THE SOVIET JOURNAL OF ATOMIC ENERGY VOL. 8 NO. 1

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• Document Creation Date: December 27, 2016
• Document Release Date: February 19, 2013
• Sequence Number: 1
• Publication Date: April 1, 1961
• Content Type: REPORT

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Volume 8, No. 1
THE SOVIET JOURNAL OF
' April. 1961
OMICI ENERGY
ATONHa51
1-leprlisi
rlAXSLA F.)) [[OM
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EDITORIAL BOARD OF
ATOMNAYA ENERGIYA
A. I. Alikhanov
A. A. Bochvar
N. A. DollezhaP
D. V. Efremov
V. S. EmePyanov
V. S. Fursov
V. F. Kalinin
A. K. Krasin
A. V. Lebedinskii
A. I. Leipunskii
I. I. Novikov
(Editor-in-Chief)
B. V. Semenov
VI. Veksler
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
A. P. Zefirov
THE SOVIET JOURNAL OF
ATOMIC ENERGY
A translation of ATOMNAY A ENERGIY A,
a publication of the Academy of Sciences of the USSR
(Russian original dated January, 1960)
Vol. 8, No. 1 April, 1961
CONTENTS
Influence of the Reactor Temperature Characteristics Upon the Choice of the Optimum
PAGE
RUSS.
PAGE
Thermodynamic Cycle of an Atomic-Electrical Generating Station. D. D. Kalafati . .
1
5
Number of Neutrons Emitted by Individual Fission Fragments of U235. V. F. Apalin,
10
15
Yu. P. Dobrynin, V.P. Zakharova, I. E. Kutikov, and L. A. Mikaelyan
Method of Estimating the Critical Parameters of a Body of Arbitrary Shape Made from
Fissionable Material. V. G. Zagrafov
17
23
Removal of Oxides from Sodium and Tests for the Oxide Content. P. L. Kirillov, F. A.
Kozlov, V. I. Subbotin, and N. M. Turchin
23
30
On the Change in the Color and Transparency of Glasses when Bombarded by Gamma Rays
from a Co69 Source and in a Nuclear Reactor. S. M. Brekhovskikh
29
37
LETTERS TO THE EDITOR
Mass-Spectrometric and Spectroscopic Studies of Hydrogen Discharge of an Ion Source.
A. I. Nastyukha, A. R. Striganov, I. I. Afanas'ev, L. N. Mikhailov, and M. N. Oganov
35
44
New Isotopes of Holmium and Erbium. N. S. Dneprovskii
38
46
Fission Cross Section of Th229 for Monochromatic Neutrons in the 0.02-0.8 ev Region.
Yu. Ya. Konakhovich and M. I. Pevzner
39
47
Mean Number of Prompt Neutrons per Spontaneous Fission of U238. E. K. Gerling and
Yu. A. Shukolyukov
41
49
The Effect of Boron-Containing Layers on the Yield of Secondary Gamma Radiation.
D. L. Broder, A. P. Kondrashov, A. A. Kutuzov, and A. I. Lashuk
42
49
Critical Heat Flows in the Forced Flow of Liquids in Channels. A. A. Ivashkevich
44
51
Investigation of Heat Transfer in the Turbulent Flow of Liquid Metals in Tubes. M. Kh.
48
54
?Ibragimov, V. I. Subbotin, and P. A. Ushakov
Determination of Melting Points of Binary Mixtures of Uranium Oxides with Other Oxides
in Air. S. G. Tresvyatskii and V. I. Kushakovskii
51
56
The Distribution of Iron in Microvolumes of Zirconium Alloys. P. L. Gruzin, G. G. Ryabova,
53
58
and G. B. Fedorov
Reactions of Nitrogen Dissolved in Water, by the Action of Ionizing Radiations.
M. T. Dmitriev and S. Ya. Pshezhetskii
56
59
Method of Calculating Dosage Field of Powerful Isotopic Units. N. I. Leshchinskii
59
62
Integrating Detector of Penetrating Radiation. 0. A. Myazdrikov
62
64
Measurement of Co69 y -Ray Dose Close to the Boundary between Two Bodies.
V. I. Kukhtevich, B. P. Shemetenko, and B. I. Sinitsyn
64
66
On the Efficiency of Gas-Discharge Counters. V. P. Bovin
67
68
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? 1961 Consultants Bureau Enterprises, Inc., 227 West 17th St., New York 11, N. Y.
Note: The sale of photostatic copies of any portion of this copyright translation is expressly
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CONTENTS (continued)
PAGE
RUSS.
PAGE
Airborne Radiometer-Analyzer. V. V. Matveev and A. D. Sokolov
70
70
Investigation of the Productio4 of an Electromotive Force in a System of Semiconductors
with Uranium during Irradiation in a Reactor. Yu. K. Gus'kov, A. V. Zvonarev;
73
72
and V. P. Klychkova
NEWS OF SCIENCE AND TECHNOLOGY
International Symposium on the Metrology of Radioactive Isotopes. K. K. Aglintsev and
V. V. Bochkarev
76
76
International Conference on Accelerators. A. N. Lebedev . . . .
78
78
At the Institute for Physical Methods of Separation (German Democratic Republic).
N. M. Zhavoronkov and K. I. Sakodynskii
80
81
[Uranium Production in Canada during 1958
82]
[Use of Ammonium Molybdophosphate in Treating Fission Waste Solutions . . . .
84]
Building and Designing of Atomic Powered Vessels in Western and Eastern Countries.
A. V. Klement'ev
82
85
Brief Communications
84
86
BIBLIOGRAPHY
New Literature
85
88
NOTE
?
The Table of Contents lists all material that appears in AtomnayaEnergiya. Those items
that originated in the English language are not included in the translation and are shown en-
closed in brackets. Whenever possible, the English-language source containing the omitted
reports will be given.
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INFLUENCE OF THE REACTOR TEMPERATURE CHARACTERISTICS
UPON THE CHOICE OF THE OPTIMUM THERMODYNAMIC CYCLE
OF AN ATOMIC-ELECTRICAL GENERATING STATION
D. D. Kalafati
Translated from Atomnaya fnergiya,Vol. 8, No. 1, pp. 5-14, January, 1960
Original article submitted November 18, 1958
In this article we investigate the possible temperature changes in a nuclear energy station as
a function of the thermal power of the reactor when there are two limiting temperatures: for
the shell and for the center of the heat-emitting elements. We find the changes in the al-
lowed thermal and electrical power of the unit as a function of the parameters of the thermo-
dynamic cycle. We give the reader an understanding of the boundary thermal power of the
reactor and the efficiency of the generator.
We also give the conditions under which the formulas which we have derived may be
used for a preliminary calculation of the optimum parameters of the thermodynamic cycle.
Our analysis gives the curves which show the increase in the parameters and the efficiency
of the electrical generating station as a function of the material of which the shell is con-
structed and of the type of nuclear fuel used.
Changes in the initial parameters of the thermody-
namic cycle of atomic-electrical generating stations and,
consequently, of the temperature of the heat carriers leads
to changes in the thermal power of the reactor as well as
to changes in the efficiency of the cycle; therefore, the
optimum parameters of the thermodynamic cycle and of
the heat carriers are determined only by a simul-
taneous analysis of the operating conditions of the
cycle and the reactor. Besides, in order to calculate the
thermal operation of the reactor we must first know the
optimum initial parameters of the cycle and of the heat
carriers. This is difficult to do merely by means of varia-
tional calculations.
The following formula (1) was obtained on the ba-
sis of using the condition of minimum cost of electrical
energy In a preliminary calculation of the optimum
mean temperature of the heat supply for the heat cycles
in the steam turbines of the atomic-electrical generating
stations
711V
(1)
where T1. is the limiting temperature of the shell Tls. or
of the center T& of the heat-emitting elements (HEEL)
of the reactor; T2 is the temperature in the condenser;
z= nt + CT (nt is the thermal efficiency of the cycles, or
is the thermal component of the cost of the electrical
energy).
For a small thermal component where we can as-
sume that or = 0, formula (1) corresponds to the condi-
tion of maximum electrical power of the generating
station [2]:
T ?I) yin = "771772-4K (2)
Formula (2) gives the value of the optimum mean
temperature not of the heat carriers, as in the formula
obtained by G. Melets [3, 4],but of the thermodynamic
cycle. As a result of the completely identical results for
limiting temperatures of the center and periphery [1, 2],
in formulas (1) and (2) the temperature Trimust corres-
pond to the limiting shell temperature or the limiting
center temperature and which of the temperatures is
the limiting one in a given reactor. Since the optimum tem-
perature of the cycle differs basically, it is necessary to estab
lish which optimum is preferable for nuclear energy in-
stallations: that determined on the basis of the limiting
temperature of the shell or that determined on the basis
of the limiting temperature of the center.
In addition to this we often assume that the optimum
temperatures exist simultaneously at the periphery and at
the center. The question then arises as to how we can in
such a case, determine the optimum cycle parameters.
Possible Temperature Characteristics of
the Nuclear Energy Station
Let us examine the possible temperature changes in
a given nuclear energy installation for changes in the
1
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thermal power of the reactor, due to,changes in the ini-
tial parameters and to the thermodynamic cycle. Let the
form, the surface, the number of HEEL be given and let
us choose the velocity and consumption of heat carriers.
Under these conditions, the thermal power of the reactor
is proportional to the difference in the limiting tempera-
tures of the shell (or center) of the HEEL and the average
temperature of the heat supply pipes in the cycle [1]:
1 m
Qr = kr nkr Fs (4) (Tr - Tic), )
(3)
where kr is the coefficient of nonuniformity of heat em-
ission with respect to the reactor radius, Li is the number
of HEEL, kt is the coefficient of heat transmission, Fs is
the surface of the HEEL, and co is the coefficient of utili-
zation of the possible reactor power.
The electric power of the station is equal to
Pe = Qr esrt ? A Psn = kr n kt Fs co (Trl Tay) X
T2 cy
(1- ril ) nri Tim Psn
Ti cy
where nri nm g Is me product of three efficiencies:
the relative inner, the mechanical and the generator ef-
ficiency; and APsn is the power required for the ppera-
don of the station. If we change the thermal power Qr
for the given constant thermal resistances of the HEEL,
constant heat transmission to the heat carriers and the
steam generator, then all the temperature drops in the in-
dicated elements change proportionally to the thermal
power of the reactor. However,the temperature changes
of these elements cannot be the same (Fig. 1) since they
depend upon the conditions under which the changes oc-
cur in the thermal power of the reactor.
For a small thermal power( Zone I) an increase in the
thermal flux leads to an increase in all the temperatures
of the unit except the condenser temperature Twy =
const. In Zone I an increase in the thermal power of
the reactor leads to an increase in the average tempera-
ture of the cycle, i.e., in this zone there is no maximum
electrical power. In the indicated zone we may operate
reactors that are used for study purposes,but as far as the
operation of power reactors is concerned ,it is always ad-
vantageous to increase the thermal power until the maxi-
mum peripheral power Tax up to the limiting value.
A further increase in the thermal power of the reactor
must occur for Ti = const. .This can only be accomp-
lished by lowering the mean temperature of the heat
carriers in the cycle,while at the same time increasing
the maximum temperature of the center HEEL Tglax.
Since in this process the thermal power increases and
the cycle efficiency drops, then in Zone II, according to
equation(4),we get the maximum electrical power of the
station which corresponds to the optimum mean tempera-
ture of the cycle,equation(2), if we substitute in the for-
mula Tis. for T. Then the point &corresponding to the
optimum thermal reactor power, is determined by the
(4)
r, ?c
600r
400
200
0 Qp QFnax
Fig. 1, Possible temperature changes in a nuc-
lear energy installation with qv in Zone IL
PePr
WO 'X
80
60
40
10
0
T2 cy
Ill
/p eMaX II
p
100 ToPy m 200
c m
T ?C
Fig. 2:Dependence of the thermal and elec-
trical power of a reactor with TIT m in Zone
cy
II upon Trey .
point of intersection of the lines of the optimum and al-
lowed temperature cycles (see Fig. 1).
The dependence of the thermal and electrical pow-
er of the station upon the average temperature of the
cycle for one limiting temperature of the shell or of the
HEEL of the center is discussed in papers [1, 21. For two
limiting temperatures,the allowed changes in the ther-
mal and electrical power have been computed from equa-
tions (3) and (4), for the case of an optimum in the av-
erage power Zone II, as a function of the mean tempera-
ture of the heat conductor for the cycle Tlxciy and are
shown in Fig. 2. We can see from Figs. 1 and 2 that an
2
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increase in the thermal power in Zone II for 11 = const
is possible until we reach the limiting temperature of
the center of the HEEL, after which possible changes in
thermal and electrical power can occur only for Tic=
const, i.e., in the high thermal power Zone HI. in this
case we must substitute Tic for '4 in equations(3) and (4).
Since the limiting shell temperature is bounded by
the quality of the materials used or the properties of the
heat carriers and often does not exceed 300 - 400?C,
then for a condenser pressure p2 = 0.04 atm as = 28.6?C)
and4 = 300?C we get from equation (2):
1 2yrn 17573.302 416 ?R= 143?C,
this corresponds (for the cited temperature range of the
shell) to a saturated steam cycle with an initial pressure
of 5 - 10 atm. Such steam parameters would lead to low
efficiencies (of the order of 2090 and less),therefore the
operation of atomic-electrical generating stations in
Zone II would not be economical. For the same thermal
reactor power an increase in the efficiency of the station
(the factor nisy in equation(4)] increases proportionately,
or lowers the specific capital losses. For a given electri-
cal power for the station using nuclear fuel, i.e.,
for the same depth of burning (degree of fuel utilization),
the duration of the reactor charge is directly proportion-
al to the efficiency of the station. Therefore an increase
in the efficiency of atomic generating stations is signi-
ficant even for the small fuel cost component of elect-
rical generating stations.
Since the limiting temperatures of the center of
the HEEL are significantly higher than those of the shell
(from Tic = 660?C for metallic uranium to T 2800?C
2800?C
for uranium dioxide) then the optimum mean tempera-
ture of the heat conductor during the cycle, as given by
formula (2) according to the limiting temperature of the
center of the HEEL, increases discontinuously as for
T, ?C
600 Zone I Tgla
Zone II
400 - Ts'
'Tic
Zone III
200
200 -
T2 cy
b op
Qs Qc Or
Fig. 3, Possible temperature changes in a nuclear en-
ergy installation with TfPcIT in Zone
example, for Tio = 1000?C, 'gym= 41273-302 = 623?K
= 350?C. This mean temperature necessitates the use of
steam with ultra-high parameters ,with station efficiency
of the order of 40% which is twice as great as the effi-
ciency of the station during operation in Zone II. In
connection with this it is expedient to tale such possible
temperature characteristics of the nuclear energy instal-
lation so that the lines of the optimum and possible temp-
erature cycles cross in Zone II and in Zone III; in Zone
III both the thermal power of the reactor and the opti-
mum cycle efficiency are greater (Fig. 3).
Upon reaching the limiting temperature of the
shell and of the center of the HEEL simultaneously, the
thermal power, which we shall henceforth call the
boundary thermal power of the reactor, dr), does not as
)et reach its maximum possible value, as has sometimes
been indicated in the literature, but lies only at the be-
ginning of Zone III. A further increase in the thermal
power of the given reactor in Zone III for Tcl = const is
possible if we decrease the maximum shell temperature
as well as the mean temperatures of the cycle and of the
heat carriers.
Possible changes in the thermal and electrical po-
wers of the nuclear energy installation in the presence
of an optimum in Zone III as a function of the changes
in the mean temperature of the cycle are given in Fig.
4. As we see from the figure,if we increase the mean
temperature of the cycle, when operating in Zone HI,
the electrical power of the installation increases at first,
reaches a maximum ITV (determ ined from equation
(2) by substituting ?I'? for T),and then decreases. After
we reach the boundary thermal power of the reactor,
changes in the thermal and electrical power are possible
only for the conditions of Zone U.
Thus the economy in the operation of atomic elec-
trical generating stations operating in Zone III at a high-
er thermal power and greater efficiency is significantly
Pe,Or
700X
BO
40
20
0
T2cy 100
max
TT
e
200 igy 300 Timcy.
Fig. 4. Dependence of the thermal and electrical po-
wer of a reactor with TPN,n in Zone III upon Tfacy.
3
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greater than that for electrical generating stations oper-
ating in Zone II where the optimum cycle parameters
are determined by the limiting temperature of the shell.
Therefore the best conditions for the operation of atom-
ic-electrical generating stations are the conditions
prevailing in Zone III where the optimum cycle para-
meters are determined by equation(2) according to the
limiting temperature of the center of the HEEL. Since
in Zone III the temperatures of the shell and cycle de-
crease relatively slowly, it is more probable that the
operation in Zone III will be in the vicinity of point M ,
(Fig. 5).
Due to the independence of the coefficients of con-
ductivity and thermal emission of the mean temper-
ature,the possible temperature characteristics take the
form of line segments. Fig. 3. If the indicated coeffi-
cients change somewhat with temperature, then these
lines will have an insignificant curvature,but the shape
of the diagram and the division of the characteristics
into three characteristic zones will not change. We
wish to underline the fact that the diagram we have
shown is not a diagram of the changing mode of opera-
tion of the reactor during power regulation in the ex-
ploitation process (for example, at average heat carrier
temperatures T cont, corm,. see dotted line in Fig. 1) but
the characteristic temperature changes in the unit due
to the choice of thermal power of the reactor.
Fig. 5. Possible temperature changes in a nuclear
energy installation for a reactor operating with
c?b
Limiting Thermal Power of the Reactor
and Greatest Electrical Power of the
Station
Depending upon the relationships between the limit-
ing temperatures of the shell and the center, the rela-
tionships between the thermal resistances of the HEEL,
4
the processes of heat transfer to the thermal carriers and
the resistances of the steam generator, an intersection of
the lines giving the possible changes in the mean tem-
peratures of the cycle with the lines of optimum mean
temperature in Zone III is not always possible. In par-
ticular,this is impossible when the limiting temperature
of the shell of a given reactor in Zone III is lower than
the optimum mean temperature of the cycle according
to (2) with respect to the limiting temperature of the
center, i.e., if
Tj ;cy > Ts' ?
The indicated temperature relationship occurs,for
example,in uranium dioxide water-water reactors.
Since,for WWER (water-water element reactors) Tic =
2200?C and due to the absence of the boiling away of
the heat carriers for PT = 100 atm,it follows thatTis-
309?C [5]. Then according to the equation(5)
(5)
1/2473.302=860?K > 582?K,
i.e., for the indicated type of reactor it is impossible to
obtain the optimum mean temperature of the cycle in
Zone III,clue to the low limiting temperature of the
HEEL of the shell. For this case, the mean temperature
of the cycle must be as near as possible to the limiting
temperature of the shell, since it is entirely expedient
to raise the possible temperature characteristics,and the
extent to which they are raised is limited only by the
necessary optimum temperature drop in the steam gen-
erator &msg. The temperature characteristics of such a
unit are shown in Fig. 5, while the possible changes in
thermal and electrical power,as a function of the mean
cycle temperature or of the heat carriers,are shown in
Fig. 6. For the case under consideration,there is no
maximum electrical power either in Zone II or in Zone
III, since the limiting temperatures of the HEEL of the
shell and center are reached simultaneously for the
point when, in one of these zones, the maximum is ob-
talaed. Howeve4 on the boundary of Zones II and III,
for the limiting thermal power of the reactor, the great-
est electrical power is obtained at the point of intersec-
tion of the curves which show the changes in electrical
power in Zones II and III (Fig. 6).
The optimum mean temperature of the cycle, cor-
responding to the value of greatest electrical power, is
always located between the two values of optimum
mean temperature of the cycle which are determined
from equation(2) if we substitute first the value of the
limiting shell temperature and then the limiting temp-
erature of the center of the HEEL. The value of the
mean temperature of the cycle corresponding to the
maximum electrical power cannot be found from equa-
tion (2). Therefore,the attempt [6] to find Pglax by in-
troducing, in equation(2), the limiting temperature of
the shell plus a correction factor cannot be successful.
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However,for the case of the limiting thermal power we
get from the condition of the simultaneous existence of
the limiting temperatures of the shell and of the center
of the HEEL a single-valued determination of the mean
temperature of the heat carriers. This solves the problem.
For this case the optimum mean temperature of the
cycle is determined from the expression
Top
icm b _Atom
y
(6)
If,for the maximum electrical power there was a
flat part of the power curve for which it would be pos-
sible that a small deviation of the mean temperatures of
the cycle and of the heat carriers from the optimum
would not result in a drop in the electrical power?then
the derivative dl3e/dTrcy would have a discontinuity.
At this point E on the electric power curve we get a sharp,
peak (see Fig. 6) Therefore, even a small deviation of
the mean temperature of the heat carriers from the op-
timum can lead to a noticeable lowering of the electri-
cal power of the installation. For example, the maxi-
mum temperature of the center of the HEEL, 1200?C,
for the atomic generating station in Shippingport [7],
had not yet reached the limiting value for uranium dio-
xide, i.e., the steam pressure p1 = 39.2 atmospheres,
which was too high for the given installation, corresponds
to point III on Fig. 6, and does not insure the maximum
possible electrical power of the station.
Thus in the case under study, when the limiting
temperature of the center of the HEEL is reachethit is
expedient to raise the temperature characteristics for the
mean cycle temperature, but if for the given installation
max .
Tc < T . c, Is expedient to lower the mean tempera-
/00
III pill.
80
pmax
too ??,2120 m 300
Ticy ?C
Fig. 6. Dependence of the thermal and electrical
power of a reactor with Qllupon
ture of the cycle so that the limiting temperature of the
center is not reached.
Power Efficiency of the Steam Generator
For the greatest electrical power output of the in-
stallation there is a boundary value for the thermal power
of the reactor,but for a constant consumption of heat
carriers there exists a mean temperature to which the
heat carriers are raised. For this case,changes in the pa-
rameters and in the efficiency per cycle of the installa-
tion can occur only as the result of changes in the temp-
erature drop within the steam generator due to changes
in its surface heating or in the coefficient of heat trans-
mission kht.
11, duringalternations in the thermal power of the
reactorichanges in the steam generator temperature drop
influence the coefficient of utilization of the thermal
power of the reactor [1, 2]:then for a limiting thermal
powers changes in the mean temperature drop in the
steam generatoridue to changes in its surface heattin-
fluence only the changes in the thermal efficiency of the
cycle.
Evaluations made in the literature regarding the
quality of the steam generator sometimes make use of a
value of the steam generator which takes into account
the heat losses.These can usually be neglected.
For a given reactor,thermal power Qii?= const due to
the fact that the heat exchange process in the steam gen-
erator is not reversible, the index of thermodynamic per
of the steam generator must be set up not in
terms of the heat but in terms of the power efficiency of
the steam generator and be equal to the ratio of the max-
imum work capability of the heat,before and after the
heat exchange in the steam generator:
ALCY
ifn
sg A L [ev iirtev
m ?7;c) 71)13(7)
? T20),) 72),'
where ALF represents the operation of an ideal steam
cycle (Fig. 7) and ALrtev represents the maximum pos-
sible work capability of the heat received by the heat
carrier, which is equivalent to the operation of the re-
versible cycle,abcda,with an alternating temperature in
the heat carrier heat supply. The work ratio in equation
(7) is equal to the ratio of the efficiencies of the steam
and reversible cycles expressed in terms of the tempera-
ture,since they represent the same amount of supplied
heat.
In order to evaluate the thermodynamic perfection
of the steam generators in atomic-electrical generating
stations, we wish to point out, for example, that the pow-
er efficiency of the steam generator for a station with
(WWER) computed from equation (7) is = 0.92,that
for the atomic icebreaker "Lenin ? is trn =0.835, i.e.,
sg
the power efficiency of the steam generators is close to
the thermal efficiency of the boilers. The optimum
5
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T,?C
700 ?
600 -
500 -
400 -
300
200
100
T2h
0
1.0
1.5
Fig. 7- Loss in the working capability of
the heat during nonreversible heat exchange
in the steam generator.
temperature drop in a steam generator is uniquely de-
termined by comparing the surface heating of the steam
generator and the energy losses during heat exchange,
however, this requires a special derivation.
Influence of the Fuel Component Cost of
Electrical Energy Upon the Optimum
Cycle Parameters
Previously we have, for simplicity.examined in-
stallations in which the cost of the fuel components of
the electrical energy was so small that it could be neg-
lected, i.e., for which the optimum parameters were de-
termined by the condition of maximum electrical pow-
er.
When the cost of the fuel component reaches 0.1
- 0.2 and higher,the optimum mean temperature of the
cycle must be determined from the condition of the
minimum electrical energy cost. Changes in the cost
of the electrical energy may be expressed as a function
of the electrical power and the efficiency of the station
K V
Ce -=CKf CT = ? cents/kw hour, (8)
where K denotes the capital outlay7amortization, sal-
aries, and other, exploitation expenses which are propor-
tional to time and computed per hour of operation of
the atomic power generating station,and V is the cost of
nuclear fuel used per kilowatt hour of heat generated.
The optimum mean temperature of the cycle, tak-
ing the cost of the nuclear fuel into account for K
constiis determined from equation(1). This preserves all
the previously obtained conclusions regarding the influ-
6
ence of the possible temperature characteristics of the
installation upon the optimum mean temperature of the
cycle.
The optimum mean temperature and efficiency of
the cycle corresponding to a minimum cost of electri-
cal energy for ? either Zones n or III (determined res-
pectively from the 1},tniting temperature of the shell and
the central HEEL) will be somewhat higher than the
temperature and the efficiency corresponding to maxi-
mum electrical power (2). .
However, if the unit operates at the limiting ther-
mal reactor power,then as a result of the discontinuity
in the power derivative dPeklincy at the point E (see
Pig. 6) then the derivative of the costs dCe/dTFIcy will
also have a discontinuity at this point. Instead of ob-
taining the minimum cost for the limiting thermal reac-
tor power, we will get the minimum value of the cost of
the electrical energy (except for the boundary portions
at points M and P, Fig. 5). Thus,for the limiting ther-
mal power of the unit the maximum electrical power
usually coincides with the condition of minimum cost
of electrical energy.
For uranium,for Tic= 650?, cT = 0.40 and Tit =
0.45, the coefficient z is 0.18. Under these conditions,
the optimum mean temperature of the heat supply is
equal to
m y923.302
q? = 585? K = 312?C.
PcY 1-0.18 =
At the same time for the cycle we have used for pi
= 90 atm, t1 = 500?C and th = 215?C (temperature to
which the water is heated), the mean temperature of the
heat supply is given by:
iiin ___ 810.1-220,4
Tm - ? 585? K=312? C.
cy sn 1.5934-0.5866
It follows from the example cited, that the optimum
initial cycle parameters for atomic?electric generating
stations,using metallic uranium with T1 = 650?C as de-
termined from the conditions for the minimum electri-
cal energy cost,consist,for example,of 90 atm pressure
and 500?C. For the type of fuel considered a further in-
crease in the initial steam parameters would be inad-
visable. This conclusion coincides with the data of the
project for the possible improvement in the cycle of an
atomic-electric generating station using uranium with a
sodium graphite reactor SGR [8]; in this project an in-
crease in the initial steam parameters from 56 atm
(440?C) to 88.5 atm (510?C) was foreseen. In this pro-
cess the electrical power of the station does not increase,
and an increase in the steam parameters results only in
a decrease in the cost of the electrical energy. A fur-
ther increase in the cycle parameters was advisable only
for an increase in the temperature of the central HEEL,
i.e., in the case where another nuclear fuel or an alloy
with a greater limiting temperature was used.
? The amortization time of an electrical generating
station is taken as eight years.
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The Line of Optimum Temperatures for
the Heat Supply During the Operating
Cycle of an Atomic-Electric Generating
Station
All the positions which we have examined for the
line giving the optimum mean cycle temperature in the
various zones,can be connected with one line of opti-
mum mean cycle temperatures in 'Mr coordinates,
this is the heavy line in Fig. 8.
The point of intersection of the line of possible
temperature characteristics of the cycle, which can be
drawn during the planning of the unit, with the line of
optimum cycle temperatures will correspond to the op-
timum operating conditions of the given atomic-elec-
tric generating station. For the case of operation at the
limiting thermal reactor power, the point of intersection
of the possible changes in the mean temperature of the
heat carriers with the vertical portion of the line giving
the optimum conditions corresponds also to the mean
optimum temperature of the heat carriers.
If we take into account the component giving the
fuel costs of the electrical generating stations,the line
showing the optimum cycle temperature in Zones U and
III is raised,depending upon the coefficients z = cfnt in
formula (1); this corresponds to the dotted lines in Fig.
8. We wish to underline however,that all the points on
the optimum temperature line of the cycle are of equal
weight. The best conditions, which insure simultaneous-
ly the maximum thermal power and efficiency of the
unit,lie in Zone III near point M.
The optimum mean temperatures of the cycle or of
the heat carriers,for a given nuclear energy installation
having a given form of, number of and type of surface
TI 'C
1200
1000
Tcmax
800
600
400
100
0
Zone I
Zone II Zone III
Tsma
Fig. 8. Line of optimum temperatures for 'lay?
of an atomic-electric generating station.
HEEL, and with a given velocity and utilization of heat
carriers and with a constant surface heating of the steam
generator, were considered previously. .
If the characteristics of the possible temperature
changes in a nuclear energy installation do not insure
an optimum mean cycle temperature in Zone III (de-
termined by equation (2) from the limiting center tem-
perature),then we should raise the line of the possible
temperature characteristics of the heat carriers in the
cycle by changing the ratios of the thermal resistances
of the HEEL, the heat transmission to the heat carriers,
and the steam generator resistance, in order to insure the
choice of the optimum parameters. Such an increase in
the temperature characteristics of the heat carriers and
of the cycle is possible if we change the diameter and
heat conduction of the HEEL, the surface temperature of
the steam generator,and the coefficient of heat trans-
mission, depending upon the speed and parameters of
the heat carriers and the working substance. It is pos-
sible to entirely eliminate Zone II and obtain only Zone
III and its left boundary.
The method of obtaining more favorable thermody-
namic operating conditions for the nuclear energy in-
stallation consists in raising the possible temperature
characteristics. The expediency of such an increase in
the indicated characteristics must be verified by cal-
culations.
In order to evaluate the applicability of the pre-
viously derived conclusions,we show in Fig. 9 curves of
the optimum mean temperatures of the heat supply dur-
ing the cycle computed from equation (1) as a function
of the limiting temperature of the shell and of the cen-
tral HEEL and the fuel cost component of the electrical
energy. Points 1 - 17 , Fig. 9, correspond to given
mean temperatures of the thermodynamic cycles of the
constructed or proposed electric generating stations
listed in the table.
The computations for points 1 - 4 (Fig. 9),which
we have carried out either as examples or to be used for
double-purpose stations agree well with the theoretical
curves computed using the limiting shell temperature;
and points 5 - 11 characterize stations using uranium as
a fuel,computed using the optimum cycle temperature
for the limiting temperature of the central HEEL and for
a fuel cost component of electrical energy from 0 ?
30%.
When we considered the case of uranium dioxide
as the nuclear fuel,we assumed that the temperature of
the center was 2200 - 2760?C,and that the optimum
mean temperature of the operating cycle of the atomic-
electrical generating station (points 12 - 17, Fig. 9)
was higher than the limiting temperature of the shell.
Therefore such stations operate at the limiting thermal
reactor power.
For a limiting temperature of the central HEEL,of
the order of 1000 - 1200?C, the optimum parameters
7
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Mean Temperature of the Heat Supply over the Heat Cycles in the Installation
Londition
Point No.
(see Fig.9)
Name of Reactor or Station
1 ?C
'. ,
T m
icy. ?C
1
Uranium-graphite reactor (calculations in
For a limiting tempera-
2
[9])
230
118
ture of the shell HEEL
Uranium-graphite reactor (calculations in
300
137
3
[4])
4
Two-purpose reactor at Marcoule (France)
400
408
157
165
Reactor at Calder Hall (England)
5
First atomic generating station (USSR)
370
185*
6
Station at Henderstone (England)
569
227
7
Heavy water reactor with organic heat car-
riers (Switzerland)
600
224
8 tkanium-graphite reactor using super-
For a limiting temper
heated steam (USSR)
550
312
9
I
Sodium-graphite reactor at Santa Susana
ture of the central
(USA)
642
245
HEEL
/0
Reactor SGR (USA), variation 1 [8]
650
269
10'
Reactor SGR (USA), variation 3[8]
650
297
11
Reactor "Enrico Fermi" (USA), variation 1
713
262
11'
Reactor "Enrico Fermi" (USA), variation 2
713
287
12 Generating station at Shippingport (USA)
1200
241
For a limiting thermal
13 oiling reactor at Kale (ERG)
14 IWWER reactor (USSR) [5]
1760
2200
2,47
235
power of the reactor
15 IDresdenreactor (USA)
2520
258
16 "Yankee Atomic" station (USA)
2600
243
17 Reactor SGR (USA)
2760
297
*For points 5, 8, 10, 12,
and 14 in paper [6] the values given for TIrdy are not correct: 40-60?C lower
without taking regeneration into account
''Point 6, Fig. 3, paper [1] for the
station in Shippingport is erroneous.
1000
T?ym
800
700
600
500
400
300
200
100
0
FAr
A
........
mai
gi
mai
.....-
____
am,
a
.
0
......."".
---",
a
M
ril
EMI
?o'4%
---
---
?iRli.
, ,I
..?
MMEM!
NEM
t335?C
min
Napo
-;
.
. II
?ts=303
12
130
c
OA
o
15
17
0/6
rro?-?
, 7
vim
266*c
mil
0 100 ZOO 300 400 500 600 700 800 800 1000 1200
1400
1600
1800
2000
2200
01)
1
T 0r, C
Fig. 9. Comparison of Inc), for stations in operation, being planned or being built,with the theoritical
curves for TPtym for various fuel components.
will become so high that they will be unattainable for
cycles utilizing ultrahigh parameter steam. Then the
choice of the cycles for steam turbine installations may
be based on the parameters attainable for steam and the
determination of the optimum parameters will be nece-
ssary only for gas-turbine installations.
We have so far considered the temperature limita-
tions of HEEL. There are also other limitations, for ex-
ample,the critical thermal loading, the limiting temp-
erature of the moderator, the radiational instability,
etc., which affect the temperature characteristics
which we have presented in TQr coordinates and which
require a special analysis for each case.
On the basis of the data presented and also of rhe
typical computations shown in papers [1, 2],we can con-
clude that equations (1) and (2) may be used to obtain a
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preliminary estimate of the optimum parameters for the
thermodynamic cycle of the steam turbine installations
of atomic electric generating stations. A theoretical
analysis using the indicated formulas enables us to find
the factors which influence the optimum cycle para-
meters and also shows us how to develop and improve
the thermodynamic operating cycles of atomic-electric
generating stations.
LITERATURE CITED
1. D. D. Kalafati, Symposium Physics and Thermal
Engineering of Reactors [in Russian](Atomizdat,
yoscow, 1958) p. 164.
2. D. D. Kalafati, Works of the Moscow Power Institute
[in Russian] (1958) Vol. 30, p. 186.
3. Zh. Ibon, Materials of the International Conference
on the Peaceful Uses of Atomic Energy (Geneva,
1955) [in Russian] (Fizmatgiz, Moscow, 1958) p.
397.
5.
6.
7.
8.
9.
P. A. Petrov, Nuclear Power Installations [in Russian]
(Godnergoizdat, Mosdow. 1958).
S. A. Skvortsov, Atornnaya trier& 5, 3, 245(1958).1'
Yu. D. Arsen'ev and K. E. Averin, Teplo6nergetika
5, 29 (1959).
George Simpsoni et al., Materials of the Internation-
al Conference on the Peaceful Uses of Atomic
Energy (Geneva. 1955) [Russian translation] ( Godner-
goizdat, Moscow-Leningrad, 1958)yo1.31). 269
Ch. Starr, Materials of the International Conference
on the Peaceful Uses of Atomic Energy (Geneva,
1955) [Russian translation] (Gosenergoizdat. Moscow-
Leningrad, 1958) Vol. 3, p. 131.
A. I. Alildianov, V. V. Vladimirskii, P. A. Petrov,
and P. I. Khristenko, Atomnaya tnerg-i, 5 (1956).t
f Original Russian pagination. See C. B. translation.
9
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Declassified and Approved For Release 2013/02/19: CIA-RDP10-02196R000100050001-8
NUMBER OF NEUTRONS EMITTED BY INDIVIDUAL
FISSION FRAGMENTS OF U235
V. F. Apalin, Yu. P. Dobrynin, V. P. Zakharova
I. E. Kutikoy, and L. A. Mikaelyan
Translated from Atomnaya nergiya ,Vol. 8, No. 1, pp. 15-22, January, 1960
Original article submitted July 1, 1959
A large detector filled with a liquid organic scintillator containing cadmium has been used to
measure the number of neutrons emitted by individual fragments in U235 fission by thermal
neutrons. Using 4 ir geometry the dependence of the number of neutrons emitted by fragment
pairs on the mass ratio has been measured. The excitation energy used in neutron evaporation
is determined on the basis of the semiempirical Weizsicker formula. A sharp asymmetry in the
distribution of excitation energy between the heavy and light fragments is noted. The data
which are obtained are found to be in disagreement with the statistical theory of fission pro-
posed by Fong.
Introduction
The distribution of excitation energy between frag-
ments is an important characteristic of the fission pro-
cess in heavy nuclei. In fission by thermal neutrons, the
initial excitation energy of the nucleus is equal to the
binding energy of the the neutron in the intermediate
nucleus which is formed and is approximately 6 Mev,
a figure which is many times smaller than the mean
value of the excitation energy of the fragment pair
which, in fission of uranium isotopes, is approximately
30 Mev. Considerations based on a quasi-static process
[1] indicate that the fragments remain in an unexcited
state up to the moment directly preceding the division
of the neck which connects them.
Bohr and Wheeler [2] have indicated that the exci-
tation of the fragments is basically connected with the
fact that the shape of the fragments directly after for-?
mation does not correspond,to equilibrium; the energy
of deformation is consequently transformed into energy
of internal degrees of freedom. B. T. Geilikman [3]
has considered this question in detail, relating the ex-
citation energy of each fragment with the deformation
parameters and the shape of the nucleus at the instant
preceding the actual division into fragments. The ex-
citation energy Ee is, as is well known, dissipated in the
emission of "prompt" neutrons and y rays;
E (A/1)e,-- v (M) 8(M) el, (M.),
where M is the mass of the fragment; r) is the mean
number of neutrons emitted by the fragments and E y
is the energy carried away by the y photons; E(M) is
the mean energy required for the evaporation of a sin-
gle neutron. The energy carried away by the y pho-
10
tons is a very weak function of the ratio of fragment
masses [4] and their excitation energies [5]. On the
other hand, direct experiments show [6] that an increase
in the excitation energy of the nucleus leads to an in-
crease in the number of neutrons emitted in fission and
that on the average the emission of a single neutron re-
quires an energy of approximately 7 Mev. Hence,an
investigation of the neutron yield from the separate
fragments makes it possible to obtain data on the dis-
tribution of excitation energy from the individual frag-
ments and thereby, information on the deformation of
the fragments at the time of formation. The depen-
dence of excitation energy of a fragment pair on mass
ratio is of interest from the point of view of checking
the statistical theory of fission proposed by Fong [7];
this theory predicts an increase in the excitation energy
of the fragment pair characterized by the most probable
mass ratio.
The neutron yield from individual fragments in
U233 fission by thermal neutrons was first measured by
Fraser and Milton [8] in 1954. The results obtained by
these authors indicate that in fission,which is almost
symmetrical in mass,the excitation energy is distributed
between the fragments in a manner which is far from
symmetrical; for a fragment mass ratio of 1:1 the light
fragment emits approximately four times more neutrons
that the heavy fragment. The total neutron yield is a
weak function of the mass ratio. In the region of the
most probable mass ratio there is apparently a small in-
crease in the number of emitted neutrons. This last
feature has been interpreted by Fong [7] as evidence of
the validity of his theory. From the point of view of
fission physics it is interesting to determine whether the
pattern observed by Fraser and Milton is an accidental
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one, arid is characteristic only of the fissile nucleus
U234 or whether the excitation energy distribution,which
has been observed,is a general feature which pertains
under certain conditions for all nuclei (similarly, for
the fission asymmetry).
In the present work we have measured the average
number of neutrons emitted by the individual fragments
and the fragment pairs, in fission of U2s5 by thermal neu-
trons.
Experimental Apparatus
The measurement of the neutron yieldv(M) from
individual fragments is based on the fact that the an-
gular distribution of the neutrons with respect to the di-
rection of motion of the fragment is highly anisotropic:
approximately seven times more neutrons are emitted
in the direction of motion than at an angle of 90?,
while the emission of neutrons in the backward direc-
tion is essentially negligible [9]. A schematic arrange-
ment of the apparatus is shown in Fig. 1. A layer of
U235, 30 g/cm2 thick is deposited by evaporation on a
colloidal film 20 1g/cm2 thick which is placed on the
central electrode of a double grid ionization chamber.
The chamber is filled with a mixture of carbon dioxide
and argon (partial pressures of 50 and 900 mm Hg res-
pectively). The angle of emission of the fragments
with respect to the normal to the layer is defined by
Fig:
iron lead
p77.11
con-
water crete
boroo...olus
paranm
1. Diagram of the apparatus: 1) double grid ioni-
zation chamber; 2) scintillation tank for neutron de-
tection; 3) photomultipliers; 4) collimated neutron
beam.
the collimator; this is a plate of phosphor bronze 0.4
mm thick in which an aperture 0.4 mm in diameter has
been drilled. The ,most probable emission angle for the .
fragments is approximately 25?. The uranium layer is
located at a distance from the neutron detector such
that the most probable angle at which neutrons are de-
tected is also approximately 25?.
The neutron detector is a hexagonal tank with a
volume of 200 liters which is filled with a liquid scin-
tillator. The scintillator is a solution of 2,5-diphenyl-
oxazole (PPO) in dioxane with a concentration of 4 g/
liter which contains an almost saturated water solution
of cadmium nitrate in amounts such that there is one
cadmium atom for each 400 hydrogen atoms. The scin-
tillation flashes,produced by the captured y photons,are
recorded by 32 FEU-24 photomultipliers with cathodes
78 mm in diameter. At the center of the detector there
is an aperture 113 mm in diameter through which the
collimated neutron beam passes. The lifetime of the
neutrons in the scintillator is 11? sec. The measured ef-
ficiency for detection of neutrons from U235 fission in the
detector is 62%. The efficiency is determined by locat-
ing the layer of fissile material at the center of the de-
tector. With the exception of the scintillator,the detec-
tor is essentially the same as that described in detail by
Reines, Cowan, et al. [10].
The operation of the electronic system is controlled
by the coincidence pulse from the fragments. This
pulse opens for 25 ?sec a gate which transmits pulses
from the detector to a high-speed counting system and
pulses from the double ionization chamber to the input
of the ratio analyzer. The gate is opened after a delay
of approximately 0.6 ? sec from the fission time in or-
der to avoid detection of the prompt y rays. The re-
solution time of the neutron counting channel is approx-
imately 0.4 ?sec. Information for each event (the mag-
nitude of the ratio and the number of neutrons) is recor-
ded on a recording system. The ratio range from 2.2
to 1/2.2 is covered by 30 channels of the analyzer.
Cases in which the light fragment is emitted in the di-
rection of the detector for ratios from 1/2.2 to 1 are an-
alyzed by the first 15 channels while cases in which the
heavy fragment is emitted in the direction of the detec-
tor for ratios from 1 to 2.2 are recorded by the remaining
15 channels. Under operating conditions approximately
80 fissions/min are recorded.
We measured 500,000 fission events in the course
of these measurements; this corresponds to approximate-
ly 215,000 neutron pulses of which 85,000 were caused
by fission neutrons,with the remainder due to the back-
ground of scattered y rays and neutrons from the beam.
The data on the total yield of neutrons from frag-
ment pairs can be obtained by measuring the neutron
yield from the individual fragments v(M). However, in
order to obtain the quantity v(M), it is necessary to in-
troduce a correction in the experimental results; this
11
Declassified and Approved For Release 2013/02/19: CIA-RDP10-02196R000100050001-8
Declassified and Approved For Release 2013/02/19: CIA-RDP10-02196R000100050001-8 *
correction takes account of the dependence of neutron
detection efficiency on angular distribution with respect
to the fragments. To determine the total yield indepen-
dent measurements are made in which the ionization
chamber containing the layer of fissile material is
placed at the center of the detector and the neutrons are
detected in a 4it geometry. The apparatus is operated
in the same way as in the measurements of neutron yield
from the individual fragments with the only difference
being that the ratios x and 1/x, corresponding to the
same mass ratio for the heavy and light fragments,are
entered in the same channel of the analyzer. In these
measurements the counting rate for coincidences be-
tween fragments is15/minwhile the background is equal
to one count per fission. In all approximately 70,000
fission events were recorded.
Corrections for Absorption in the Layer
and Ionization Defect
In the ionization chamber used to measure the neu-
tron yield from individual fragmentsone of the frag-
ments passes through the colloidal film and the colli-
mator whereas the other loses energy only in the uran-
ium layer. The average energy loss in the uranium lay-
er is less than 0.4% and no corrections for this effect
have been made. The energy loss in the film and the
collimator are determined from the displacement of the
point corresponding to symmetric fission with respect to
the analyzer channel which records equal-amplitude
pulses. The energy losses of the fragment in symmetric
fission are found to be approximately 5 Mev. The ap-
propriate corrections are introduced in the experimen-
tal distribution of fragment mass ratios. In introducing
the corrections account has been taken of the depend-
ence of initial ionization of the fragments on velocity
In the measurement of the total neutron yield,one
of the fragments passes through the collimator while the
other passes through the film. The energy losses of the
fragments are approximately the same in magnitude and
the displacement of the mass-ratio distribution curve is
less than 1%. Hence,we have not deemed it necessary
to introduce corrections for absorption,and record events
characterized by the ratio x and 1/x in the same chan-
nel.
The yield curve for the fragments is also corrected
for the ionization defect. In introducing this correction
we use the values 5.7 and 6.7 Mev [11] for the ioniza-
tion defect of the most probable light and heavy frag-
ments respectively. It is assumed that the defect is a
linear function of fragment mass: AE(M) = (4 + 0.019M)
Mev [8].
fraction of the neutrons emitted by it which enter the
detector and are recorded.
The angular distribution of isotropically emitted
neutrons from a fragment converted to the laboratory
coordinate system has been given, for example, in [9].
In introducing corrections, we assume that the neutron
detection efficiency n(M,q) for neutrons which are emit-
ted in the coordinate system of a fragment with energy
q is proportional to the probability for emission of a
neutron at an angle 00 in the laboratory coordinate sys-
tem. Under these conditions
(M, q) = const (1 + r)2, r =17 E (M)
Mq (1)
where E(M) is the kinetic energy of a fragment with
mass M. For the most probable energies q and ?E the
value of r is slightly smaller than unity. In going from
symmetric to the most probable fission the efficiency
n varies by approximately 20%. It can easily be shown
that the magnitude of this variation is a very weak func-
tion of the energy q in the range 0.5 - 2.0 Mev, which
covers most of the neutrons. Hence, although the neu-
tron spectrum is continuousiit may be assumed that the
detector efficiency is determined by the mean neutron
energy q(M) emitted by a fragment of a given mass.
The mean value of q(M) for the most probable mass de-
pends on theexcitation energy and is given by
0.62(g+ 1) 2 Mev, where Y is the mean number of neu-
trons .which appear per fission event (Terrel [12]). For
U235 OS 1.15 Mev. Since,experimentally,one observes
a strong dependence of fission excitation energy on
mass, the corresponding change in mean neutron energy
is taken into account. It is assumed that
q (M) = 1.5 + [ v (M)? .
The factorjj can be found either from the relation
q = 0.62(v + 1) 2 Mev or from the experimental results
by studying the change in fragment temperature as a
function of excitation energy [13]. The quantities
found by these two methods differ somewhat and the
average value is taken: k = 0.25 Mev/neutron. Thus
q(M)-0.84? v (M) 0.25.
Substituting the value of q(M) in Eq. (1) and expressing
the fragment energy in terms of its mass and the total
kinetic energy of the fragment pair E0 (x) with respect
to the mass ratio x, finally we have
Correction for Neutron Detection
I 11l/Mo?Ml/E0(x)
(M) = const
(2)
Efficiency
This correction must be introduced only in the
measurements of neutron yield from the individual frag-
V M0 (0,844-0,25v
(m))
ments. The larger the fragment velocity, the greater the
12
Declassified and Approved For Release 2013/02/19: CIA-RDP10-02196R000100050001-8
Declassified and Approved For Release 2013/02/19: CIA-RDP10-02196R000100050001-8
where Mo is the mass number of the fissile nucleus.
The value of the constant is found from the normaliza-
tion condition: the results must be normalized to the
known average value of v for U215 which is taken to be
2.45.
Discussion ?of Results
The results of the measurements are shown in Figs.
2 and 3. The mass ratio of the fragments is plotted
along the abcissa axis. The fragment yield per unit
mass ratio, corrected for the ionization defect and ab-
sorption, is shown in Figs. 2a and 3a. For purposes of
comparison we also show the results of radiochemical
and mass-spectrometer studies of fission products [14]
(Fig. 3a, dashed curve).
In Fig. 2b is shown the neutron yield for individual
fragments corrected for the efficiency of the neutron
detector. Analysis shows that on the average the light
fragment emits about 17'o more neutrons than the
heavy fragment. In Fig. 3b the points indicate the
measured neutron yield from the fragment pair while the
crosses denote values of v (x) computed from the results
of the measurements of v from individual fragments. A
comparison of the calculated and measured values shows
1
10
2
0.6
Ca
0
that although the correction for detector efficiency is
based on a large number of simplifying assumptions, the
error is less than approximately 5'/o when these correc-
tions are taken into account.
The following remarks should be made with regard
to these results. The values of v obtained experiment-
ally are averaged over some range of ratios. This aver-
aging takes place primarily because of the finite resolv-
ing power of the ionization chamber. The resolving
power A x/ x (A x is the dispersion in the value of x) can
be determined from a comparison of the obtained frag-
ment yield curve with the adcurate data obtained by
radiochemical and mass-spectrometer analysis. An an,-
alysis such as that carried out by Leachman [15] shows
that in the present experiment A x/x = 0.08. It is as-
sumed that for all values of x the error distribution is
given in a Gaussian form with dispersion 6 x which depends
linearly on the ratio: A x= const
The effect of the finite resolving power is specially
noticeable where the fragment yield falls off sharply.
Hence, in the region close to symmetric fission ( x: - ,
by E..N.`1;yustikh- ,
k ' k
,?,_ . _
The classie theories of Airy, Pratt, Dutton, and others ar6 discussed, criticized;and amPlified' ,
- ? in the light of new data. The methods of 'gathering this- information, the means of analysis,-
and the applications of 'original Soviet research are expounded Italy both in the text and on
,
related maps. Present theories-related to isostatic rebound, compensation and 'overconipensa-, e?
tion, gravitational anomalies showing concentrations of denkty, etc., are -illustrated with-
-accompanying /pertinent data. Designed to produce a,clearer,and.more 'Up-to-date picture of .
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IN . ONE-DIMENSIONAL COKITINUOUS NONHOMOGENEOUS. MEDIA -
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TRUbif? No. 39' 7 ' t '',' ,e.by B. N. Ivakin - , ? ' . (
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This -book discueS the Problems orthe structure of waves propagating in Continuous.. non-
homogeneous and generally absorbing media, with a single spatial booidinate, pver intervals
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problems 'posed, are presented in operatcfr notation, making it, possible ' to study nonsteady-
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The resUlts of Work cdnducted by the"GeophySics? Institute of the Academy of Scienc7es, -
-USSR, since, 1948 on the. investigation of fault plane displacements are documented in this
volume. During this, period a method was evolved which-makes it possible to determine the?
,
mechanical type; of fractures -at the 4acus, the dip and strike; off the, fault plane, 'and the
' direction of the?displadement, and-order of -the relative intensity ofthe first sho61C. Many, of ,
the Methodological conclusions and results of interpMtations are being published for the
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