transuranium ele-
ments if the redistribution of these costs is described by the system of equations from [1].
The equations which describe depletion of isotopes are of standard form (e. g., see [2, 3]). Let us intro-
duce the following notation: x(i)(t), number of nuclei of isotope i at time t; Ei, depletion rate of isotope i;
4-1, formation rate of isotope i due to the depletion of isotope i - 1; Xi, decay constant of isotope i; and
al-1, decay constant of isotope i - 1 with the formation of isotope i. Then
dx(t)
_TF
with i = 1, ... , n, where n is the number of isotopes in question; E? _ A, = 0.
If we arbitrarily separate (as has been done,. e. g., in [2, 3]) the neutron flux density into a thermal part
U and a resonant part w, then one can represent the reaction rate E in the form
E = oU -I- I ~ (x) (0, (2)
where v and I are the thermal cross section and the resonant integral, and the factor takes account of block-
ing of the resonant integral for the isotope x to which E corresponds.
Equations Which Describe Cost Redistribution. Let
Y(h) (t) =Ck-n (t)'x(h n) (t), k=n-}-1, ..., 2n (3)
be the cost of all the nuclei of the isotope k - n at time t [then Ck_n(t) is the cost of a single nucleus of iso-
tope k - n], and correspondingly let V be the average cost of a single neutron. According to [1], the following
system of equations occurs:
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 84-86, February, 1980. Original article sub-
mitted March 26, 1979.
0038-531X/80/4802-0093$07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
dy(k) y(h) E Vx(k-n-1)- (h)
dt + k-n-1) y( k-n k-n) f k-n-1 g
If we use Eq. (2) for Ek_n_1, the product Ek-n-1V is transformed to the form
Ek_n_1V = ck-n-1VUU+Ik-n-lbV o , - _
where VU and V. are the costs of thermal and resonant neutrons, respectively.
Functional to be Analyzed. The systems of equations (1) and (4) should be supplemented with a func-
tional zI to be -analyzed of the form
J = f f(o) dt.
0
Here T is the irradiation time, and the function f(?) depends on x(1) (i = 1, ... , n, y(k), k = n + 1, ... , 2n) and
the reaction rate.
Conjugate Functions and the Hamiltonian. Let us denote the conjugate functions in x(1) by 41i and those
in y(k) by Xk. Then the Hamiltonian ' of the systems of Eqs. (1) and (4) supplemented by the functional (6)
is written in the form
cy~ 'pot') n ,I, 2n
5 = + Wit') + `J xkg(k).
1=1 k=n+1
where 00 is a nonpositive-definite constant and the conjugate functions Oi and Xk satisfy the equations
dips-_ ON dXk-_aCW
at axi ' at ayk .
If the reaction rate E has the form (2), Eqs. (8) are transformed to the form
dipi af(0) a (MIX0)) ,~I' a (Ei+1x(i)) X (i+n) 8Ei (i+n) 82i +V a (Elx(t))
dt - - Po ax(i) +'(I>i ax(i) Y'i+1ax(i) + i+ny 8s(i)-Xi+n+l (y ax(t) ax(i)
dxk h al(O)
dt (xk-xk+l)(Ik-n+%k-n)-Vu ay(k)
and the derivatives of the reaction rate with respect to the variable x are not equal to zero by virtue of the
dependence of the blocking factor t on x.
Boundary Conditions. The systems of equations for the phase variables (1) and (4) and for their conju-
gate functions (8) or (9) should be supplemented with boundary conditions. All the quantities x(i)(0) and y(k)(0)
are specified at the start of irradiation at t = 0. At the end of the irradiation at t = T usually neither x(i)(T)
nor y(k)(T) are specified* and the boundary conditions are
*1 (T)=xk(T)=0; i=1, ..., n; k=n+l, ..., 2n. (10)
Perturbation Theory. Let the reaction rate be of the form (2) and let a be one of the functions U, w,
VU, or V. or one of the parameters a or I. Then if the systems of equations (1), (4), and (9) are solved for
some value a (t) and the corresponding functional J is determined from Eq. (4), the variation 6J is expressed
[4] in the following way in terms of the variation 6a:
T (11)
SJ = OCT Sac (t) dt,
with 00 = -1. 0
Control in the Problems. We will assume that E has the form (2).. Then U(t) or w(t) can figure as the
control in optimization problems. It is necessary to find such temporal variations of the function U(t) or w(t)
(which one is immaterial) which would result in a minimum of the functional J. It turns out [5] that the neces-
sary condition for this to occur is the satisfaction of the maximum principle, which requires that the Hamil-
tonian as the control function attains a maximum. For the class of problems under discussion the Hamiltonian
(7) is linear with respect to control and can be represented in the form
If some of the x(i)(T) and y(k)(T) are specified, the transversality condition (10) is modified in a standard way
(e. g., see [41).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 1. Main Physical Constants Entering
into the Reaction Rate
18
90
?12
1100
2000
720
Index ?I o,b I i.?b
1-. 2
2-3
18
90'
1100
2000
where the functions F1, F2, and F3 depend only on the phase variables and the conjugate functions but do not
depend on the controls. Therefore, satisfaction of the maximum principle requires either sign determinacy
of the switching functions F2 and F3 for the limiting values of the corresponding controls or - in the case of
special controls [6] - equating the switching functions to zero.
Two Types of Optimization Problems. The following types are evidently of greatest interest.
1. Minimization of costs for the production of a given isotope. In this case J(T) = y(k)(T) and the func-
tion f(0) can be selected in the form f(0) = g(k).
2. Minimization of the costs for the production of the sum of all the isotopes appearing in Eq. (1). Then
2n n
d
dtI Y(h) I'X(b
k=n+1 i=1
follows* from the system (4). Thus minimization of the costs for the production of the sum of all the isotopes
is determined only by the total number of absorbed neutrons. In this case
n
i=1
and consequently it is not necessary to discuss system (4) for solution of the optimization problem.
General Nature of the Solution of Eqs. (1), (4), and (9). Let us discuss the simplest example which has
a purely methodological meaning. The most characteristic features of the solution of the systems of Eqs. (1),
(4), and (9) will be clear from an analysis of it. Let us take 242Pu as the initial. isotope i 1. Then the iso-
topes 243Am and 244Cm will correspond to the indices i = 2 and i = 3. The main physical constants entering into
the reaction rate are given in Table 1.
To simplify matters we have assumed all t = 1. A specially written computer program has been used
for the solution of the systems of Eqs. (1), (4), and (9). The calculations were carried out with U = 1014 neu-
trons/cm2 ? see, w = 0.3 neutrons/cm2 ? see, and T = 1.2 years. We adopted x(1)(0) = 1, x(2)(0)? = x(3)(0) _
0 as the initial conditions for x(1)(0). The following alternative initial conditions were considered for y(k)(0)
(with VU=Vw=1):
1) y`') (0) = y(s) (0) = y`ei (0) = 0;
2) y") (0) (0) = y`6) (0) = 0;
3) y(a) (0) = 2; y(5) (0) = yO (0) =01
J = y(s)(T) was selected as the functional to be analyzed. The dependences X(3) (t) and y(s)(t) and the switching
functions F2(t) and F3(t) are given in Table 2 for the corresponding alternatives. The results obtained permit
formulating the following conclusions within the framework of the example considered.
In the first place it is completely natural that both y(6)(t) and y(6)/x(3) increase as y()(0) increases.
However, the ratio [y(3)(t)x(3)(O)]/[y(6)(0)x(3)(t)] is, within the limits of computational error, a universal func-
tion of t, i.e., it does not depend on the alternative number.
In the second place, the temporal dependence of the switching functions F1 and F2 indicates that in order
to reduce y(6)(T) the flux of thermal neutrons should be less at the end of the irradiation than at the start, and
the flux of resonant neutrons should be less at the start of the irradiation than at the end. We note the uni-
versality of the functions F2(t)/F2(0) and F3(t)/F3(0).
* If the chain (1) is being considered for n isotopes, it is necessary to discard the term (En +;kn)y(211) in Eq.
(4) for y(21). We have the situation in mind in which we are speaking of a certain logical inconclusive-
ness of [1].
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 2. Results of the Calculation of Alternatives 1-3
Temporal
t, years
Alternative
function
0,0
0,2
0,4
0,6
0,8
1,0 , 1,2
For all
I
x(3) (t)
I
0,000
I
0,037
0,113
0,197
0,271
0,330
0,371
alternati ves
1
Y(6)g)
0,000
0,077
0,251
0,463
0,680
0,884
1,068
(3
y(e)i
2,000
2,081
2,221
2,350
2,509
2,679
2,879
F2 (t)
-0,045
-0,051
-0,058
-0,068
-0,080
-0,094
-0,112
F3 (t)
-2,723
-2,703
-2,677
-2,645
-2,606
-2,557
-2,497
2
y(')(t)
0,000
0,116
0,376
0,694
1,020
1,327
1,602
y(')/x(3)
3,000
3,135
3,327
3,523
3,764
4,021
4,318
F2(t)
-0,067
-0,076
-0,088
-0,102
-0,119
-0,141
-0,169
F3 (t)
-4,084
-4,053
-4,015
-3,967
-3,309
-3,836
-3,745
3
y~s> (t)
0,000
0,154
0,502
0,926
1,360
1,769
2,137
y(e)/xc3>
4,000
4,162
4,442
4,700
5;018
5,361
5,760
F2 (t)
-0,089
-0,101
-0,117
-0,136
-0,159
-0,188
-0,225
F3(t)
-5,445
-5,404
-5,353
-5,290
-5,211
-5,114
-4,993
The universal nature indicated above for the functions (y-(6)(t)X(3)(0)]/[y(I){0)X(l)(t)l, F2(t)/F2(0), and
F3(t)/F3(0) is a rigorous law which is due to the form of Eqs. (1) and (4) and the initial conditions on x(1)(0)
and'y (k) (0)
In the third place, given the very same neutron flux.alternatives, the larger the absolute value of the
variation of of the functional is, the higher is the cost of the target material.
1. Yu.. P. Kormushkin, A. V. Klinov, and Yu. G. Toporov, At. Energ., 41, No. 2, 102 (1976).
2. A. D. Galanin, The Theory of Nuclear Reactors Operating on Thermal Neutrons. [in,Russian], Atomizdat,
Moscow (1959).
3. A. K. Kruglov and A. P. Rudik, Artificial Isotopes and a Method for Calculation of Their Formation in
Nuclear Reactors [in Russian], Atomizdat, Moscow (1977).
4. A. P. Rudik, Nuclear Reactors and Pontryagin's Maximum Principle [in Russian], Atomizdat, Moscow
(1971).
5. ' A. S. Pontryagin et al., The Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz,
.Moscow (1965).
6., R. Gabasov. and F. M. Kirillova, Special Optimal Controls [in Russian], Nauka, Moscow (1973).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
MEASUREMENT OF THE CROSS SECTIONS FOR RADIATIVE
CAPTURE OF NEUTRONS BY 238U AND "'Au RELATIVE TO
THE CROSS SECTION FOR THE ELASTIC SCATTERING OF
NEUTRONS BY PROTONS
A. N. Davletshin, S. V. Tikhonov, UDC 539.125.5
A. 0. Tipunkov, and V. A. Tolstikov
The study of the cross sections for the radiative capture of fast neutrons by 238U and 197Au is of interest
mainly because of the practical requirements of fast reactor calculations involving the breeding of nuclear
fuel. The differences in the results obtained by various experimenters who have investigated these cross sec-
tions are still rather large. Most of the measurements have been made relative to standard cross sections
which have a complex structure, and this can introduce further errors. In order to obtain more accurate ex-
perimental data we have measured the 238U and 197Au capture cross sections relative to the smoothly varying
n-p scattering cross section for neutron energies from 0.35 to 1.4 MeV.
Bombardment of Samples. Samples were bombarded at an electrostatic accelerator using the T(p, n)3He
and 7Li(p, n)7Be reactions. Figure 1 shows schematically the geometry of the placement of the sample and the
hydrogen-filled counter during bombardment. The sample and counter were located at an angle of 0? with re-
spect to the proton beam.
The neutron flux density at the center of the sample is (3-6) ? 106 neutrons/cm2 ? sec; the relative effi-
ciency (the ratio of the number of interactions to the number of incident neutrons) for radiative capture by
samples of U308 is (0.5-0.9) -10-2% , and for Au samples (0.8-2) ? 10-2%. The attenuation of the neutron beam
by the sample in the container at energies between. 350 and 1400 keV is 3.5-9%. The construction of the coun-
ters is described in [1]. The counters are filled with pure hydrogen or methane.
The cross section for the radiative capture of neutrons of energy En was calculated from the expres-
5 6 6
Fig. 1. Geometry of:' a) measurements of neutron
flux; b) bombardment of samples; c) structure of
assembly for bombarding samples; 1) target; 2)
location of shadow cone; 3) H-counter; 4) sample;
5) target support; 6) sample holder; 7) cadmium
container; 8) sample.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 87-91, February, 1980. Original article sub-
mitted April 23, 1979.
0038-531X/80/4802-0097$07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
= E N!1 f(7~, t) nn.coVcoCco6 E. (1)
Q (
rod n)_ i1Nin Cm mn sq Csa co( n)
Here t is the efficiency of the Ge(Li) detector; f(A, t), time factor; nnco+ number of hydrogen nuclei per cm3;
Vco, sensitive volume of the counter; mn sa, number of activated nuclei in the sample, oco(En), .n- p scat-
tering cross section [2]; arad(En), cross section for the radiative capture of neutrons; and C(~, correction
for the time variation of the neutron source strength.
The geometric factors for the counter and sample are of identical form:
vco
co= Vco1zncooc
vsa
Gsa__ mn. asa
In these expressions v is the absolute efficiency of the corresponding detector. In both cases v is calculated
for an isotropic disk source of neutrons and a uniform cylindrical detector located coaxially [3].
The quantities Nyo and Nin in (1) are calculated from the expressions
NvAv
N
(4)
vo= T
dr
Neis (x)
=
N
(5)
TdpA1, (x) Knep (x), -
in
where Ny is the area of the total absorption peak; Tdr, correction for the dead time of the analyzer recording
the y spectrum; Neis(x), area of the recoil proton spectrum (RPS) for the threshold x = Ep/En [Ep, recoil
proton energy; i.e., Neis(x), experimental integral RPS]; and Tdp, correction for the dead time of the ana-
lyzer recording the RPS; Kncp(), integral RPS calculated by the Monte Carlo method for the chosen value of
the threshold [4]. Equation (5) can also be written for the differential RPS. Problems related to the calcula-
tion of Nin are discussed in detail in [5].
It is important that effects in the sample N,yo and. in, the counter Nin in Eq. (1) are produced by nearly
monoenergetic neutrons. This condition is not satisfied in the bombardment of samples. The dependence of
the response function on neutron energy is different for sample and counter, and therefore corrections for
background effects must be introduced into the experimental results so that ultimately the values obtained cor-
respond only to neutrons incident on the detector directly from the target.
The measured value of the background correction Ay to the activity of a sample takes account of the ef-
fect of the room and the finite mass of the sample, container, target support, and sample holder. In addition,
a correction is introduced for the anisotropy of the neutron source, and therefore the spread of neutron ener-
gies indicated in Tables 1 and 2 is produced by the thick target only. This correction is discussed in detail
in [6].
The background correction A, (x) in the experimental RPS includes the effect of the room, the walls and
ends of the counter, the target support and sample holder, and the attenuation of the neutron beam by the layer
TABLE 1. Cross Sections for the Radiative Capture of Neutrons by 138U
N
t
n
Radiative ca
ture
Hydrogen-filled counter
Ge(Li) detector
eu
ro
energy, keV
p
cross section, mb
type
volume. cm
type
p10 N/
I
2
RPS shape
volume,
3
eff.,o/
-
m
parameter
cm
597+16
127,1?3,9 %
1 -1
112,2
H2
1,65
0,487
32
1,66?0,03
590+23
130,8?3,6 %
K-1
99,3
H2
2,03
0,558
32
1,66?0,03
792?22
135,7+4,2 %
K-1
99,3
H2
2,03
0,497
32
1,66?0,03
1026?22
124,2?3,6 %
K-1
99,3
H2
2,03
0,411
32
1,66?0,03
352?25
117,4?3,1 %
K-2
179,7
H2
1,86
0,632
55
70
0
1,98?094
98+0
?4
1
700?41
128,8?2,8 %
K-2
179,7
H2
1,86
0,
3
7
,0
,
1192+33
87,4?3,1 %
K-2
179,7
H2
1,86
0,375
70
1,98?0,04
348?23
119,9?2,8 %
K-1
99,3.
H2
0,90
0,586
50
1,87?0,02
348?15
122,3?3,0 %
K-1
99,3
H2
0,90
0,586
50
1,87?0,02
603+36
114,6+2,7 %
K-1
99,3
H2
0,90
0,456
50
1,87?0,02
1400?31
69,6?2,3 %
K-15
255,0
CH4
3,04
0,632
50
1,87+0,02
1400+31
75,9?2,7 %
K-18
177,8
H2
2,60
0,392
50
1,87+_0,02
350?24
12i,8?2,8 %
K-1
99,3
H,
0,90
0,586
50
1,87?0,02
600+22
114,0?2,5 %
K-15
255,0
CH4
3,04
0,677
50
1,87?0,02
1400?23
71,7?2,5 %
K-15
255,0
CH4
3,04
0,632
50
1,87+0,02
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 2. Cross Sections for the Radiative Capture of Neutrons by 197Au
Radiative
Hydrog
en-filled counter
Ge(Li) detector
Neutron
energy keV
ca lure cross
section, mb
type
olume.
cm3
gas 1
I ressure,
105N/m2
RPS shape
paramete
volume.
cm3
eff.,oi
n,V(U)
as (Au)
597+16
126,6?3,2%
1-1
112,2
H2
1,65
0,487
32
2,24?0,007
1,004+3,8%
590+23
131,53,5%
K-1
99,3
H2
2,03
0,558
32
2,24?0,007
0,995?3,9%
352?19
212,7?3,1%
K-2
179,7
H2
1,86
0,632
70
3,01?0,06
0,552?3,9%
700?41
121,0?2,9%
K-2
179,7
H2
1,86
0,553
70
3,01?0,06
1,060+3,4%
1188?38
74,8?3,4%
H-2
179,7
H21
1,86
0,375
70
3,01?0,06
1,168?3,7%
348?23
200,8?2,7%
H-1
99,3
H2
0,90
0,586
50
2,71+0,007
0,597?3,3%
348?15
223,0?2,7%
H-1
99,3
H,
0,90
0,586
50
2,71?0,007
0,548?3,4%
1400+27
67,7?2,7%
11-15
255,0
CH4
3,04
0,632
50
2,71?0,007
1,028?3,0%
of air, This correction was measured for each position of the counter and neutron energy in the form of a
correction spectrum for the differential or integral RPS. Figure 2 shows the measured values of Ae(x) for
several values of the neutron energy. The experimental absolute value of the correction is normalized to the
RPS corresponding to neutrons incident on the counter directly from the target. The data on Fig. 2 refers to
a K-2 counter (cf. Tables 1 and 2) located 70 cm from the target.
Efficiency of Ge(Li) Detector. Samples of the same composition as those used in measurements at the
electrostatic accelerator and two foils were bombarded simultaneously by a beam of thermal neutrons (Fig. 3).'
If the thermal neutron flux density is constant through the sample and foil, the efficiency can be calculated
from the expression
71= Am 101, (6)
where M and m are,. respectively, the masses of the sample and foil.
The activity A of the sample was measured with a Ge(Li) detector by the total energy absorption peaks
Ey = 74.7 keV for U308 samples and 412 keV for gold samples. The absolute activity a of a foil was deter-
mined by the 47r/3 - y coincidence method.
For the arrangement shown in Fig. 3 the flux densities qP1, cp, and cy2 are not identical. If we denote by
C2 the transmission of the arrangement, it can be shown that
n = Tli/C = C71,, (7)
where 711 and 712 are the efficiencies calculated for foils 1 and 2 by Eq. (6).
Consequently, from the results of bombarding the two foils and the sample, the efficiency of the Ge(Li)
detector can be determined from the expression
I=vr)irl2-
At
494
0,90
0,88
0,98
0,94
0,90
?
?
I
Fig. 2. Background correction
A8(x) for neutron energies of: a)
350; b) 700; c) 1200 keV.
Fig. 3. Bombardment of samples
by a beam- of thermal neutrons:
1) neutrons; 2) foil; 3) sample;
4) container.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 3. Components of Total Random Error
of 238U Cross section
Qualit
Error, %
y
Time factor t (X, t)
0,2
0,2
Correction for coast 'neutron source
strength, C
0,1
0,1
P
No. of hydrogen nuclei/cm3, nnco
0,2
0,2
Vol. of counter, Vco
0,6
0,6
No. of nuclei in sample, mnsa
0,1
0,1
Geometric factor for counter,
Gco
0,3
0,3
Geometric factor for sample. Gsa
0,6
0,6
np scatterin cross section, o co
1,0
1,0
Eff. of Ge(L[) detector n
0,9
0,9
Total statistical error of calc. and
expt.
0,6
0,6
Parameters of calc.
0,5
1,0
Bkgd. correction for counter AE(x)
0,6
0,9
Bkgd. correction for sample, A
2,0
1,4
Y
Total random error
2,8
2,7
The absolute activity of,a U308 foil was measured by the method of 47r/3-y coincidences with a subse-
.._quent correction for the counting efficiency in the (3 channel for sources of finite thickness [7]. The absolute
activity of a gold foil was found by the method of double linear extrapolation of the 0 counts to a value of the
counting efficiency equal to unity [8]. The area of a total absorption peak in the measurement of the activity
of samples by the Ge(Li) detector was determined by the trapezoid method [9].
Experimental Results. The measured values of any for 238U are listed in Table 1, and those for 197Au
in Table 2. Preliminary values of some of these quantities were published in [10, 111. Subsequently, back-
ground corrections to the activity of the samples were refined, and the present paper reports the final results.
The errors indicated in the tables correspond to a 68% confidence interval.
The tables list information on the detectors employed. The use of various Ge(Li) detectors, hydrogen-
filled counters, the change of composition and pressure of the filler gas, decrease the unknown systematic
error connected with the parameters of these detectors and the whole set of our data introduced in using them
to estimate radiative capture cross sections. The possible systematic errors of the background correction to
the activity at En = 350 keV are from -2 to +3% for 197Au, and from -1.5 to +2% for 238U; for En = 1400 keV
the limits of the ranges are approximately half as large.
In using hydrogen-filled counters it was not required that the shape of the RPS be close to that of a uni-
form distribution. Therefore, in using a counter over a wide range of energy the RPS differed strongly from
a uniform distribution. Tables 1 and 2.list values of the RPS shape parameter for each counter. This param-
eter is the value of the calculated integral RPS ap(x = 0.3) for the neutron energy under consideration. For a
uniform distribution of the pulse amplitudes from x = 0 to x = 1, ap(x = 0.3) = 0.7.
Table 3 lists the random errors of all the factors in (1) for the end points of the energy range. Informa-
tion is also presented on the random errors in a somewhat different form: for En = 350 keV the error of all
quantities related to the measurement of activity is 2.4%, and for quantities referring to the hydrogen-filled
counter, 1.6%. For En = 1400 keV these errors are 1.9 and 1.9%, respectively.
Discussion of Results and Conclusions. Figure 4a, b shows the results of our measurements with indi-
cated random errors and the energy spread of the bombarding neutrons, and also our estimates of the radia-
tive capture cross sections for 238U [12] and 197Au [13] and estimates from ENDF/B IV [2].
Our results for 238U are in better agreement with estimates in [12] than with those in [2], and those for
197Au differ from very close estimates in [13] and [2]. At the lower boundary of the energy range our results
are higher than the estimated values by (3 ? 2)% on the average for 238U, and by (15 t 3)% for 197Au. For En =
1.4 MeV our results are lower by (7 ? 2)% on the average for 238U and by (9 ? 5)% for 197Au. For En 1 MeV
our data for both elements on the average agree with estimates in [2, 12, 131. Thus, for both elements the
energy dependence of our data is different from that for the estimated data. We note that approximately the
same energy dependence of ony for 197Au was obtained in [14] by the time-of-flight method.
This conclusion is certain. All our measured values of cross sections differ from one another in at
least one of the experimental conditions: the neutron energy, the Ge (Li) detector, the counter and the pressure
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
t 150
lO 50
Fig. 4. Cross section for the radiative capture of neu-
trons by: a) 238U; b) 197Au, and the ratio of any for
238U to any for 197Au; a, b, 0) our data; 0) estimated
data from [12] for 238U and [13] for 197Au; -) estimated
from [12]; - - -) mean-square spread of estimated
experimental data in [13] equal to 6.5%; c, 0) our data,
^) ratio calculated from data in [2]; - - -) data from
[15]; -) data from [14].
of the gas in it, the target support. The mean-square spread of the average values at values of the energy for
which experiments are repeated is 4.5%. The average random error of our data is 3.1%. The difference be-
tween these estimates of random errors clearly arises from systematic errors in the cross sections intro-
duced by the values of 17, AE(x), nn co, and Vco in Eq. (1).
Using the measured cross sections, the ratio.of the radiative capture cross sections of uranium and
gold was calculated. The errors of quantities pertaining to the recoil proton counter do not enter into the
error of these ratios except statistically. Figure 4c shows our results and data from [2, 14, 151. The values
closest to our results were obtained from estimates in [2].
The necessity of reliable information on any for 238U requires further measurements by the procedure described
to decrease possible systematic errors of the results obtained. It is desirable to extend the energy range both
toward lower neutron energies by using y-ray discrimination, and toward higher energies by using methane-
and hydrogen-filled counters.
LITERATURE CITED
1. S. N. Baikalov, V. S. Korolev, and V. V. Chubinskii, in: Metrology of Neutron Radiation at Reactors
and Accelerators, Vol. 1, Proc. Second All-Union Conf. [in Russian], Moscow (1974), p. 58.
2. B. Maguro, ENDF/B IV Cross Section Measurement Standards, BNL-NCS-504464, August (1975).
3. N. A. Vartanov and P. S. Samoilov, Applied Gamma Spectrometry [in Russian], Atomizdat, Moscow
(1969).
4. A. N. Davletshin, V. P. Platonov, and V. A. Tolstikov, in: Nuclear Constants [in Russian], No. 9,
Atomizdat, Moscow (1972), p. 107.
5. A. N. Davletshin and V. A. Tolstikov, At. Energ., 42, 43 (1977).
6. A. N. Davletshin et at., At. Energ., 48, 113 (1980).
7. E. F. Garapov et at., Preprint FEI-501, Obninsk (1974).
8. H. Menke and J. Fahland, Standardization of Radionuclides, SM-79/18, Vienna (1967)..
9. IEEE Trans. Nucl. Sci., NS-19, No. 1, 155 (1972).
10. A. N. Davletshin, A. 0. Tipunkov, and V. A. Tolstikov, in: Neutron Physics Data of Third All
Union Conf. on Neutron Physics) [in Russian], Part 4, TsNllatominform, Moscow (1976), p. 109.
11. A. N. Davletshin et at., ibid., p. 99.
12. V. N. Vinogradov et at., in: Nuclear Physics Research in the USSR [in Russian], No. 22, Atomizdat,
Moscow (1976), p. 4.
13. V. N. Vinogradov et al., in: Neutron Physics (Data of Third All-Union Conf. on Neutron Physics) [in
Russian], Part 1, TsNllatominform, Moscow (1976), p. 165.
14. W. Poenitz, Nucl. Sci. Eng., 57, 300 (1975).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
15. R. Spenser and F. Keappeler, in: Proc. Fourth Conf. on Nuclear Cross Sections and Technology,
Vol. 2, Washington, March 3-7 (1975), p. 620.
SOLUBILITY OF NITROGEN IN WATER
Yu. A. Ka4aida, Yu. -D. Katkov,
V. A. Kuznetsov, A. Yu. La-sto.vt-sev,
A. P. Lastochkin, and V..-S. Sysoev
UDC 621.039.5.-629.1
The question of the solubility of nitrogen in, water at increased parameters of it has taken on great practi-
cal significance in recent years in connection with the use of nitrogen as a working body in systems of compen-
sation for the volume in water-cooled-water-moderated reactors. This leads to an extremely substantial
saturation of the coolant of the first circuit of nitrogen.
An increased nitrogen concentration in the coolant (C = 2000-3000 normal ml N2/kg H2O) can disrupt the
normal operation and can be the cause of breakdown of circulation pumps, filters of the system of purification
of heat cells, and other first circuit equipment [1-4].
An analysis of the published data on the solubility of nitrogen in water [5-12] has shown that there is a
sufficiently large number of experimental data, in relatively good agreement, for low pressure and tem-
perature, while there are few data for moderate and high pressure and temperature, and they sometimes dif-
fer substantially from one another.
One of the causes of these discrepancies, in our opinion, is the absence of an objective method of deter-
mining the limiting (equilibrium) value of the nitrogen concentration in water, at various parameters. In all the
studies the evaluation of the limiting solubility was to a definite degree subjective, since it depended on the
experimental conditions.
In view of this, the authors of the present work undertook the following tasks:
to develop a method that would permit an objective determination of the limiting value of the nitrogen
concentration in water;
to experimentally investigate the solubility of nitrogen in water in the region of moderate and increased
parameters, typical of water-cooled-water-moderated reactors.
The investigations were conducted on a special stand with forced circulation, equipped with systems for
compensation and air and gas removal. A peculiarity of the stand was a universal volume compensator (VC),
which can be used in gas, steam, and steam - gas. systems of operation. The circulation circuit included a
thermally insulated sample collector of special design (capacity 1047 ? 5 ml), equipped with an autonomous
cooling system. The stand and sample collector were equipped for measuring the pressure with standard
manometers (error no greater than +0.0025 MPa), standard mano-vacuummeters (error no more than ?0.001
MPa), differential transformer induction pickups with secondary indicating and recording instruments (error
no more than ?0.06 MPa); and for measurement of the temperature, thermocouples (error no more than
?1?C) with the same instruments.
To find the limiting values of the nitrogen concentration in water, we developed a method of phase trans-
formations, permitting a determination of the concentration of the solution Ci without overflow and cooling of
the sample. The method was based on the phenomenon of abrupt variation of the pressure and temperature in
a closed volume at the moment of phase transition of the'solution from an undersaturated state to a state of
limiting saturation and oversaturation.
Forced circulation of degasified water (using a VC in the steam system) or water saturated with nitrogen
to some value of Ci (using a VC in a steam - gas or gas system) was carried out through the sample collector.
After stabilization of the parameters, the sample collector was disconnected from the circulation circuit and
the external pressure created by the VC. The change in the pressure and temperature in the disconnected
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 91-94, February, 1980. Original article sub-
mitted March 26, 1979; revision submitted June 27, 1979.
102 0038-531X/80/4802-0102807.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
15-20sec
Fig. 1. Scheme of variation of the parameters in
the disconnected sample collector: -) two-phase
.gas -liquid mixture; - - -) degasified water
(Ci = 0); - ? -) water saturated with nitrogen (Ci ~
0); time of transitional process 15-20 sec. -
sample collector was recorded synchronously on the tapes of automatic recording instruments. Figure 1 shows
the variation of the temperature t = f1(T) and pressure tot = f2(T) in the sample collector after it was discon-
nected (point 1). The processes 0 -1- 21- 3' correspond to experiments with degasified water (Ci = 0), the
processes 0 - 1 - 2" - 3" to experiments with water saturated with nitrogen to some value of Ci. The pressure
and temperature of saturation are established at the point 2', and a pressure and temperature differing from
the parameters of saturation at the point 2". The experiments show that there is an unambiguous relationship
between Ci and the pressure difference at the points 2' and 2".
In our opinion, for the pressure and.temperature at the point 2", the given value of Ci is the limiting,
equilibrium value, i.e.; Ci = Clim(P2nt2"). At these parameters, the gas component of the solution is still in
a bound state, at the boundary of transition to the free state. The relationship between the limiting gas content
and the parameters of the solution at the moment of the phase transformation can be found according to Henry's
law, keeping in mind that tot = Pen:
Ci =(Ptot -P8)Ikr.:; (1)
where kp,t = f(Ptot, t) is the solubility coefficient, dependent on the pressure and temperature of the solution,
MPa ?kgH2O/normalN2. Thus, in contrast to the methods of other researchers, in this method the limiting gas
saturation is determined objectively according to the pressure jump at the moment of the phase transformation.
The method of phase transformations permits monitoring of dissolved gas without overflow of the sample
according to the parameters of the phase transformation. In this case the monitoring is performed according
to the nature and form of the graphs of t = f1(T) and Ptot = f2(T), according to the presence or absence of a
"break," corresponding to the parameters of the phase transformation. The absence of a break (processes
0 - 1 - 2 in Fig. 1) is evidence that the turned off sample collector contains a two-phase gas - liquid mixture.
The phase transformations evidently cannot occur in the two-phase system. The nature of the pressure change
in this case is determined by the system of cooling of the sample collector. In the case under consideration,
Ci > Clim. The same nature of the change in the pressure and temperature in the sample collector will exist
when Ci = Clim?
The presence of a break is an indication that a homogeneous medium was found in the sample collector.
If the parameters of the phase transformation correspond to the parameters'of water at the Line of saturation,
then degasified water was found in the sample collector (processes 0- 1- 21- 3' in Fig. 1). In this case Ci = 0.
If the parameters of the phase transformation differ from the parameters of water at the line of saturation,
then a homogeneous solution of gas in water was found in the sample collector (processes 0 - 2 - 211- 3" in
Fig. 1). In this case Clim > Ci > 0. The value of Ci can be determined according to the parameters of the
phase transformation, if the solubility coefficient kp,t is known. Thus, for a concrete determination of the
nitrogen concentration in water by the method of phase transformations without overflow of the sample, the
function kp,t = f(Ptot, t) should be known.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
To find this dependence we used the method of sample collection, followed by cooling. Forced circula-
tion of water saturated with nitrogen to some value of Ci was performed through the sample collector. After
stabilization of the parameters, the sample collector was disconnected from the circuit and the external pres-
sure created by the VC. The autonomous cooling system was turned on,- and the sample was cooled to 15-20?C.
Then the pressure in the sample collector was measured. The gas concentration in water Cis corresponding
to the limiting parameters P2n and t2n was determined according to the difference of the specific volumes of
the hot and cooled samples, considering a correction for the residual. nitrogen concentration in water accord-
ing to the formula
cool ff
Ci =C. (P2-1t2-) ptot -P'. "hot -U ) 273 -}- Cmm] normal ml N2/kg H2O, (2)
lim` Po +Of {lot cool -f .-I
where Pcotol is the total pressure in the sample collector after cooling, MPa; Ps, saturation pressure at
Tcool, MPa; Tcool, temperature of the water and gas in the cooled sample collector, OK; vhot and vcool,
specific volumes of water in the hot and cooled state, normal ml/kg; . f , temperature coefficient of volume
expansion of the metal of the sample collector, 1/deg; Cress residual nitrogen concentration in water at Pa =
0.1 MPa and tcool, normal ml N2/kg H2O. The investigation was performed in the following range of param-
eters: 0 < Pmt 592?K, just as the activities
a1, a2, and a3 at any values of the temperature, to the basic standard state; and u and A, constants of inter-
action between components, J/mole. Equations (6), (10), and (11), unlike the Van Laar equations, contain an
additional term 0 for components with a molecular volume different from that of the solvent. By solving the
systems of equations relating the measured equilibrium parameters for a number of particular cases of the
Na-O-H system [2-4, 10] and the activities (5)-(10), with allowance for reactions (1)-(4), we found the values
of the constants in Eqs. (5)-(11): u12 = 27840; 02 = 6660 - 14.492 T; u13 = 26340, u14 = 0; u23 = -13,040; 03 =
22,110+38.165 T; u24=17,190; 04 = -53,510+16.978 T; u34 = 15,600
Thus, all the necessary quantities for calculating the equilibrium parameters of the Na - 0 - H system
(pressure, phase boundaries, concentration, activity, etc.) have been found by the ordinary methods of
chemical thermodynamics. Comparison of the calculations and practically all published measurements of the
equilibrium parameters [2-4, 11-13] showed that the discrepancies lie within the limits of the error of mea-
surement. This allows the equilibrium concept discussed to be recommended for solving various problems of
sodium technology. Thus, e. g., of great interest for sodium technology RBN as well as for the production of
sodium, sodium hydride, and potassium by alkali exchange, etc., is the Na - NaOH phase diagram published in
part earlier [3, 41 for high NaOH concentrations. A more complete diagram (Fig. 1) was constructed by in-
corporating the data of [4] on the temperature of phase transitions of the solutions aL2 and /3L2.
LITERATURE CITED
1. Yu. V. Privalov, Preprint NIIAR P-16(310), Dimitrovgrad (1977).
2. Yu. V. Privalov, Preprint NIIAR P-6(300), Dimitrovgrad (1977).
3. 9. M. Mitkevich and B. A. Shikhov, Zh. Neorg. Khim., 11, No. 3, 633 (1966).
4. B. A. Shikhov, Zh. Neorg. Khim., 12, No. 4, 545 (1967).
5. V. A. Likharev, Preprint F1 I-612, Obninsk (1975).
6. E. A. Melvin-Hughes, Physical Chemistry [Russian translation], IL, Moscow (1962), p. 675.
7. H. Katsuta and K. Furukawa, Nucl. Technol., 31, No. 2, 218 (1976).
8. D. Vissers et at., Nucl. Technol., 21, No. 3, 235 (1974).
9. K. Claxton, in: Proc. Int. Conf. on Liquid Metal Technology in Energy Production, Champion, Penn.,
May 3-6 (1976), Paper VB6.
10. K. Myles and F. Cafacco, J. Nucl. Mater., No. 67, 249 (1977).
11. H. Uhlmann et at., in: Problems of Technology and Corrosion in Sodium Coolant and Protective Gas [in
Russian], Central Institute of Nuclear Research, Dresden, German Democratic Republic (1977), Vol. 1,
p. 16.
12. F. A. Kozlov et at., in: Proc. Engineering Physics Institute [in Russian], Atomizdat, Moscow (1974),
p. 120.
13. R. Pulham and P. Simm, in: Proc. Conf. Brit. Nucl. Energy Soc., Nottingham, April 4-6 (1973), p. 5.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
NONSTEADY TEMPERATURE IN NUCLEAR-REACTOR CHANNEL
A. S. Trofimov and A. V. Sobolev UDC 621.:039.517.5
As is well known [1], in calculating the nonsteady temperature in elements of the active: region with defi-
nite relations between the fuel-element and heat-carrier parameters, a quasisteady representation of the tern-a
perature distribution over the fuel-element cross section is possible. At the same time, it is necessary to
take into account its distribution over the height. When the heat-carrier flow rate and the heat-transfer coef-
ficient are variable over time, it is impossible to obtain an analytical solution of this problem. Consider one
of the methods of approximate, solution applied to a multilayer rod fuel element and a single=phase heat carrier
[2]. In this case, the thermal processes may be described, in dimensionless form, by the following system of
equations:
1+G (t) =ku+{1-G) Ti (z), 0- 0.4 gives good accuracy of the calculations: the discrepancy is no more than - 6%. This provides the
basis for recommending the approximate model for practical calculations; which allows the laborious proce-
dure of numerical solution of Eq. (1) to be avoided. The integrals in Eqs. (4) and (5) are sufficiently simple to
calculate on a computer. Graphoanalytic methods may also be used.
LITERATURE CITED
1. A. Ya. Kramerov and Ya. V. Shevelev,' Engineering Calculations of Nuclear Reactors [in Russian];
Atomizdat, Moscow (1964).
2,. A. S. Trofimovand B. F. Gromov, :Inzh-Fiz. Zh? 7, No. 8., 31 (1964).
A /i-RADIATION SOURCE BASED ON POLYSTYffENE
CONTAINING TRITIUM
V. M. Gu l ' ko , E. I Kn i z.hn i k , UDC 539.124.03:546.11.023:078.046
V. K. Rudishin, and .A . 1. Yashchuk
The important' advantages of tritium over other radionuclides - low toxicity [1, 21, relatively long half-
life, relatively simple methods of introducing it into compounds [3, 4] - has led to the wide use of tritium
sources [3-5]. The design and characteristics of the usual tritium sources have been discussed in [3, 5]. A
matter of considerable interest is the use in a source of tritium in a chemically bound state, e. g., in a hydrog-
enous polymer. Such a source will have amore uniform distribution of tritium, small mass, and no brems-
strahlung from the tritium-bearing layer; furthermore, it will be possible to prepare a source of arbitrary
shape.
In the present paper we present the first results of a study of characteristic sources of /3 radiation based
on polystyrene (PS) containing tritium. To prepare the sources, we used PS-7,8 3H in a benzene solution [6]
with a specific activity of 600 mCi/ml or 682 mCi/g of solution (or 31 Ci/g of polymer) and a PS concentration
of 19 mg/ml. The layer of PS was applied to a molybdenum backing 1.0 mm thick which had a titanium layer
0.8 ?m thick sprayed onto it. The ionization current of the source was measured by means of an ionization
chamber and a U5-6 electrometric amplifier. The desorption of tritium from the source was determined by
accumulation in a spherical chamber, for 1 h, of the gas emitted by the source, followed by pumping it into the
ionization chamber of a "Biota" radiometer with fixed volume, and measuring the concentration. The thickness
of the PS layer was determined by weighing on a VLM-20M balance.
Table 1 shows the characteristics of a group of six sources; for 6 months after preparation, the ioniza-
tion current remained practically unchanged. It can be seen that the desorption increases with time, and for
sources with a higher current the desorption increases more rapidly. Evidently, this is related to the radioly-
sis of the PS under the action of the characteristic p radiation.
The dose absorbed by the PS was calculated by the formula [4]:
D 1.6.10=14 NEM-1. (1)`
TABLE 1. Characteristics of the Sources
No. of
source
Thickness of
PS layer,
10-4g/cm2
onization
current,16 0
/cm2
3,2
3,1
2,0
2,5
3,0
2,1
Desorption,10-8Ci/cm2? h
after I6 months
preparation later
0,6
2,1
0,4
0,8
2,2
2,8
3,2
1,3
1,1
4,4
3,2
Translated from Atomnaya Energiya, Vol. 48, No. 2, p. 111, February, 1980. Original article submitted
April 12, 1979.
0038-531X/80/4802-0131.$07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
For a source with a specific activity S = 31 Ci/g the number of disintegration per half-year was N -
1.8.1019. Then for an average /3-particle energy of E = 5700 eV and a mass of M = 1 g, the dose amounts to
1640 Mrad. According to the data of [71, the working capacity of the PS should remain practically undiminished
(without taking account of the isotope effect).
The expected degree of decomposition of the PS (K) was estimated by the formula [4]:
K = (1 - exp (-FESG (-M) 6.14.10-16 ti} 100%. (2)
The degree of decomposition of the tritium-bearing PS, taking account of the absorption by the PS of the
characteristic 0 radiation (F = 1), the half-year period of operation t = 1.57. 107 sec, E = 5700 eV, and S = 31
Ci/g, was 1.7, 8.8, 16.8, 24.1, and 20.8% when the number of irreversibly damaged molecules per 100 eV of
absorbed energy G(-M) was equal to 0.1, 0.5, 1.0, 1.5, and 2.0, respectively.
It is expedient to use PS-based sources when the use of the traditional tritium emitters is less effective
or is completely impossible.
Neutralization of Electrostatic Charges. In the neutralization of static electricity it is very important
that the ions should be formed as close as possible to the zone of generation of the electrostatic charges. How-
ever, it is practically impossible to construct a usual type of tritium source in an arbitrary shape. On the
other hand, a PS source is technologically convenient and is easily applicable to the surface of various mate-
rials. This makes it possible for each specific case to construct a source of the necessary shape and place it
in.the immediate vicinity of the spot where the charges will appear, in particular on the surface of machinery
and mechanisms.
X-Ray Structural Analysis. In multicomponent x-ray structural analysis, we require a source of charac-
teristic x-ray emission from which several lines are emitted simultaneously. If tritium-bearing PS is applied
to a backing which contains the elements being analyzed, then under the action of 0 particles from the tritium,
the backing will emit characteristic x rays which can pass easily through a thin layers of PS. Such a system
makes it possible to obtain practically any line of any element, and the PS film itself will not have any brems-
strahlung, so that the background level will be considerably reduced; this is an advantage which distinguishes
such a source from the traditional kind.
Calibration of /3 Spectrometers. The method described in [8] makes it possible to prepare polymer trit-
ium sources with a controlled thickness from 5 to 30 pg/cm2 with a high degree of uniformity, which are used
for calibrating (3 spectrometers. They are distinguished by a relatively high and stable yield of i3 particles and
by.satisfactory radiation safety.
Atomic Batteries. Polymer tritium sources are promising for use in atomic batteries. They can be
made very thin, which makes it possible to concentrate in a small volume a considerable surface emitting
electrons. In addition, such batteries will be much lighter than the usual kind.
LITERATURE CITED
1. Basic Rules of Hygiene for Work with Radioactive Substances and Other Sources of Ionizing Radiation,
OSP-72 [in Russian], Atomizdat, Moscow (1973), p. 18.
2. Norms of Radiation Safety, NRB-76 [in Russian], Atomizdat, Moscow (1976), p. 22.
31 G. D. Gorlovoi and V. A. Stepanenko, Tritium Emitters [in Russian], Atomizdat, Moscow (1965).
4. E. Evans, Tritium and Its Compounds [Russian translation], Atomizdat, Moscow (1970).
5. A. Manin, Bull. Inf. Sci. Tech. CEA, No. 178, 65 (1973),
6. V. M. Kaloshin et at., Compounds and Products Containing Radioactive Isotopes. A Catalogue [in
Russian], V/O "Izotop," Moscow ( 1975), p. 14.
D. Bopp and W. Parkinson, in: The Effect of Radiation on Organic Materials [Russian translation],
Atomizdat, Moscow (1965), p. 445.
R. Davis and C. St. Pierre, Nucl. Instrum. Methods, 64, 348 (1968).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
COMPARISON OF THE RESULTS OF CALCULATING-
FAST-NEUTRON PASSAGE THROUGH HYDROGEN
,A TD ABBON LA-Y-ERS
19. B. Brodkin, A.. N_ Ko-z-kevnikov,
V. -G. Madeev, V. A. Utkin,
and A. V. -h-rustale
-UDC 539.125.5,17.52
Although our theoretical understanding of radiation transfer is now sufficiently complete, and the possi-
bility now exists of realizing even the most rigorous method of solving transfer equations, the problem of
reliability of the results obtained arises in calculating the protection of power reactors by a single program.
The simplest method of estimating the indeterminacy of the calculation is to compare the results obtained
using several programs, preferably of different classes, using independent systems of constants.
As experiments show, the main causes of discrepancy in the results are the initial microconstants used
in the calculation, the methods of transforming them, and the model adopted to describe radiation transfer.
The aim of the present work is to analyze the effect of these factors on the results. This analysis is best
carried out in conditions of the simplest radiation-source geometry, so that the effect of other more signifi-
cant factors is eliminated. In the present work, the dependence of the fast-neutron flux density on the thick-
ness of hydrogen and carbon layers is calculated.
The hydrogen (p = 0.111 g/cm3) and carbon (p = 1.65 g%cm3) media are represented in the form of an
infinite plate of thickness 120 cm, and the neutron source in the form of an infinite plate of thickness 1 cm with
isotropic sources pI = 10-4 g/cm3 uniformly distributed over the'volume. The neutron energy distribution of
the source corresponds to the fission spectrum. The programs used in the calculations are described briefly
Program ROZ-5 [1] is intended for the solution, in the multigroup approximation, of problems on the
passage of neutrons (neutron problems), primary (arising in the fission of uranium) and secondary (formed in
the capture and inelastic scattering of neutrons) y radiation in one-dimensional plane geometry, and also for
the solution of corresponding combined problems and the calculation of perturbation-theory functionals. ROZ-5
is based on the discrete-ordinate method. Finite-difference equations are solved by an iterative method, using
accelerated convergence according to the mean-flux method. Calculations using the ROZ-5 program were car-
ried out with the ARAMAKO-2F system of constants, providing for the representation of the elastic-scattering
cross section in the P5 approximation. The neutron energy range (from thermal to 10.5 MeV) was represented
in the form of 26 groups.
The MOKDIF program [2] is intended for the calculation of the spatial -energy distribution of neutrons
in a heterogeneous medium of one-dimensional geometry (a sphere, infinite cylinder, or plate). The program.
algorithm is based on a combination of the Monte Carlo method and the spherical harmonic method (Pi approxi-
mation). The program is combined with the NEDAM system of group (52 groups) constants [3] for Monte Carlo
calculations (at an energy > 0.1 MeV) and a 21-group system (for an every 6.5 MeV; M) calculation by the
MOKDIF program with vacuum conditions at the bound-
ary to the left of the source; R) calculation by the
ROZ-5 program, with the same conditions; S) calcula-
tion by the SABINE-3 program with "reflection" condi-
tions at the source - medium boundary.
20 40 60 80 100
Distance from source, cm
10-61 i 1 1 1 v
0 20 40 60 80 100 120
Distance from source, cm
Fig. 2. Spatial distribution of neutron flux density in
carbon at E > 0.1 MeV: M) calculation accordingto the
MOKDIF program, with vacuum conditions at the bound-
ary to the left of the source; R) calculation by the
ROZ-5 program with the same conditions; S) calcula-
tion by the SABINE-3 program, with "reflection" con-
ditions at the source - medium boundary.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
The results calculated for the spatial distribution of neutrons of different energy groups in hydrogen and
carbon for the same formulation of the problem according to the above programs are shown in Figs. 1 and 2.
It is evident that the results of calculations for the two materials differ with increase in thickness (by more
than a factor of two for a thickness above 100 cm). As was assumed, the cause of the discrepancy in the re-
sults can be analyzed sufficiently thoroughly for the case of hydrogen, since the neutron interaction cross sec-
tion is known with good accuracy for this element over practically the whole of the given energy range, neu-
trons are scattered only elastically, and the differential scattering cross section is expressed by a simple
formula.
In the initial calculation by the ROZ-5 program, an 8-group representation of the neutron spectrum was
used in the range 0.1-10.5 MeV, in accordance with the ARAMAKO-2F system of constants. Since the neutron
flux density calculated by ROZ-5 with this representation of the energy distribution was found to be less than
the same neutron flux density as calculated by the MOKDIF program, it was concluded that 8 groups are insuf-
ficient for the representation of the spectrum in this range.
To verify this conclusion, the ROZ-5 program was used to calculate the spatial distribution of the neutron
flux density in the energy range 0.1-13.5 MeV in a 30-group representation and in the range 6.5-13.5 MeV in an
11-group representation. The total group interaction cross sections were calculated on the basis of the cross
sections used in the MOKDIF program. The group scattering indices were determined from the analytic for-
mula for elastic scattering. Comparison of the results obtained by the MOKDIF and ROZ-5 programs with the
same system of constants (Fig. 1) shows that they are in good agreement over the whole of the thickness range
(0-120 cm). This indicates that the reason for the discrepancy in results obtained using programs realizing
more rigorous models of radiation transfer should be sought primarily in the system of constants used together
with the computational program.
Analysis of the reason for the discrepancy is complicated, of course, when the comparison is of results
obtained using programs in which different degrees of rigor are adopted in modeling the neutron-transfer pro-
cess, or when there are several types of interactions of the neutrons with nuclei of the medium, and their
cross sections cannot be expressed by simple dependences. This is the case when comparing results obtained
using the SABINE-3, ROZ-5, and MOKDIF programs, both for hydrogen (in comparing SABINE-3 with ROZ-5
and MOKDIF) and for carbon (in comparing any pair of programs). As yet, it has not been possible to perform
a sufficiently complete analysis of the discrepancy in the results for the calculated versions of the spatial dis-
tribution in carbon. However, in view of the significance of the results in themselves, it seemed useful to
present them here.
In conclusion, note that analysis of the identity of results obtained from different programs using some
system of constants is one of the most urgent, and inadequately solved, problems in the investigation of all
possible radiation-field characteristics.
1. T. L. Germogenova et at., in: Problems of Reactor Protection Physics [in Russian], No. 4, Atomizdat,
Moscow (1972), p. 22.
2. A. N. Kozhevnikov et at., Preprint IAE-2877, Moscow (1977).
3. L. N. Zakharov et at., Preprint IAE -2994, Moscow (1978). .
4. P. Niks, G. Perlini, and K. Ponti, in: Physical Problems of Reactor Protection [Russian translation],
Atomizdat, Moscow (1971), p. 5.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
ANALYSIS OF ACTIVATION METHOD FOR MEASURING
FAST-NEUTRON INTERACTION CROSS SECTIONS
A. N. Davletshin, A. 0. Tipunkov, UDC 539.125.5
S. V. Tikhonov, and V. A. Tolstikov
Data obtained by various experimenters using various methods, even for such well-studied nuclides as
2381J and 197Au, show appreciable divergences. This is particularly true for energies 31 MeV. Not only are
these differences in data obtained by time-of-flight and activation methods, but even the results obtained by
various experimenters using the activation method show divergences. We are convinced that these differences
result from an incorrect account of the background corrections for the effects of neutron scattering.
In irradiating samples at an electrostatic accelerator it is necessary to determine the activity Nyo in-
duced in a sample by neutrons reaching it directly from the target. However, some neutrons leave the target
and undergo various interactions in structural elements before reaching the sample. The spectrum of these
neutrons may be considerably different from that of neutrons arriving directly from the target. These back-
ground neutrons induce activities in the sample which we shall call sample backgrounds. There are also other
reasons why the measured effect differs from NYo.
We describe briefly the sources of sample backgrounds and methods of measuring them.
1. Room Background ABI. This background is the result of neutron scattering from the walls of the
laboratory, and is assumed constant far from the walls.
For long half-lives it is convenient to determine this background by comparing the activities of samples
irradiated simultaneously under normal conditions ("j 4 cm from the target) and at a distance of - 2-3 m from
the target, or by measuring the activity of the sample as a function of the distance from the target. By extrap-
olating this relation to an infinite distance, we obtain the value of AB1.
2. Sample Background AB2. Most of the neutrons which interact with the sample undergo elastic and
inelastic scattering. The mean free path of these neutrons after scattering in a disk sample is appreciably
longer than the sample thickness. Such neutrons can increase the activity of the sample as a result of radia-
tive capture. This effect can be determined by using samples of various masses and extrapolating the experi-
mental values of the cross section to zero mass. Since this background amounts to less than 2% of the activity
of the sample, it was calculated.
3. Container Background AB3. A U3O8 sample is usually packed in a nickel container. In addition, it
is also packed in a cadmium container to decrease the room and target support backgrounds. This leads to a
decrease in the neutron flux incident on the sample. At the same time, neutrons scattered in the containers
cause further activation of the sample. The combination of these effects leads to an increase in the activity of
the sample. The value of this background is determined by measuring the activities for containers of various
masses.
4. Target Support Background A$4. The target support is a very massive structure, and is located close
to the sample. Its main elements affecting the activation conditions of the sample are a layer of cooling water
and a brass cover. Neutrons leaving the target outside the solid angle subtended by the sample are scattered
and cause additional activation when they strike the sample. This effect is decreased to a certain extent be-
cause of the attenuation of the direct neutron flux in the target support. This background is also determined by
measuring the activity for target supports of various masses.
5. Background Resulting from the Anisotropy of the Neutron Source A$5. The activation of the sample
by neutrons from the target is a linear function of the geometric factor Gsa, which depends on the dimensions
of the source and sample, and the distance between them. Measurements of the activity of the sample for
various distances from the target showed that at distances < 5 cm the activity of the sample, is lower than it
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 113-115, February, 1980. Original article
submitted April 23, 1979; revision submitted July 10, 1979.
. 136. 0038-531X/80/4802-0136 $07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
m,116 m-~~~ Uj08
hj~
0,2 0,4 Q6 0,8 1,0 1,2
4
2
v
Fig. 1. Relative values of backgrounds of: a) room DAB I; b) sample
AAB2; c) containers for U3O8 and Au samples AAB3. Here and in
Fig. 2: 0) experiment; -) least squares average.
Fig. 2. Relative values of backgrounds of target support AAB4, ani-
sotropy of neutron source AAB5, and sample holder DABS for U308 and
Au samples.
should be for a linear law. There are two reasons for this. First, the differential cross sections for the
T(p, n)3He and 7Li(p, n)7Be reactions decrease with increasing angle of departure of the neutrons. Second,
neutrons emerging at larger angles are more strongly attenuated by the target support structure. At the same
time,. this effect is partially compensated by neutrons which emerge at larger angles and have lower energies
than neutrons which emerge at 0?. The background AB5 is measured as follows: The sample is irradiated at
the normal distance of 4 cm from the target and at a distance of 6 cm, for which the linear law of variation of
activity with Gsa is still valid. The difference between the normalized activities is the background sought.
6. Sample Holder Background AB6. Some of the neutrons scattered by the brass sample holder fall on
the sample and give rise to further activation. The value of this background can be determined by using sam-
ple holders of various masses. -
Figures 1 and 2 show the results of measurements of various sample backgrounds in the form of the
relative contribution DABS for 350-1400 keV neutrons. If the background is different for U308 and Au samples,
the results are shown on separate graphs. The backgrounds of the containers and sample holder are shown as
functions of the total microscopic cross section of the corresponding element, and normalized to unit mass.
This is convenient in view of the presence of resonances in the cross sections.
The value of DABI for uranium was calculated from the estimate of AA BI for gold samples. In addition, this back-
ground was determined for three values of the neutron energy from the dependence of the activity of the uran-
ium samples on the distance from the target. These values with errors are also shown on the graph. The
calculated and measured values are in complete agreement.
The IAB4 background is larger for gold than for uranium, although the energy dependences are similar.
This results from the fact that neutrons scattered in the target support and falling on the sample have substan-
tially lower energies than neutrons incident at 0?. The probability of their capture by a gold nucleus is larger,
since the resonance integral for gold is 5.5 times as large as that for uranium.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
BAB
0,80
0,751 . i I
O,Z 44 0,6 0,8 1,0 1,2 E,, MeV
Fig. 6. Total background correction as a function
of neutron energy for U308 and Au samples.
Most of the experimental values of the background AA$5 were measured as described above. DABS for
uranium was determined for.three values of the neutron energy from the dependence of the activity of the sam-
ples on distance (2-40 cm). These values and the experimental errors were plotted. Agreement with the re-
maining data is good.
Using the background estimates obtained, the total background correction 6AB was calculated for the
experimental radiative capture cross sections of 238U and 197Au. The calculated results are shown in Fig. 3.
In the neutron energy range considered the total random errors of the corrections vary from 1.4 to 1.9% for
gold, and 1.3-2% for uranium.
The main contribution to the total random error comes from MAB4. The conditions of measurement of
this background are such that it may have an appreciable systematic error. An estimate shows that for En =
350 keV this error for gold (MAB4 = 12.5%) may reach 3%. The reason is that the target support makes a large
contribution to the background, and cooling it with water does not decrease it significantly. In addition, added
background mass cannot be distributed in the same way relative to the target as the main mass. It follows
from the above that it is necessary to lighten the target support as much as possible and to coot it with gas in
order to lower the contribution of the background MAB4 and to decrease its systematic error appreciably.
Thus, taking careful account of background corrections changes the value of the experimental capture
cross section appreciably, even for neutrons with energies less than 1.5 MeV. There is no mutual compensa-
tion of the scattering corrections in activation measurements. An underestimate of the effects investigated in
this paper can cause the difference in values reported by various experimenters.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
YIELD AND ANGULAR DISTRIBUTIONS OF
PHOTONEUTRONS FROM THICK LEAD TARGETS.
A. P. Antipenko, V. G. Batii,
V. Ya. Golovnya, V. I. Kasilo.v,
N. I. Lapin, L. A. Makhnenko,
and S. F. Shcherbak
The purpose of this study is to investigate the yield and angular distributions of photoneutrons from lead
targets of different thicknesses in the impinging-electron energy range of 60-200 MeV.
The measurements were made by the activation method on a beam from the LUP-300 linear electron
accelerator. We used the reaction 27A1(n, p)27Mg with T1/2 = 9.8 min. Threshold detectors, which were alu-
minum disks 48 mm in diameter and 4 mm thick, were.placed at a distance of 50 cm from a lead target over a
range of angles from 0 to 165? with the axis of the impinging electron beam, spaced 15? apart. The activity of
the detectors was measured with a scintillation y spectrometer which had an NaI(Tl) crystal measuring 63 x 63
Data on the integral neutron flux were obtained with an error of f10(70.by the method of effective threshold
cross sections [1]. The total integral neutron flux was determined from,the relation
' ._ Kq) (Eeff,
where K is a coefficient taking account of. the contribution made by the neutrons with energies less than the ef-
fective reaction threshold. A value of K 12 was obtained from an estimate of the shape of the photoneutron
spectrum given in [2], The error in determining was ?20%.
Figure 1 shows the variation of the fast-neutron flux density (En > 4.5 MeV) at different angles as a func-
tion of the thickness of the lead target for an electron energy of 200 MeV. The diameter of the target was con-
stant, equal to 43 mm. It can be seen that for a thickness of more than 18 radiation lengths (1 radiation length
equals 5.6 mm) there is practically no increase in the neutron yield at all angles. In the rest of our study we
used a lead-target thickness of 100 mm for the measurement of the angular and energy variations.
0 0 y
~ .n
?oh
0 2 4 .6 8 10 12 14 16 .18 20
Fig. 1
6, deg
90
40 30 20 10 0 -10 20 30
V, neutrons?secy1 cm-2
Fig. 2
Fig. 1. Fast-neutron flux density as a function of target thickness at angles of
30? (.), 90? (0), and 150? (A) at a. distance of 1 m from the center of the target,
with an electron-beam current of 1 ?A.
Fig. 2. Angular variation,of the fast-neutron flux density for an impinging-electron
energy of 60 (1), 125 (2), and 200 (3) MeV and a beam current of 1 ?A.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 115-116, February, 1980. Original article
submitted April 23, 1979.
0038-531X/80/4802-0139 $07.50 ? 1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
20
15
c
8
101 1
50 100 150 ' 200
Ee, MeV
Fig. 3. Variation in the shape of the graph of fast-neutron
flux density vs angle as the target thickness is varied (elec-
tron-beam current 1?A, distance from center of target
1 m): 1) d = 1; 2) 2; 3) 3; 4) 4; 5) 8; - 6) 16 radiation
lengths; 0) experimental points.
Fig. 4. Neutron flux as a function of impinging-electron
energy at an electron-beam power of .1 kW.
Figure 2 shows the angular distributions of fast neutrons, which demonstrate the anisotropy of the neu-
tron yield,.with a maximum at 90?. In a number of earlier experimental studies [3-5] measurements were
made on the angular distributions of fast photoneutrons from targets with a thickness of > 10 radiation lengths
with Eymax = 22-55 MeV. The investigators also observed anisotropy of the neutron yield, with a maximum
at angles close to 90?. This effect can be explained essentially by the small contribution of the statistically
emitted neutrons in the energy region En > 4.5 MeV. The angular distributions of such neutrons are usually
described by the sum of the first Legendre polynomials [3, 6, 7].
Figure 3 shows the variation in the shape of the graph of the fast-neutron flux density vs angle for dif-
ferent lead-target thicknesses, with an electron energy of 200 MeV. For a target thickness of 1 to 4 radiation
lengths we observe a striking anisotropy, with a maximum at small angles. For a target thickness greater
than 4 radiation lengths, the neutron yield at 90? increases considerably.
The absence of a 90? maximum in the angular distribution and the presence of an anisotropy in the forward
direction when the target thickness is less than 4 radiation lengths is explained by the attenuation of the neutron
flux by the target material at angles close to 90? (by a factor of 1.6, according to our estimates); the flux of
neutrons flying forward remains practically unattenuated, and the flux of the neutrons flying backward is atten-
uated only slightly (for a target with a thickness of only 1 radiation length and 0 = 165? the attenuation factor is
about 1.1). It is also apparent that for a small target thickness the bremsstrahlung spectrum is harder, and
consequently the contribution of the reactions which yield isotropy, e. g.. (y, 2n) and others, is greater [8].
Figure 4 shows the variation of the total neutron flux from a lead target 100 mm thick as a function of
the impinging-electron energy calculated per unit beam power. It can be seen that the specific neutron yield
for an electron energy of more than 100 MeV reaches its maximum value of 2.2 f 0.4 ?1012 neutrons/sec ? kW,
and for higher electron-energy values it remains practically constant. This value is in good agreement with
the results of the calculations in [9] for a lead target 102 mm thick and 50 mm in diameter, which showed 1.6
1012neutrons/sec - kW (using the cross section obtained by Harvey et al.) and 2.8: 1012 neutrons/sec - kW (using
the cross section obtained by Miller et at., and also with the data of an experimental study 1101 for a lead tar-
get 60 mm thick and 25 mm in diameter, which showed (2.7 ? 0.8) ? 1012 neutrons/sec ? kW.
The above experimental results may be useful in the design of fast-neutron sources based on linear elec-
tron accelerators.
1. E. A. Kramer-Ageev et at., Activation Methods of Neutron Spectrometry [in Russian], Atomizdat,
Moscow (1976).
2. D. Gayther and P. Goode, J. Nucl. Energy, 21, No. 9, 733 (1967).
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
3. G. Price, Phys. Rev., 93,. 1279 (1954).
4. G. Reinhardt and W. Whitehead, Nucl. Phys., 30, No. 2, 201 (1962).
5. F. R. Allum et al., ibid., 53, No. 4, 545 (1964).
6. R. Baker and K. McNeill, Can. J. Phys., 39, 1158 (1961).
7. J. Rawlins et al., Nuct. Phys., A122, 128 (1968).
8. K. McNeill et al., Can. J. Phys., 46, 1974 (1968).
9. R. Alsmiller and H. Moran, Nucl. Instrum. Methods, 48, 109 (1967).
10. V. I. Noga, KhFTI Preprint, No. 78-34, Kharkov (1978).
A NEW SYSTEM OF GROUP CONSTANTS FOR THE.
L. N. Abagyan, N. O. Bazazyants, . UDC 621.039.51.134
M. N. Nikolaev, and A. M. Tsibulya
A good deal of work is now being done on a new version of the BNAB-78 system of group constants, which
now includes data for 17 elements and isotopes: for fuel materials - 235U, 238UI 239Pu, and 240Pu; for struc-
tural and technological materials - Fe, Cr, Ni, Mn, Na, 0, C, and 4He; for materials of the control compo-
nents - 10Bu and Eu; and also for D, 3He, and Er. Efforts to extend this system are being made. In the
study of isotopes for which new group constants have not yet been prepared, data from the earlier version of
the system of constants [1, 21 can be used.
The work on the BNAB-78 was carried on in two stages. The first stage took account of the data pub-
lished in 1977. for differential microscopic experiments alone. The result of this stage was the development
of a system of constants which has come to be known as BNAB-MIKRO. The choice of the variation of the
cross sections of 235U, 239Pu, and 240Pu as functions of energy was based on estimates made by Kon'shin et.
al. [3-5]; in the case of Fe, Ni, and Cr the choice was based on estimates made at the Nuclear Data Center
[6-8]. The results of,these estimates were corrected, taking account of newly obtained experimental infor-
mation. The constants for carbon and 10B were based on estimates taken from the ENDF/B library [9]. The
remaining data were obtained from the results of our own estimates.
The second stage consisted in an analysis of the divergences between the results of experiments con-
ducted on fast critical assemblies and the results of calculations by BNAB-MIKRO system. We con-
sidered data obtained on 21 assemblies with uranium fuel and 13 assemblies with plutonium fuel; in five cases
these experiments related to media with k., = 1.
We observed a contradiction between the new experimental data on the excitation cross section for in-
elastic scattering of the 47 keV level of 238U [10, 11] and the results of measurements of the ratios of the fis-
sion and capture cross sections in 238U to the fission cross section of 235U in a medium of metallic uranium
with 5.56% enrichment and k,o = 1. These measurements were independently made by different methods in the
USSR, the Federal Republic of Germany, France, and Great Britain [12, 13] and led to very exact results (1%a)
which were in excellent agreement. To explain these data, we had to reduce the cross section of inelastic
scattering by 238U for an energy of hundreds of keV to the level of the earlier results obtained by Smith [14]
(which served-as the basis for. the earlier version of the BNAB constants [1]). The capture cross section of
238U used in BNAB-MIKRO [15] in the region from 2 to 40 keV also had to be reduced to the level. of the esti-
mate made by Tolstikov [16]. The results of the analysis of macroexperiments also indicated a need to in-
crease the fission cross section of 239Pu by 1.5%, which was done. Unlike the change in the cross sections of
238U, this change is completely consistent with the latest experimental data [17], which were not taken into
account in the BNAB-MIKRO system.
The system of constants with the indicated changes in-the cross sections of 238U and 239Pu has been given
the name of BNAB-78. In addition to the groups of the BNAB-70 system of constants, the BNAB-7.8 system
includes a group 0 (10.5-14 MeV) and a group -1 (14-14.5 MeV); it includes data on the characteristics of
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 117-118, February, 1980. Original article
submitted May 8, 1979.
0038-531X/80/4802-0141 $07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 1. Divergences between Calculation and-Experiment in the Criticality Coefficients,
Cross-Sectional Ratios, and Reactivities of Small Specimens in the Centers of the Active
Zones of Fast Critical Assemblies, %a
No.of
Divergence
Accurate
Divergence
Characteristic
experi-
BNAB 70
I
BNAB-MIKROBNAP m-
I
BNAP-78
of one
av.
ENDF/n-1v
JAERf
FAST
.n]NDt.-t
ments
I
xpt.
h3,p(235U)
16
-0,4
-0,9
-0,1
-0,1
0,8
0,2
0,4
0,4
0,7
/c3 (D (239pu)
12
-2,6
-1,9
-1,0
-0,2
0,9
0,3
--0,3
-0,3
0,1
of (238U)af (2350)
32
-0,7
2,2
1,3
1,4
5,3
0,9
2,8
2,9
-0,1
6c (238U)/af (235U)
17
2,4
3,9
0,3
0,3
2,3
0,6
-2,6
-1,8
-1,4
oj(235Pu)/af(235U)
30
-4;7
---2,1
-2,0
-0,5
3,3
0,6
-0,7
-1,9
---3,1
of (240Pu)/af (235U)
13
-0,8
2,6
2,1
2,4
9,9
2,8
7,3
6,8
1,2
(238U)/() (235U)
13
-4,4
--0,8
-2,8
--1,6
9;1
2,5
--5,1
--0,8
(;,7
(2391)11)/1) (2351j)
20
-3,2
-2,4
-2,0
-0,2
3,6
0,8
-1,8
-u,4
.--3,1
(,?B)/p(2351.J)
19
-22
--16
-14
-13
11
2,5
-17
-9,7
-8,6
p (Fe)/p (235U)
12
-11
6
6
6
27
8
8
1,4
-15
p (Ni)/p (295U)
10
-5
17
19
20
12
4
8
15
9
p (Cr)/p (235U)
9
-3
19
20
21
16
5
28
131
-8
?BNAB-M differs from BNAB-MIKRO only in the change of the 238U cross sections; the fission cross section of 239Pu
remains the same.
delayed fission neutrons; the resonance structure is described both with the aid of self-shielding factors and
in the subgroup representation; the anisotropy of inelastic scattering is described to within the P5 approxi-
mation; group cross sections are given for the most important reactions: (n, 2n), (n, p); (n, a), and others.
Table 1 contains data on the average divergences between calculation and experiment in the characteris-
tics of critical assemblies obtained by different versions of the BNAB constants and also by the foreign sys-
tems of constants ENDF/B IV [18], JAERI-FAST, and JENDL-1 [19].. It also shows estimates of the errors
in the results of individual experiments (according to the mean-square distribution and the errors of the
average divergences between calculation and experiment (less by a factor of V7 than the error of an individual
experiment; N is the number of experiments of a given type). The latter relate only to the results of the cal-
culation using the BNAB constants, since the calculations by the foreign; systems of constants were carried
out only for some of the critical assemblies we considered. The data show that the use of BNAB-78 ensures
the calculation of the characteristics which determine the neutron balance, to within experimental errors.
The calculated reactivity of 10B is found to be too low regardless of what system of constants is used.
We assume. that the reason for this lies in some still unidentified methodological errors in the experiments
and/or the calculations. The same cause may be responsible for the considerable divergences in the reactiv-
ities of Cr and Ni: in the experiment on the KBR-3-3 assembly [20], in which these reactivities were mea-
sured and calculated most reliably, the divergences between calculation and experiment are small.
The BNAB-78 system of constants is recommended for use in physical calculations for fast reactors
and neutron shielding. According to our estimates, the errors obtained with it for the calculated prediction
of keff and the coefficient of reactivity of a large plutonium breeder reactor with partly burned-up fuel are
1%o, 2%, and 3%, respectively. These errors are due to the inaccuracy of the data on the cross sections of
parasitic capture (chiefly in fragments), and in the case of the coefficient of reactivity they are also due to
inaccuracies in the value of a. -
It should be noted that at the time of publication of this paper, the BNAB-78 system has been supple-
mented by revised group constants for 7Li, 11B, Al, Si, Ca, Cd, Cd, and Pb. For all the materials, tables
of the formation of y quanta in neutron reactions (for 15 y groups) have been formulated, so that we can
recommend these constants for the calculations of radiation shields as well.
1. L. N. Abagyan et at., Group Constants for the Calculation of Nuclear Reactors [in Russian], Atomizdat
(1964).
2. L. V. Antonova et at., in: Proceedings of the Trilateral Soviet - Belgian - Dutch Symposium on Some
Problems in Fast-Reactor Physics [in Russian], Vol. 1, Report 18, Moscow (1970).
3. G. V. Antsipov et at., in: Problems in Atomic Science and Technology. Nuclear Constants Series [in
Russian], Part 2, No. 20, Izd. TsNllatominform, Moscow (1975), p. 3.
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4. V. A. Kon'shin et at., ibid., No. 16, 329 (1974).
5. C. V. Antsipov et al., in: Nuclear-Physics Research in the USSR. A Collection of Abstracts [in Rus-
sian], No. 21, Obninsk (1976), p. 45.
6. V. M. Bychkov et at., in: Problems in Atomic Science and Technology. Nuclear Constants Series [in
Russian], Part 1, No. 20, Izd. TsNllatominform (1975), p. 46.
7. V. M. Bychkov and V. I. Popov, in: Problems in Atomic Science and Technology. Nuclear Constants
Series [in Russian], No. 25, Izd. TsNllatominform, Moscow (1977), p. 55.
8. V. M. Bychkov et at., in: Neutron Physics. Materials of the Fourth All-Union Conference on Neutron
Physics [in Russian], Part IV, Moscow (1977), p. 91.
9. B. Magurno, ENDF/B IV Cross Section Measurements Standards. Inform. Analysis Center Report.
BNL-11973, Upton, New York (1975).
10. P. Guenther and A. Smith, in: Proc. of the Washington Conf. "Nuclear Sections and Technology,"
Vol. II, NBS (1975), p. 862.
11. P. Guenther, D. Havel, and A. Smith, Fast Neutron Excitation of the Ground-State Rotational Band of
236U. Report ANL/NDM-16 (1975).
12. M. Darrouzet et al., in: Proc. Int. Symp. on Physics of Fast Reactors, Vol. I, Tokyo (1973), p. 537.
13. J. Chaudat, M. Darrouzet, and E. Fisher, Experiment in Pure Uranium Lattices with Unit k,". Assem-
blies: SNEAK-8/8Z, UK 1 and UK 5 in ERMINE and HARMONIE. KFK-1865 (CEA-R-4552) (1974).
14. A. Smith, Nucl. Phys., 47, No. 4, 333 (1963).
15. G. N. Manturov and M. N. Nikolaev, Preprint FEI-666, Obninsk (1976).
16. V. A. Tolstikov and V. S. Shorin, in: Problems in Atomic Science and Technology. Nuclear Constants
Series [in Russian], Part 2, No. 20, Atomizdat, Moscow (1975), p. 61.
17. In: Proc. of the NEANDC/NEACRP Specialists Meeting on Fast Neutron Fission Cross Sections of 233U,
235U, 238U, and 239PU, Argonne, June 28-30, 1976, ANL-7690.
18. R. Hardie, R. Schenter, and R. Wilson, Nucl. Sci. Eng., 57, No. 3, 222 (1975).
19. I. Otake, in: Proc. Specialists Meeting on Neutron Data of Structural Materials for Fast Reactors,
Geel, December 5-8, 1977, Report IA-6.
20. V. I. Golubev et al., in: Problems in Atomic Science and Technology. Nuclear Constants Series [in
Russian], No. 28, Izd. TsNllatominform, Moscow (1978), p. 41.
COLLATION OF SEVERAL METHODS OF PULSED
y-RAY DOSIMETRY
Yu. P. Bakulin, V. N. Kapinos, UDC 539.12.08
A. P. Korotovskikh, and Yu. A.. Medvedev
At the present time devices are being developed [1-5] for measurements of the dose and dose rates of
pulsed ionizing radiation, but they do not include standard means of measurement. It is therefore of great
interest to compare the results of dosimetric investigations carried out by various methods. Such a compari-
son is made in the present paper for y-ray pulses with a duration of roughly several tens of nanoseconds and
a characteristic leading edge of about 10 nsec.
The experiments were performed with a highly stable pulsed source of bremsstrahlung, ensuring a
maximum dose rate of 8.106 A/kg. In our collation we compared the shape of the dose-rate pulses recorded
by high-frequency [2, 5, 6] and scintillation [7] methods and integral doses measured by high-frequency and
thermoluminescent [8] methods.
To record the pulse shapes by high-frequency methods we used a detector with a dynamic range of 2.5
103-8.105 A/kg. The choice of precisely this detector was due to the fact that the upper limit of its dynamic
range corresponded to the upper limit (^? 2.5 A/kg) of the range of the scintillation counter used in the
collation.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 118-119, February, 1980. Original article
submitted July 3, 1979; revision submitted August 27, 1979.
0038-531X/80/4802-0143 $07.50 ?1980 Plenum Publishing Corporation 143
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Time, nsec
Fig. 1. Normalized copies of oscillographic
records of y-ray dose-rate pulses recorded
by high-frequency (1) and scintillation (2) de-
tectors with pulse duration of 40 nsec.
TABLE 1. Bremsstrahlung Doses Recorded
by High-Frequency and Thermo luminescence
IKS-A Dosimeters
Ex t.
No.
D?109
~C/kg I
D?10",
C/kg
DID'
Expt.
No. {
D?109,
C/kg
D?109,
C/kg
DID '
1
2,2
2,0
1,1
0
3,0
2,5
1,2
2
2,4
2,0
1,2
7
25
20
1,3
3
2,3
3,3
0,7
8
28
30
0,9
4
2,3
2,2
1,0
9
38
34
1,1
5
3,0
2,7
1,1
We compared the shapes of pulses recorded by high-frequency and scintillation methods (Fig. 1). The
pulse duration z at half-height (FWHM) was 41 and 36 nsec, respectively. Analysis of the normalized curves
indicates good agreement between the shapes of dose-rate pulses, A(t) and A"(0, recorded by high-frequency
and scintillation detectors, respectively. The value of the integral dose was found from the readings of the
high-frequency and scintillation detectors, D and D', by using the relation
D = kA max s, (1)
where Amax is the maximum value of A(t) and k is the form factor of the dose-rate pulse, as given by
k = A (t) dt/D'. (2)
The results of comparisons of the integral doses are given in Table 1. In.the plot corresponding to the
thermoluminescence method the values given for the doses are averaged over the readings of two or three
IKS-A thermoluminescent dosimeters arranged on the cylindrical surface of the high-frequency detector. The
doses of the pulsed ionizing radiation, found from the readings of the high-frequency and thermoluminescence
detectors, agree to within 30%.
Since there was practically no distinguishable spread of the readings of the high-frequency detector when
the experiments were repeated many times, the deviations given in Table 1 for the readings of the high-fre-
quency and thermoluminescence detectors are entirely due to the spread of the readings of the thermolumines-
cence dosimeters.
Analysis of the normalized curves of the time dependence of the y-ray dose rate, recorded by high-
frequency and scintillation detectors, showed that the observed difference lies within the limits of experimen-
tal errors which are determined primarily by the error of the oscillograph recorder (^' 10%). The slower
decay of the pulse at the output of the scintillation detector is explained by the existence of slow components
in the pulse characteristic of the plastic scintillator [7] and, possibly, by the energy dependence of the detec-
tors tested. In conclusion, let us point out that the time resolution of the high-frequency method is estimated
to be roughly 10 nsec [5].
1. V. N. Kapinos et al., Metrol. Tochnye Izm., No. 2, 21 (1970).
2. V. N. Kapinos and Yu. A. Medvedev, in: Int. Sci.-Tech. Conf. of COMECON Member-Countries on
Scientific Instruments "Nauchpribor SEV-78," Digest of Papers [in Russian], Izd. TsNII Priborostro-
eniya, Moscow (1978), pp. 170, 172.
3. V. N. Kapinos et at., in: Digest of Papers, All-Union Sci.-Tech. Conf. "State of the Art and Prospects
for Development of High-Speed Photography and Cinematography and Metrology of Fast Processes" [in
Russian], Atomizdat, Moscow (1978), p. 118.
4. V. N. Kapinos, Yu. A. Medvedev, and B. M. Stepanov, in: Digest of Papers, All-Union Sci.-Tech.
Conf. "State of the Art and Prospects for Development of High-Speed Photography and Cinematography
and Metrology of Fast Processes" [in Russian], Atomizdat, Moscow (1978), p. 120.
5. V. N. Kapinos et at., in: Digest of Papers, All-Union Sci.-Tech. Conf. "State of the Art and Prospects
for Development of High-Speed Photography and Cinematography and Metrology of Fast Processes" [in
Russian], Atomizdat, Moscow (1978), p. 121.
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
6. V. N. Kapinos and Yu. A. Medvedev, At. Energ., 46, No. 2., 112 (1979).
7. Z. A. A1'bikov, A. I. Veretennikov, and O. V. Kozlov, Pulsed-Radiation Detectors [in Russian],
Atomizdat, Moscow (1978), p. 63.
8. K. K. Shvarts et al., Thermoluminescence Dosimetry [in Russian], Zinatne, Riga (1968), p: 56.
CORRECTIONS TO NEUTRON FLUX MEASUREMENTS
B Y GOLD FOIL METHOD
G . M. Stukov and I . A Yaritsyna UDC 539.125;5.08
We have determined highly accurate corrections to the perturbation of the thermal neutron flux density
in water by the gold foil method under specific conditions of measurement. At the same time, we have found
the correction to the gold activity measured by the 41rp - y coincidence method for foils of finite thickness when
the p-counting efficiency (ep) is less than unity. The foils used in the experiment were 20 mm in diameter and
of nine different thicknesses from 1.6 to 47 mg/cm2.. The mass of each foil was determined to within 0:05%. A
foil of each thickness was irradiated twice (with and without a cadmium cover 0.7 mm thick) in a tank of dis-
tilled water with a neutron source at the center. The activity of the foils was measured with a standard 47rr - y
coincidence counter. The correction to the gold activity (1 + a) was first determined as a function of the
parameter f = (1 - Ep)/ep [1], which was varied by shielding with very thin unactivated gold foils of various
thicknesses. This varied ep from 85 to 42%, The results of the experiment are showh in Fig. 1. The least-
squares method was used to find the required correction to the activity for any value of (1 - cp)/cp (the straight
.line in Fig. 1). The relation obtained was used later to find the time activity of gold foils in measurements with
a 4vp - y coincidence counter.
The specific activity (AT) of 198Au induced by thermal neutrons was determined for each foil from the
usual formula for the cadmium difference, and the required correction for the perturbation for each foil thick-
ness can be calculated from the expression
where A0 is the specific activity of an infinitely thin foil corresponding to an unperturbed thermal neutron flux
density. The value of A0 can be determined by extrapolating the available values of AT, to zero foil thickness t = o. It is
convenient, however, to extrapolate to t = 1/AT, since in this case the approximating function is linear, and
the least-squares method can be used. In accord with [2] we have
K =AT = +E
A0 2?at T+ (;j./2) g'
To Apo (Nat)
2?at 2?at
co (fiat)- 21L at 1+21Aat (for ?at < 1).
Fig. 2
20 .10 t, mg/cm2
Fig. 1. Correction to gold activity as a function of
(1 - E~j)/EIR
Fig: 2. Reciprocal of specific activity of gold foil
as a function of foil thickness.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 119-120, February, 1980. Original article
submitted June 26, 1979.
0038-531X/80/4802-0145$07.50 ?1980 Plenum Publishing Corporation
(4)
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Substituting Eqs. (3) and (4) into (2) we obtain
1/AT = (1/A,) + Bt, (5)
where t is the foil thickness and B is a proportionality factor.
Applying Eq. (5), the results were processed by the least-squares method (Fig. 2). The value of A0 was
determined to within 0.1%.
Thus, the correction to the perturbation of the thermal neutron flux density by gold foils in water was
determined under conditions frequently encountered in practice, when the flux density varies within the dis-
tance between source and foil. The error of this correction is reduced considerably. Thus, e. g., for foils
20 ?m (39 mg/cm2) thick, the thickness most frequently used in measuring neutron fluxes at the UEN-3,
amounts to' 0.2%. The decrease in the error of this correction led to a significant increase in the accuracy of
the absolute measurement of the neutron flux by the method of activation of gold foils.
A. Baerg, Metrologia, 2, 23 (1966).
K. Beckurts and K. Wirtz, Neutron Physics, Springer-Verlag, New York (1964).
DETERMINATION OF THE LANTHANUM, CERIUM,
PRASEODYMIUM, AND NEODYMIUM CONTENT OF
SOLUTIONS BY AN X-RAY SPECTRAL METHOD
USING THE SRF-5 INSTRUMENT
I. M. Krasil'nikov, I. D. Skorova,
A. V. Sholomov, P. A. Konstantinov,
and A. P. Matyushin
The automatic regulation of processes for the extractive separation of complex mixtures of rare-earth
elements (REE) provides for high-speed checking of the amounts of three or four different REE at specified
stages of the technological process.
An x-ray spectral method [1] was used for conducting such a check. The measurements were made on
the SRF-5 x-ray fluorescent spectrometer on the basis of the K series of the characteristic radiation of the
REE, since the small energy values of the characteristic radiation of the L series (4.6-7.6 eV) would have
made the high-speed analysis much more difficult [2]. The advantages of using the characteristic radiation
of the K series for the analysis of the REE were noted earlier in [3]. In order to avoid the accumulation of
"tails" in determining one of the REE (the range of measured concentrations is 0.05-30 g/liter, and the total
amount varies from 1 to 300 g/liter), a high resolution is required in the spectrometric device, and the SRF-5
instrument provides such high resolution. Although the SRF-5, in order to take account of the matrix effect,
is equipped with an obturator device, which makes it possible to use the standard-and-background method,
in the present case it could not be used, since the specific intensity of the signal and the background does not
vary uniformly when the composition of the matrix varies. For example, determination of lanthanum, cerium,
and praseodymium by the standard-and-background method leads to a deviation of 35-55% between the analysis
results and the true values. The study of the components of the background radiation requires separate con-
sideration. However, the relatively high energy of the characteristic radiation of the K series of lanthanum,
cerium, neodymium, and praseodymium and the similarity of their absorption characteristics were prerequi-
sites for making corrections in the measurement results by using an estimate for the variation of the absorb-
ing properties of the samples investigated and of the standard specimens.
Such an estimate is made by means of an additional scintillation counter, which records a narrow beam
(1.5 mm in diameter) of the primary emission of the x-ray tube and trans illuminates the cuvette with the solution
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp..120-121, February, 1980. Original article
submitted June 25, 1979.
0038-531X/80/4802-0146$07.50 ?1980 Plenum. Publishing Corporation
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TABLE 1. Coefficient of Variation in the
Determination of the Concentration of Various
REE by the x-Ray Spectral Method, Taking
Account of Matrix Effects, %
Cc
La
Nd
oC ncen-
tration
,/liter
Coefficient
of variation
Concen-
Element tration Coefficient
g/liter of variation
Nd
Pr
0,62
3
0,22
3
3
6
being analyzed. The elctrical signals from the scintillation counter are discriminated by a one-channel ampli-
tude analyzer in the -40 keV energy range and are transmitted to a counting device. If we take account of the
fact that the energy resolution of a scintillation counter with an NaI(Tl) crystal (thickness 10 mm) is 30-40%
for an energy of - 35 keV, we can take it that the counter registers radiation with an energy of 30-40 keV.
The characteristic radiation of the Ka t lines of cerium, lanthanum, praseodymium, and neodymium falls into
this energy range. Thus, using an additional counter, we can determine the variation in the absorptive prop-
erties of the samples investigated in the range of energy of the characteristic radiation of the elements being
analyzed.
The measurement of the intensity of the Kat lines of REE on the SRF-5 and the additional transillumina-
tion required 2.5 min and 40 sec, respectively, i.e., the total analysis time is not increased.
An analysis of the solutions for the amounts of the listed REE was conducted on the basis of one standard
specimen with a known content of each element being analyzed. The concentration of the relevant REE in the
sample was calculated by the formula
C det = CoB /same
U
where Cdet is the concentration of the element being determined in the sample; Co, concentration of the ele-
ment determined in the standard specimen; B, ratio of the values of the intensity of the radiation which passed
through the sample and through the standard specimen, measured with an additional scintillation counter;
Isamp, intensity of the Kai line of the determined element in the sample being studied; Io, intensity of the Kai
line of the element being determined in the standard specimen. The accuracy of the method is characterized
by the variation coefficients obtained (Table 1). The lower threshold of sensitivity of the determination of the
concentration of lanthanum, cerium, praseodymium, and neodymium, calculated by the 3a criterion, is 0.02
g/liter.
The above-described method was successfully used in practice in an analytical laboratory and enabled us
to carry out high-speed checks without preliminary preparation of the sample (analysis time - 5 min) on the
lanthanum, cerium, neodymium, and praseodymium content in liquid products of the extractive separation of
REE. This method can be used for determining the amounts of other REE, in particular samarium, europium,
and gadolinium, which makes possible the high-speed checking of the entire technological process of REE
separation.
LITERATURE CITED
1. S. M. Barskii and N. I. Komyak, Apparatura i Metody Rentgenovskogo Analiza, No. 11, 76 (1972).
2. G. I. Rekhkolainen and A. P. Kosinov, ibid., No. 10, 134.
3. G. V. Bondarenko and M. A. Blokhin, Zavod. Lab., No. 4, 531 (1967).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
AXIAL STABILITY OF VVER-1000 REACTOR WITH CONTROL
WITH MINIMUM STANDARD DEVIATION
A. M. Afanas'ev and B. Z. Torlin UDC 621.039.56
The xenon height stability of the neutron field in the VVER-1000 reactor with the rods of the automatic
controller (AC) inserted to various depths and with pickups at various locations was studied in [1]. The
present paper gives the results of investigations on the stability of a reactor which, in addition to an auto-
matic controller, has a height distribution regulator (HDR) based on an auxiliary control rod (CR) or a special
shortened absorption rod (SAR). The HDR was controlled by using either a special ionization chamber (IC),
generating an imbalance signal which sets the CR in motion, or two ionization chambers whose difference sig-
nal causes a displacement of the SAR. Since data from numerous pickups can be used to control the-height
field of the VVER-1000, it is of interest to analyze how this would affect the stability of the reactor.
The analysis was carried'out with the improved IRINA programs (2, 31, making it possible to calculate
the influence function of each CR or SAR on the neutron field as well as to calculate the complex values of the
frequencies of xenon oscillations over a wide range of variation of their real parts. In the calculations we
used the same reactor parameters as in [11 and also deviated somewhat from the calculated [4] power coefficients
of reactivity, (local c j and integral ai) to reduce their absolute values. The resulting decrease in stability
made the reactor more sensitive to the effects studied and permitted a more definite observation of the ten-
dencies in the behavior of the neutron field under a change in the number or position of the pickups.
The reactor stability will be characterized by the die-away time T of the least stable (first) axial normal
mode [2]. In all the examples considered the dying-away process was oscillatory [2]. The period of the oscil-
lations varied from variant to variant and averaged 33 h (with a spread of ?5 h). The algorithm for the opera-
tion of the rods was determined by the requirement that the following condition be fulfilled:
M
Y
jaji(F'i=0, 1=1, 2, ..., N,
(1)
where M and N, respectively, are the numbers of pickups and rods; cpi, deviation of the neutron flux from
the steady-state value at the location of the i-th pickup; and aji, weighting factors. It can be shown that
. M
.mini14pi, i.e., the minimum standard deviation of the neutron flux from its steady-state distribution is attained
if for aij we take 4ji, the value of the influence function of the j-th rod at the site of the i-th pickup. It is
precisely this kind of control of a neutron field with an AC and SAR that Table 1 gives the values of T for
various numbers of pickups, uniformly arranged over the height of the reactor core. The end of the AC rod
and the center of the SAR, whose absorbing part is equal to half the height of the reactor core, are at the
middle of the reactor.
TABLE 1. Values of T for Optimal Control
with AC and SAR, h
at I
ai I
M=3
M=4 I
M=8
M=3*
-0,005
-0,0045
17,2
11,2
11,3
29,0
-0,095
-0,002
0
0
17,9
23,1
11,0
12,4
10,6
10,7
55,2
-36,4'
-Here and in Table 2 the pickups were located at 1/3,
1/2, and 2/3 of the height of the reactor core.
t Here and in Table 2. the time constant of the oscilla-
tions of the neutron field.
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 121-122, February, 1980. Original article
submitted July 9, 1979.
148 0038-531X/80/4802-0148 $07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
TABLE 2. Values of T for Nonoptimal TABLE. 3. Values of T for. Optimal Control
Control with AC and SAR, h with Two CR, h
-0,005
-0,0045 10,5
28,6
-0,005
0 11,2
9,0
8,0
30,4
-0,002
0 15,6
10,8
9,1
-69,4t
0
0 23,5
-0,005
-0,005
-0,002
-0,0045
0
0
10,9
11,5
17,4
8,3
8,3
9,2
7,2
7,1
7,7
Table 2 gives the values of T for the same variants as in Table 1, but here the weighting factors in Eq.
(1) for AC were taken to be unity instead of 1]i. The data of Table 2 permit the conclusion that increasing
the number of pickups not only can improve the quality of the transient process, but can also have a positive
influence on the speed of the control system. The data in the last columns of Tables 1 and 2 are interesting
in that they were obtained with the pickup arranged most closely to each other in the central part of the reac-
tor core. It is easily seen that this resulted in a loss of stability. When a1 = -0.002, the reactor even proved
to be unstable. However, if in this variant the central pickup is disconnected, the system immediately becomes
stable with an oscillation die-away time of T = 18.9 h. The system can be made even more stable if the remain-
ing pickups are moved to the edges of the reactor. Thus, with the pickups placed at 1/4 and. 3/4 of the height
of the reactor core, the die-away time is reduced to 6.9 h. An example of an unsuccessful use of pickups was
mentioned in [1]: the AC rod is actuated by the IC placed in the central part of the reactor core; the SAR is
controlled by a difference signal from the upper and lower IC. In this case, even with al = -0.005 and ai =
-0.0045 the system is unstable with a xenon-oscillation time constant of 44.1 h.
In conclusion, we look briefly at the stability characteristics of a reactor with two CR which ensure con-
trol of the neutron field with minimum standard deviation and which are placed at 1/3 and 2/3 of the height of
the reactor core. Table 3 gives the die-away time T for variants with two and five pickups, arranged uni-
formly over the height, and with three pickups, one of which is at the center and the other two are at a dis-
tance of 1/6 of the core height from the core edges. The data of Table 3 also indicate that increasing the num-
ber of pickups uniformly arranged over the height is conducive to improving the stability and that a noticeable
effect in enhancing the stability can be achieved by moving the pickups closer to the edges of. the reactor core.
1. A. M. Afanas'ev and B. Z. Torlin, At. Energ., 44, No. 6, 530 (1978).
2. A. M. Afanas'ev and B. Z. Torlin, At. Energ., 44, No. 6, 487 (1978).
3. A. M. Afanas'ev and B. Z. Torlin, Preprint ITi-2, Moscow (1978).
4. I. Ya. Emel'yanov, P. A. Gavrilov, and B. N. Seliverstov, Control and Safety of Nuclear Power
Reactors [in Russian], Atomizdat, Moscow (1975).
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
YIELDS OF 181Re, 182mRe, 182Re, 183Re, 184mRe,
184 Re, AND 186Re IN THE BOMBARDMENT OF
TUNGSTEN BY PROTONS AND DEUTERONS, AND
TANTALUM BY a PARTICLES
P. P. Dmitriev and G. A. Molin UDC 539.172.12
Radionuclides of rhenium are obtained with a high yield in "carrier-free" form in the bombardment of
tungsten by protons an d deuterons, and tantalum by a particles. We have measured the dependence of the
181Re, 182MRe, 182Re, 183Re, 184mRe, and 184Re yields on particle energy for a thick tungsten target bombarded
with protons and deuterons with energies up to 22.3 MeV, and tantalum bombarded with a particles with ener-
gies up to 43 MeV. Theoretical yield curves were calculated for 186Re. In measuring the yields of radio-
nuclides the following values of half-lives, energies, and quantum yields of y lines were adopted: 181Re (20 h,
.365.5 keV, 56.4% [1]), 18uRe (64 h, 1121.28 keV, 23% [2]), 182Re (12.7 h, 1121.28 keV, 31.9% [2]), 183Re (700
days, 291.72 keV, 3.31% [3]), 184mRe (165 days, 920.93 keV, 8.3% [4]), 184Re (38 days, 792.07 keV, 37.4% [4]).
The half-lives of the radionuclides are convenient for research and applications.
Stacks of foils were bombarded in the deflected beam of the FEI cyclotron. The tungsten foil was 98
mg/cm2 in thickness, and the tantalum 36 mg/cm2. The energy of the particles after passing through each
foil was determined from data in [5]. The average energy of the particles was determined to within 1.5% by
2000
ci 1750
1500
1250
1000
750
Proton energy, MeV Deuteron energy, MeV
Fig. 2
Fig. 1. Yields of 181Re, t82mRe, 182Re1183Re1184mRe, 184Re, and 186Re as functions of
proton energy for a thick tungsten target: 0) t8tRe; ^) 182mRe (x 5); ?) 182Re; o)
183Re; ^) 184mRe (x 25); A) t84Re; - - -) 186Re.
Fig. 2. Yields of 181Re, 182mRe, 182Re, 183Re, I84mRe, 184Re, and 186Re as functions of
deuteron energy for a thick tungsten target: 0) 181Re (x 2); ^) 18unRe (x 5); r) 182Re;
A) 183Re; ^) 184mRe (x 20); A) 184Re; - - -) 186Re (:10).
Translated from Atomnaya Energiya, Vol. 48, No. 2, pp. 122-124, February, 1980. Original article
submitted July 9, 1979.
ZL
.1120
35 < . V
960
30
6 800
25 s
E
o
640
20
480
15
} 1P 320
0038-531X/80/4802-0150$07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
1600
1400
1200
h
m
e 1000
800
600
4 18 22 26 30 34 38
a-particle energy, MeV
Fig. 3. Yields of 181Re, 182mRe, f82Re, 184mRe, and
184Re as functions of a-particle energy for a thick
tantalum target: 0) 181Re (x 2); 0) 1821n (x 5);
?) 182Re; 0) 183Re; ^) 184mRe (x 100); A) 134Re (x 10).
measuring the absorption of the beam current in aluminum. The radionuclides were identified by y energies
and half-lives. The activity of the nuclides was measured by the photopeaks of selected y lines (in measuring
the activity of 184Re the small contribution of the 1341nRe - 184Re decay branch was taken into account). The
photopeaks were measured on a y spectrometer with a DGDK-50 Al Ge(Li) detector having a resolving power
.(FWHM) of 3.2 keV at, 1332,51 keV (60Co) and 1.7 keV at 122.06 keV (57Co). The photoefficiency of the detector
was found with a set of OSGI radiators. The integrated beam current was determined from the 65Zn activity n
copper monitor foils 18 mg/cm2 thick. From an analysis of the data of [6-8] and our measurements of the
relative behavior of the excitation functions, the following values of the monitor reactions were adopted:
?6Cu(pn)68Zn, a = 46 mb, E = 22.5 MeV;
6'Cu(d2n)6'Zn, a = 525 mb, Ed 22. = 5 MeV;
89Cu(a, pn + 2n), a = 325 mb, Ea = 44 MeV
Figures 1-3 show the experimental values of the nuclide yields. The error in measuring the yields is 12-14%,
and is due mainly to systematic errors in measuring the activity and integrated current. Strong interference
of the 182Re y lines of nearly the same energy prevented the measurement of the 186Re activity by the photopeak
of the 137.15 keV y lines, and therefore the 186Re yield curves were calculated theoretically as in [9] (r0 =
1.3 fermi).
When tungsten is bombarded with protons and deuterons 186mRe (Ti/2 = 2.0 years) is formed also.
The spins of 186mRe and 184mRe are both 8+, and an estimate of the 186mRe yield from the 184mRe yield [only
for the (p, n) and (d, 2n) reactions] gives a 186mRe yield of 2.7 ? 10-8 ?Ci/?Ah for protons and 8.9 .10-7 ?CilpA - h
for deuterons, both at 22 MeV.
Some data on yields and cross sections with the formation of rhenium nuclides are given in [10-13].
Hermes et at. [10] measured the excitation functions of the 181Ta(a, 2n)183Re reaction up to E. = 48 MeV,
181Ta(a, 3n)182(m+q)Re up to Ea = 58 MeV, and 181Ta(a, 4n)181Re up to Ea = 80 MeV. Integration of the excita-
tion functions gives 10.8 and 263 ?Ci/?Ah, respectively, for the 183Re and l81Re yields at Ea = 43 MeV, which
are in satisfactory agreement with our results. At Ea = 80 MeV the 181Re yield is 2900 ?Ci/?A ?h. Since the
(a, 3n) cross sections for 182nRe and 182Re are not reported separately in [10], we cannot compare these data
with ours.
The excitation functions of the 186W(d, 2n)186Re reaction were measured by Pement and Wolke [11] at
energies up to 14 MeV, and by Nassiff and Menzel [12] for energies up to 16.7 MeV. The values of the cross
sections in [12] are approximately twice as large. Our theoretical calculations are in good agreement with
data in [11]. For example, the cross section at the maximum of the excitation function is 380 mb according to
our data, and 350 and 647 mb, respectively, according to [11, 12]. Nassiff and Menzel measured the activity
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 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030002-2
of '86Re by the photopeak Ey = 137.15 MeV, and the overestimate is possibly related to the background of i82Re
y lines of nearly the. same energy. Pement and Wolke bombarded a W target enriched to 97.2% in 186W, and
:measured the 186Re activity by 0 radiation. The yield curves for 183 Re and 184Re in the bombardment of tung-
sten by 22 MeV protons and deuterons given in [13] differ appreciably from our results. It is difficult to indi-
cate the reasons for these differences, since it is stated in [13] that the values of the quantum yields of y lines
in the measurements of the activity of 183Re and 184Re were taken from [14], but only the relative intensity of
the y radiation for 183Re and 184Re is given in [14].
The authors thank Z. P. Dmitrieva for performing the calculations.
1. N. G. Gusev and P. P. Dmitriev, Quantum Radiation of Radioactive Nuclides [in Russian], Atomizdat,
Moscow (1977).
2. M. Schmorak, Nucl. Data Sheets, 14, 559 {1975).
3. A. Artna-Cohen, Nucl. Data Sheets, 16, 267 (1975).
4. M. Martin and P. Stetson, Nucl. Data Sheets, 21, 1 (1977).
5. C. Williamson, J. Boujot, and J. Picard, Rapport CEA-R, 3042 (1966).
6. P. P. Dmitriev et at., At. Energ., 24, 279 (1968); R. Colle et at., Phys. Rev., C9, 1819 (1974).
7. P. P. Dmitriev and N. N. Krasnov, At. Energ., 18, 184 (1965); C. Fulmer and I. Williams, Nucl.
Phys., A155, 40 (1970); D. Williams and J. Irvine, Phys. Rev., 130, 265 (1963).
8. N. Porile and D. Morrison, Phys. Rev., 116, 1193 (1959); F. Houck and J. Miller, Phys. Rev., 123,
231 (1961).
9. P. P. Dmitriev et at., At. Energ., 32, 426 (1972).
10. F. Hermes et al., Nuci. Phys., A228, 165 (1974).,
11. F. Pement and. R. Wolke, Nucl. Phys., 86, 429 (1966).
12. S. Nassiff and H. Menzel, Radiochim. Acta, 19, 97. (1973).
13. I. 0. Konstantinov et al., At. Energ., 44, 183 (1978).
14. W. Bowman and K. MacMurdo, Atomic Data, Nucl. Data Tables, 13, 285 (1974).
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