SCIENTIFIC ABSTRACT SOBOLEV, V.V. - SOBOLEV, V.V.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

JBJECT USSR / PHYSICS CARD I / 2 PA - 1989
aUTHOR SOBOLEV,V.V.
TITLE -'r1re--Tr-a:ff-9p-0Yt- of Radiation in an Inhomogeneous Medium.
PERIODICAL Dokl.Akad Nauk 111, fasc-5, 1000-1003 (1956)
.Issued: 1 9_5_7
The present work investigates a special case of the problem mentioned above,
viz. the determination of the luminescence of a semi-infinite medium con-
sisting of plane-parallel plates in the case of a spherical indicatrix of
scattering. The ratio between the scattering coefficient and the sum of the
coefficients of scattering and true absorption (i.e. the probability of the
survival of the quantum on the occasion of the elementary act of scattering)
is here denoted by and this quantity is l6oked upon as a function of the
optic depth T.
This problem is reduced to the solution of the following integral equation:
OD
.B(-r) 2 (o B(-.1) Ei I -r - -r1j dT1 + g(-r). Here the function g(-r) is
immediately connected with the sources of radiation. The intensity of the radi-
ation emitted from the medium under the angle arccos @ with respect to the
normal is expressed by the following formula:
I @OD B(T) eT/It (d-r/j
.For the soi.tion of this problem also a method will be found suitable which
consists in the introduction of the exit probability of a quantum from the

Dokl.Akad.Nauk-111, fasc-5, 1000-1003 (1956) CARD 2 / 2 PA - 1989
medium. If this probability is known, the intensity of the radiation emitted
by the medium can be expressed by means of a formula mentioned here for any
radiation sources acting upon the medium. For the function p(T,@ ) an inte-
gral equation is given the solution of which offers no difficulties. p(r'@
here denotes the probability that a quantum absorbed in the optic depth T
leaves the medium under the angle arcco8 'q with respect to the normal. How-
ever, in order to determine p(,C,'q ) also another equation can be set up, in
which case the probability for the exit of a quantum from the depth T + & T
is determined, i.e. the quantity p(T + 6 T 11). Also for this case the inte-
gral equation is given. However, if /@ depends on T, this equation no longer
holds good. But also in this case it is possible to write down a still more
general integral equation. For this purpose the author studies the totality
of the media in which the probability for the survival of the quantum is
equal to A (-r + a), where a is a parameter.
In conclusion the equations obtained are specialized for three special
cases.
INSTITUTION: State University LENINGRAD

SOBOLEY, V.V.
[Moving shells of stare] Dvizhusbchies@a obolochki zveid. laningrod,
Izd-vo Leningradskogo goo. ordena lenina universiteta, 1957. 111 0-
(Stars--Atmompheres) (NLRA 10:6)
(Stars--Spectra)

SOBOLMV. V.V.
Diffusion of radiation with redistribution of frequencies. Part 3.
[with summary in 3nglish]. Vest. IaU no.19:135-144 157. (MIRA 11-.1)
(Stars--Radiation) (Diffusion)

AUTHOR: 'Sobolev, V.V.
33-3-5/32
TITLE: The diffusion of radiation in a medium of finite optical
thickness. (Diffuziya izlucheniya v srede konechnoy optidb-
eskoy tolshchiny)
PEIZIODIC.iiL: "Astronomicb-eskiy Zhurnal" (Journal of Astronomy),
1957, Vol-34, No-3, pp. 336-348 (U.S.S.R.)
ABSTRACT: In a previous paper (1), the author proposed a new method
of solving various problems in the theorj of diffusion of
radiation, based on calculating the probability of eacape of a
quant-um from a medium. At first only semi-infinite media were
consideied. The theory was later applied to a fln'ite medium
(2). New results are now reportcd for the latter case. Special
attention is paid to the case where optical thicknes@; of the
medium is large. The results now reported may be used in the
study of diffusion of radiation in t@Le nebulae, atmospheres of
p,lantts, etc.
The following problem is treated: the medium is assumed to
consist of plane parallel layers, and has an optical thickness
't;g . The-strength of sources of radiation is suppoBed to be
a function of optical depth le only. The probability that a
quantum will survive an elementary act of scattering is denoted i
cszd 1/7 by ?@ (the albedo of a particle). With this notation it is
desired to calculate the probabillty that a ouantum.,-absorbed
33-3-5/32
The diffusion of radiation in a medium of finite optical
thickness. (Cont-)
at a depth It will escape from the medium (in gMe=al after
diffusion) thrOuSh the plane 'r = 0 , at an angle arc cos n to
the normal and within tile solid angle dw . This probability
is denoted by P(t,ly T0)- The latter function may be deter-
mined from the f olloviing equation:
ap
whe re
'to) P(t'n' 9 'ro) d.11
dTj
V, (,to to)
2
0
(P (TI 0)
+ e- (,to
Z T17
+
T

33-3-5/32
The diffusion of radiation in a medium of finite optical
thickness. (Cont.)
both subject to the condition T 0 >> 1 . The asymptotic forms
of (p(-q, r'o) and *(-q, J;.) corresponding to case i) are:
(P(-no%;') (Kn) - C 11 (p(-q)e-2kro
1 - kT)
and
C, q)(TI)e ..kI-O
1 k-q
where C and C are constants given by:
C 'P On TI d-9 = C (P (n --,n---qdTI
1 (1 - 2 @ 1 - k 2
0 0
ftrd 4/7 and 1
(P ,q Id-O = 2k (P On -=--.qdq
(1 - k-q) 2 1 - k 2t, 2
0 0
33-3-5/32
The diffusion of radiation in a medium of finite optical
thickness. (Cont.)
The asymptotic forms of q(-9, Jb) and *(I, ZO) corres-
ponding to case ii) are: )
V +Y
0
and TI(P (-Q )
It; + Y
wheie y isaconitantandisgivenby:
2 9 (n)-n2 d-q
(P On )T)1d-n
Card 5/T Finally, the intensity of radiation emerging from a medium
is calculated for-different distributions of scurcez of radia-
tion. The intensities of indiation passing through the upper
and lower boundaries are respectively given by:

33-3-5/32
The diffusion of radiation in a medium of finite optical
thickness. (Cont.)
d'9
1(01 11 two) (It, T12 r-O)f(t)-
0 dt-
P(to
where f(V)VV is the amount of energy which comes directly
from the sources of radiation and is absorbed per second by an
elementary volume of thickness dV and unit cross-section, at
a depth It is supposed that sources of radiation are
within the medium and emit equal amounts of energy in all dir-
ections. Thus, one may put:
47r
f g(V
card 6/7 where g(t)dt is the amount of energy emitted per second by
the sources in an elementary volume 1 x dV per unit solid angle.

AUTHOR: Sobolev. V. V. 33-5-3/1;L
----------
1TLE The Diffusion of' L -radiation in i.-ebulae and Stellar
_.@nvelopes. (DiffuRiya L a-Izlucheniya v "Pumannostyakh
i Zvezdnyl:h Obolochkakh .
PERIODICAL: Astronomicheskiy Zhurnal, 1957, Vol.3L@, No-5, pp. 694-
?05 (USSR).
ABSTRACT: Photoionization of hydrogen in gaseous nebulae and the
subsequent recom bination lead to the appearance of L
quanta. Because of the large optical thickness of nhulae
in Layman lines, these quanta take some time to diffuse
through nebulae. For this reason the density of L a quanta
in nebulae L-urns out to be very high. The problem of the
diffusion of the latter quanta is of major interest for
various reasons. In particular, the radiation pressure
due to these quanta plays a major role in the dynamics of
nebulae and stellar shells. In the present paper the
problem of diffusion of L -radiation vrith full redistribu-
tion of frequences, an arfttrary absorpuion function, and
an arbitrary velocity gradient in the medium is considered.
The general solution of the problem leads to the solution
to the follouing special cases: 1. large velocity gradient
Card 113 (compare Ref. 3 by the present author) and 2. stationary

1 33-5-3/12-
The Diffusion of L .-radiation in Nebulae and St-ellar Envelopes.
6 and 11). T.here are no figures, no -Lables, 13 references,
5 of waich are Slavic, includinE 4 by the pre-sent Author.
SUBIiIIITTED: June, 4, 195?.
ASSOCIATION: Leningrad State University imeni A. A. Zhdanov.
(Lenin@,radskiy asudarstvennyy Universitet im.
A. A. Zhdanova)
AVAIIABLE: Library of Congress.
"--,-ard 3/3

Diffu3ion of R-idliation in Semiiiffinite Medium
20-1-12/44
function ch@r.-----cterizes the distribution of the radiation
,;ources. If the func@ion B(9-) i3 found, the intensities of the
radiation c.---,n be e:----)resoed by certain formulae @;iven here. The
formal solution of the initially -ivern into.-ral equ@tions has
t1re f o rm
C- d -ahere
mote;3 the .-e t3l. Next, "r. equation for the de-
termina-ti on of the 'r-ernel -ij @;iven. 'I"he further development of
the c,-,-1Put;@Aion3 is follovied. '2h(- 6eter:Anation of the JCield
of ri.oli-tion in -.t se:.Ainfinite mza'um is @-cduced to the dc-
C Li
termination of @z fun 6 or. :Text, the author invest-i-
.@ates the followin'.- speci -I cases of this Droblem: 1.) Be it
assumed , at Ge 'ahere G and 'I' -are constanta.
2.) 3e it that = where n is a integer, positive
number. 3.) Be it as@;umed that in the medium a pure scattering
of raliation takes place and the radiation sources are located
in an infinitely -reat depth. There are 3 Slavic references.
C.-@rd 2 '/3

2j@ C J@' CL @e
Voproay ko=ogm" '. 6 (Problems In Co-gony. V@i. 6) Moscow,
Izd-vo AN SSSR, 1958 367 p. 2,000 copies printed.
Sponsoring AgencY. Alcadomi7a nauk SSSR. Aatronomicheskiy so vet.
ARTICLES
Magnitakly, V.A. On the Origin and gTolution of Continents
and Oceans 5
Baramov, V.I. Latest Data In Determining the Earth-&
Absolute Age 39
X-vin, B. Yu. History or the Moon's notation and the
Rheological Properties of Ito Material 56
Safronovo V. S. On the Growth or Terrestrial Planets
Alfvoa
H
O
th
O 1
.
n
e
;
rigin of the Solar System 7
v Upper, A. Ya. and M
A. T12
Disintegration Processe
.
In Light Quanta
Their Sign1ficance In the Phyala:
of Gaseous Nebulae 98
I-J6_ Physics of Planetary Nebulae 112
UUrZ&dylLn. G.A. DYnUdO6 Of Planetary Nebulae 15T
MinIn, I.N. Light Pressure and the Dynamics or Planetary
Nebulae 211
Agekyan, T.A. Interaction or Stare with DIfru" Matter
Kaplan
S
A
M 221
.
.
,
agnetic Gas Dynamics And Problem of
Cosmogony

Farkhomenko, P,O. On the Preservation of Continuance 238
In the Formation of Elownts
P&rkho
k
265
man
o, P.O. Determining the Location of an Zqul
t*
ond
eran
P
Thermonuclear Medium
PlIvallner, S.B. On the Theories of the o1quipandorants 269
origin or Elements
0.1. Th* State Of Cosmology Today 2T3
277
REPORTS
Kakarkin, B.V. Conference an Variable Stars Sponsored
by the Hungarian Acade
my of Sciences and gold 112
Budapest an August 23-2d
1
6
95
,
To
rlst5kIY, Ya. P- Symposium 0. Problems in Elestrg- 333
nag-tic Phenomena in Cosmic ftslog

1
1
Q
op P
M
C
3
-
-
onference on Non-Fixed Stare
1:
V ont
604-y0l'yandno
, B
A 3A
v
.
. Conference on the Physics
of PlanStary NebulL
354
ftakol, Ye. T.. Conference of the C - ttee on comog
D
svOt*d to &-mining the Possibilities of th* Do-
valopment of Extragalactic As ese-411WOF
-
'ralralm, V.A. The 31zth Coamagon-1c&I-Coff-ers 359
joe
r
3Q

SOBOLEV, V.V.
Physics of planetary nebulae Lwith summary in English]. Vop.k6sm.
6:112-156 '58. (MIRA 11:10)
(Nebulae) (Cosmic physics)

16(l)
AUTHOR: Sobolev, V.V. SOV/22-11-5-2/9
TITLE: On the Theory of Radiation Diffusion (K teorii diffuzii
izlucheniya)
PERIODICAL% Izvestiya Akademii nauk Armyanskoy SSR, Serivra fiziko-mate-
maticheskikh nauk. 1958, Vol I I , Nr 5, PP 39 - 50 (USSR)
ABSTRACTs The present results generalize the results of V.A. Ambartsumyan
[Ref 1,2j and of the author LrPef 3,4, V - Integral equations
of the type
00
B(-L) = K(t-V)B(C`)d-t2 + g(Z)
are considered. Principally new results are not obtained, since
the same ecuations have been already explicitly treated by
V.A. Fok [@ef 61 . The use of a certain function of one variable
@ ( -) is only new, by which the resolvent r (1r,v ) can be ex-
pressed (Fok used Fourier series). The application of the re-
sults to the radiation diffusion in a plane layer seems to be
of interest and an probability theoretical interpretation of
Card 1/2

5
On the Theory of Radiation Diffusion SOV/22-11-5-3/9
the diffusion problem in which it is referred to the paper
Zhef 131 of L.M. Biberman and B.A. Veklenko.
There are 13 referencest 10 of which are Soviet, 1 is American,
I Japanese, and I Swedish.
ASSOCIATIONt Leningradskiy gosudarstvennyy universitet (Leningrad State
University)
SUBMITTEDt July 15, 1958
Card 2/2

OGORODWIKOV, K.F.; SOBOLEV, V,V.
Jpetr Mikhai.lovich Gorshkov; on his 75th birthday. Vest. IGU 13
no.13-5-10 158. (MIRA 11:8)
(Gorshkov, Petr Mikhailovich, 1883-)

AUTHOR: Sobolev, V. V.
SOVP-0-120-1-17j'63
TITLE: The Diff-u-s-i-o-n-of T'Radiation in a Plane Layer (Diffuziya
izlucheniya v ploskom -loye)
PERIODICAL: Doklady Akadenii nauk SSSR, 1958, Vol- 12o, Nr 1,
pp. 69 - 72 (USSR)
ABSTRACT: In a previous paper written by the author (Ref 1) the diffusion
of the radiation in a semiinfinite medium was investi.-!@ted using
a probability method (Refs 2,3) earlier proposed by the author.
The present paper invest s by means of the same method the
diffusion of the radiation in a plane laYer of the finite o,)tical
densityto. An isotropic scitterin,@ of the radiation with the
survival probability @L of the quantum occiaTed in the elementary
volume of the -,iedium. The calcul.---tion of the rad-i--tior, field
in the medium reduces to the determination of the function
B -t0 from the equ-tion
Z.
B('r' )Ei d +
B ( -t T- 0 L2J,"' 0
Card 1/3 %Y@,,ere the function E( ) rej@resents the arran.-e-i--nt of the

The Difftirion of Radiation in a Plane La@rer SCV/2o-12o-1-17/0'3
radiation sources. The solution of the above mentioned equ.%tion
can be arran.c-ed in the form
'r,
B(t 0) g(T) +1 .)S&r )d where Z r 0)
denotes the resolvent, The quantity (-r 9 T 0) represents
the probability for the fact that th. quantum radiated between
the optical depths z I and -c I + d T I is 11-Iter (i.e. after the
diffusion in the medium) radiated between the optical depths
,r and d-t. Taking into account the probability meaning of the
resolvent and using the method of the addition of the layers
as proposed by V.A.Ambartsumyan (Ref 4) a relatively simple
equation for the determination of the resolvent can be obtained.
The equations resultino after the addition of -- layer of the
small optical density AXto the upper and lower boundary of the
medium are written down and dealt with. Together with the re-
solvent r ) the probability for the e-rit of the
quantum from the medium is introduced to the prese--.t considera-
tion. The corresporidin.- intensities of the radiation emitted
throu-h the upper and lo-;.,er boundnry are calculated. The further
Card 2/3 coiirse of the calculation is followed step by ste2, V,e function

T*..e 04- 4
PRESE"TED:
SUBIMITTED:
r o r. c treated e,;, 'Jon --n.@;t ilf-y an
71 U_ 11 1 -1-
1-ble in thenry of '17c 0 * - 'h@
--nt U i f 7 of
Wher, thiz function is known t@le i-adi-tion fici(: in @Iane
layer in the case of n_rbitrar,, 3jizz-coz can be det@_r-
mined. Fin-,'-l,' the z-uthor de:-@_Is in, s'lanrt with, LI-0 "@ followinj
eptal di,,ti-ibution of the ra-14--tion viurces in 'the
.-ediuzi; the aefliu.m. is illumin@_ted by ,-railcl
at -- cer'ain an,;le; the deter-Lin'4on o' the t--'.- 1 probL2.1)ility
of the e_-rit of the c.uantum fro._@ the meclium. T'lern ,.re 4 refer-
ences, which are Sov"et.
February 0', ',.y V.A..Ambnrtcum-yan, Me-7-'@-er, _Ac:1-"_-:-y of
Sciences, USSR
February 1, 10/58
1. Radiation--Theory 2. Radiation--Scattering 3. Diffusion
--Mathematical analysis
Card' 3;3

SOV/2o-122-1-10/44
7TYOR: Sobolev, V. V.
-
TITLE: --Uh-e- -Luminosity of Hot St
On - ars (0 svetimo3ti _@oryachikh zve.,d)
PERIODICAL: Doklady Akademii nauk SSSR, 1958, Vol 122, Nr 1, PI-1 41-43
(IISSR)
ABSTRACT: This pa.,er deals with the determination of the luminosity
of the WR stars and of the white dwarfs. Stars of the type
1,11R: A conoiotent theory of the WH stars mu:it take into
@iccount that absorption is cau,,ed by real atoms (hydrog,en,
helium) and that high-frequency radiation is converted to
quanta of lower frequency in the atmosphere of the star.
The results of some papers (Refs 4, 5) may be used for the
Jetermination of the luminosity of the WR stars. Approximate-
ly, the star (without the atmosphere) is assumed to radiate
according to Planck's (Plank) law. The temperature of the
2tar can be found according, to the imDroved theory of Zanstr.
For the determination of the star radius, however, the fact
must be taken into consideration that the fluorescence ex-
cited in the atmosphere increases Vie visible brightness of
Card 1/3 the star considerably. According to the theory, the influence

On the Lum@nosity of Hot Stars
SOII/2c)-122-1-lo/144
of Vie atmosphere on the visible brightness amounts to some
star magnitu,.Ies. The influence of the radiation of the shell
on the brightness of a star may be found approxi-matell'y by
observation; this manner of determination is discussed in
hort. ':-'he white dwarfs: The ,Ii graV4tational acceleration
c hir
s
in the atiriosphere of the white dwarfs causes the following
2 effects: 1) The de,-ree of the ionization of the atoms is
Lovior in the atmo,iPhe-ro of it wlite dwarf than in the atmosphere
of an "ordinary" sLir of' the azu,.io temparature. 2) The ab-
sorption lines in the spectrura of a ly'lite (jwjjrf are vury
diffuse because of the Stark effect. It is possible that the
temT)eratures of the white dwarfs are higher 'than the general-
ly assumed vv 'Dies. The following facts are arguments in
favor of -@hi@. Tiere -Ls no Balmer discontinuity
(B;A1,7,erov skachek) in V,- @,,-Iectra of the white dwarfs. @) The
berZ of the Balmer series has
a .,.rent -influence on tliu IiZ,ht of the white dwarfs. Grenchik's
zjorjel ()f L.-L, at,-@;os-hpre of the white dwarf 40 Eridan B
0'ef 0
with T = 1j 800 and ljY dtoes not agree well with the ob-
e D
served results. 4) "i'lie radius of Sirius B is more than twice
as lar-e than the theoretical radius. 5) Some white dwarfs
'fave s
Car.] 2/3 pectra v.,ithout @Absorvtion lines and with 'a4nt emiss4on

SOBOLRV, V.V-.-..
Diffusion of radiation in a medbin with variable optical properties.
1rch.aa-p.LG'U no-2":3-13 1 50,i (MIRA 12:1)
(AsE@ophysics)

Z e 0
Y
AUTHOR: Sobolev, V. V., Corresponding Member, SOV/20-129-6-18/69

TITLE: Some Problems in the Theory of Radiation Diffusion
PERIODICAL: Doklady Akademii nauk SSSR, 1959, Vol 120, ITr 6, pp 1265 - -1268
(USSR)
ABSTRACT: The present paper raises and solves several of the problems men-
tioned in the title, which, at the first glance, appear to dif-
fer considerably, but may, in reality, be reduced to integral
equations of the same type. First, a semi-infinite medium is
dealt with, which consists of plane-parallel layers and ia able
to absorb and emit radiation. This medium is assumed to bs- bound-.
ed by a reflecting surface with a reflection coefficient 1.
this case, the function B(T) is determined by the inte@7ral equa-
co
tion X-C) = -L [Ei I -c - t I + Ei (,T + t)j B(t'dt + g (-i Fere B de-
2 .0
notes the ratio between the emission coefficient E and the ab-
sorption coefficient a. In the case under investi'gaticn, B de-
/a holds,
pends only on the optical depth T. E'urther, g(T) = 8
0
Card 113 and 60 denotes the emission coefficient due to di-re'-z radiatlon
LK

Some Problems in the Theory of Radiation Diffusion SO@F/20-112n-'-'861,60
0
v
sources. Next, a spherical planetaryl nebula with a star in -its
center is assumed. The thickness of this nebula is assumed to be
much smaller than its radius. The diffusion of L r- quanta In the
-ral equation B'-r)
nebula is described by the intep, j [EI
0
Ei(-r + t)] B(t)dt + 'S e-T. Here TES 4enotes the flux of tile L
4
quanta, which impinge upon the inner surface of thfL nebL'la from
the star. A iDoint radiation sour::e is then assumed tc@ be ir, a
homogeneous unbounded medium (eog@ a gas in a gas- or dast
nebula). According to V. A, Ambartsumyan.-. determination of the
radiation field is in this case reduced to solvin-g t1he integral
00 9
equation A(-r) [Eij-r - tj + Ei(T + t)]A(-*@ T
2 2
00 0
with A(-r) S B(t)tdt (L is the source strength. v the optical
0
distance from the source The hitherto given integral erjua-@ions
differ from one another only by their free terms. The se?ond and
Card 2/3 the third integral equation may be regarded as special cases of

68155
Some Problems in the Theory of Radiation Diffusion S C, 17/2,0 - 11 2 r, - 6 -16
the first@ The first integral equation may be solved by emulcy.
ing a method already previously described by the auti-.oT (Pef 3)-
Calculation up to solution is followed step by step, and the
resolvent is explicitly written down,, Finally, s-@vc:@ral
cases of the aforementioned first inte-Lral equat.")n are Oeal+
with. ',11ith g('r) = e--r/f , B(,,f
+ e-\. --idt holds. In the case of a 14,ght
2
B('r) La
'(,r\) and wl-fh 6(,r@ B(-c'
-7-77
There are 4 Soviet references,
S UIB15ii TTED Sei.,teniber 16, 1959
Card 3/3

MIXHAYLOV, A.A., otv.red.; ZVEILMV, M.S., red.; KULIXOVSXIY. P.G., Md.;
KASEVICH, A.G., red.; MUSTEL', E.R., rod.;-SOBCLEY, Y.Y., red.;
SUBBOTIN, M.F., red.; SAMSONMO, L.Y., red.; TUMMINA.'-X-A..
tekhn.rad.
[Astronomy in the U.S.S.R. during forty years 1917-1957; collected
articles] Aatronomiia v SSSR za sorok let, 1917-1957; abornik
statei. Red.kollegiia: A.A.Mikhailov i dr. Koskva, Goa.izd-vo
fiziko-matem.lit-ry, 1960. 728 p.
(MIRA 13:7)
(Astronomy-History)

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723 17. 2.OW copies prit.,d.
I.I.t L. V. @"h. V.; A. @@rkl= &U- -I&I r-@I: A. A. M.k.
Mylov (A-p. St. ), M. 3. 2. .11:
mW,111 7. 7. :,1 M. Y.
WVOM: This boox Is !.v@nA-d for @t"c@zr*, matr-Thys1clsts, @d of.1-3
lotom.ted in t@@ of astrnoow In tl@ MLZ.
CO.T.RA -3: ?his m,,r vor@ cm U- Linta-y of alt.-mr-,T in the a3m constats q.,
1. pmr%., revil- %ad bibllc;mphi,% -. r@t t c-cal-las . ..IJecu- f
r.Acj@A vn %.rims mz@tn qr %3tr-nmiml ms,,mrsln vrttt4a b.7 1-4ing Wriot
[e-mail] Ll kh. rl,LL.. =,f Is de_,_@@.nts of tI.
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or e.% -atto@d. :t,. -,@d eL--.J@as of 41
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V. P. T',
b.
D.
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282
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4_1
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L!st nr Ahbrejit--n, 'j,j f@r Pblica,tic.1%
375
Pj Lr t

AKBAMUNTAN, Viktor Amazaspovich; ARALWAN, M.A. (translator]; MIRZOTAN,
L.V. [translator], red.; PARSAMTAN. B.S. (translator]; TOWASTV1,
G.M. [translator]; KHACHIKTAU, E.Te. Etranalator1;,Sq#qpY,-V.V.,
red.; KAFIuWAN, M.A., tekhn.red.
[Scientific works in two volumes] Nauchnye trudy v dvukh tomakh.
Fod red. V.V.Sobolava. grevan, Izd-vo, Akad.nauk Armianskoi SM.
Vol.l. 1960. 428 p. Vol.2. 196o. 36o p. (MIRA 13:11)
1. Sotrudniki Byurakanskoy astrofizicheskoy observatorii (for
Arakelyan, Mirzoyan, Parsamyan, Tovmasyan, Khachikyan).
(Astronomy)

X:
FIT p
'
L
t- I i2 9

@111:- cff
1:p('vol on conui@';'
fla@; been vocently
,
varl-ou" '111, hors. I Lit a uimllur
ilotall by
whcl-o thi jj,,k2.(Jj@jjt jj;@j-,3 !;pjj(@j,jCLij
2
il(-@r-lected. T1 ie author aflumpt;.; "o ;-Lve
U
e ';oLululon Of the ['01
m-iterl'i I -@Phere iwitl-h @l
'.'ol@wce Lit, it's 1-112il(J(2 thit,
la J@Jvcll prolkabilit.11, 0"
alid o ),Jven -index aC diopei-,ion;
t-fle r"Al, 'Jon i'lold. In
J n'q@ lllvd to corlipi (t-
'he

'I df
f d 1. C Vi j (3 drd t -a t 1. o
f-L J" r
r'111' I's tlhe o
11-1d '--11(2 OC tl-lt-'
3 )'J, 1- d1 11 and L.; e n b t,
(IV
14E2

0 _2 e _T' n I; Z; h;
SPheric-all Nebt,-kia
SOV/33-17-1-
e_ L* s t- il eaz-iinuth -in a spilericaI. system of
_@ordinat-es: L is "he energy of radiation per second;
, "he probability of a quant-um life-time; x ( ) is
-he index of dispersion of light by an element-ary
,,, c 1 -jzne .The problem is to find the values of I and B
frLmr. ecuations (2) and (7). The authlor explains his
,-.e,;hod of solvi-g these ecuations and discusses tWO
rarticular cases: (I) There is real absorption Of
liglit in this 'field; (2) there is pure dispersion in
"his flield. He then attermpts to apply his solution to
dust- nebulae by assuming the follow-inc-, ouantit-ies kno-,.;n
.irom. observation: optical radlus 0 equal to r... and
the radius of the nebula, r 0, It is more dil-ficult to
n x ana, lvihich mair be dete=_Iined by q- dy-.' n.-
J
---e di-stribution o.,L' the bri-h-ness ove- --he re'3-_-,Iar
di3l-, The author believes that the at)PI-lication of Ilis
e A _e o
f orr.,,.ulae to dust nebulae 11 lead to a knoal 5
Card 3/4 ("he opt-ica'L properties of such nebulae and the nature

C c n c e r n'- *,' I -- B 1, n e s s o 1' a
@Teb 1-11 a
Spherilcal ..
ASSOCIAr-,-,ICN:
SUBMITTED:
78001
SOV133 -37 - /3'
c-L dust particles, There is 1 -figure and 2 references,
Soviet and 1 U.K. The U.K. reference is
Chandrasekhar, Rad4ative Transfer, in 'Russian
.ransiation.
Leningrad State University Leningradskiy
-gosudars"-vennlry universite-J
It J
Sept-ember 1 1959
Card 4/4

SOBOLEV, V.V.
Theor7 of stellar evolution. Astron.zhur. 37 no.3:387-395 P,-Je
16o. (MIRA 13:6)
1. Astronomicheska3ra observptoriya Lening-radskogo gomudarstvennogo
universitota.
(Stars)
11 1
I;I
. @ *I

SOBC)LbT@__V_.V.
Some cosmogonic consequences of the statistics of hinary stars.
I (MIRA 14:9)
Astron.zhur. 38 no.5-920-926 S-0 '61.
1. Leninfrradskiy posudarstvennyy universitet im. A.A.Zhdanova.
.1e)
(Stirs, Doul,

SOBOLEV, II.V.; MININ, I.N.
- -
Isotropic light scattering in an atmosphere with finite optical
thickness. Astron.zhur. 38 no.6:1025-1032 N-D 61. (YURA 14:11)
1. Astronomicheskaya observatoriya Leningradskogo gosudarstvennogo
universiteta im. A.A.Zhdanova.
(Light--Scattering)

ra /S 0
89727
S/on/64/136/oO3/010/027
B019/BO54
AUTHOR: __ Sobolev, V.V Corresponding Member of the AS USSR
TITLE: The Diffusion of Radiation Tnto a Medium With Mirror-reflecting
Boundaries
PERIODICAL: Doklady Akademii nauk SSSR, 1961, Vol. 136, No. 3, PP. 571
574
TEXT: The author assumes that the reflection coefficient deDends on the
an-le of incidence. For the ratio between radiation factor and the absorp-
0
tion factor he gives the relation
B T(Ei I-- -tj + K(Ir- + t)) B(t)dt + (2)
-2
a
d@
-15
K (T) = r(@)e_' (3)
r(@) is the reflection coefficient and @the cosine of the angle of inci-
dence. A similar formula has already been derived in one of the author's
Card 1/4

89727
The Diffusion of Radiation Into a Medium S/020/61/136/003/010/027
With Mirror-reflecting Boundaries B019/BO54
earlier papers, in which case-, ljowever, he did not take the angular depen-
dence of the reflection coefficient into account. The analogous relation
B*'(-c) (4) is written down. The resolvents of (2) and (4) are determined
by means of the equations
+
(t
(5)
R-e,t) andF (1r,t) are the resolvents an4(-r) =r*(o -r)
holdu Thus the problem is reduced to determination of the functionsUL)
an4 (-t@). After complex calculationsP the following integral is obtained:
Oft
C(k)e- k,r- + 2)L xe-XT A.(1 /x) dx
2 X-1 2
Rn) +(2x+ln -@-)
+1
Card 2/4

89727
The Diffusion of Radiation Into a Medium S/02o/61/136/003/010/027
With Mirrur-reflecting Boundaries B019/BO54
k(1-k2 ) ( 'I
C(k) 2 j( B(O, d f , r(@)d@ ,
2 ) 2 1-k@
+k 1 1+k@
A(7) = 1 + r(@) 2 [1 - r(@)r(@)Jd@
B(O,
2 0
In this case it is assumed that A(@) has no singularities. The expression
for * -c) is obtained from the above equation by the substitution of -r(j)
for r( ). Two further special cases of (18) are studied: Without inner re-
flectl (r = 0) and with complete inner reflection (r = 1). V.A. Ambar-
tsumyan and I.N. 24inin are mentioned. There are 4 Soviet references.
Card 3/4

GTRZADYAN, Gricor Aramovich? k-ITMiTSUWAN, V.A,,., red,.; MUSTELI, E.11-1.,
red.5 SOMMY, A.B... red,.@ ISOBOLEV, VIV., red., KULIKOV.
G.S., red., BRUMNO, K_F, tel-dm. -red.
[Planetary nebulae]Planetarnye tumaimosti. Moskvo,., Gos.izd-,vo
fizilco-matem.lit-ry, 1962. 384 P. (MIRA 15:9)
(Nebulae)

AGEKYAN, T.A.; VORONTSOV-VEL'YAMINOV, B.A.; GORBATSKIY, V.G.; DEYCH,
A.N.; KRAT, V.A.; MELINIKOV, O.A.; SO V V. ; MIXMLOV, A.A.,
10' V
otv. red.; KULIKOV, G.S., red.; AKffu,'ROD. @I.;V.' tekbn. red.
I P
[Course on astrophysics and stellar astronomy]Kurs astrofiziki i
zvezdnoi astronomii. 2. izd. Moskva, Fizmatgiz. Vol.2. [By]T.A.
Agekian i dr. 1962. 688 p. (MIRA 16:1)
(Astrophysics) (Stars) (Nebulae)

S/560/621/00-311014/1,101p- 10
AUTHOR: Sobolev, V. Xr@, and I. N. Minin
TIt LE: Light scattering in a spherical. atmosphere. I.
PERIODICAL: Akademiya nauk SSSR. Iskusstvennyye sputniki Zemli, no. 14,
4
1962, 7-12
TEXT: Li ght scattering in an atmosphere consisting of spherical layers (e. g.,-
when the sun is low on the horizon or beneath it), is examined. An approximate
solution of equations for the intensity of radiation W and the total quantity of ra-
diation (B) is proposed on the basis of a method used by V. V. Sobolev to solve
the problem of light scattering in a medium consisting of plane-parallel layers.
First order scattering is accounted.for precisely, while scattering of higher
orders is approximated. Here only the first two compoinents are used in the
expansion of the scattering indicatrix in Legendre polynomials. The equations
obtained are valid for all relationships of the coefficient of absorption (a) to the
distance (r).of an arbitrary point in the atmosphere from the center of the planet.
Card 1/2

Light scattering ... S/560/62/000/014/00la/011
T,@zo s p e c i a 1 cases are considered: 1) where ais constant in the atmosphere
and 2) where a decreases exponentially w ith height. , Case (1) may be presumed-to
exist when the sky is totally overcast and case (2), when it is clear. The compu-.
tations could be simplified if it were assumed that.the thibkness of the atmosphere
is considerably less than the radius of the planet, as is actually the case. Li ght-
scattering in the Venusian atmosphere is recognized as a special case. Here the
atmosphere consists of two layers: a cloudy layer with an approximately constant
a and an underlying gaseous layer with varying a.
Card 2 9

SOBOLEV, V,V,
Some relations in the theory of light scattering. Astron.zhur.
39 no.2:229-234 Yx-Ap 162. (MIRA 15:3)
y universitet im. A.A.Zhdanova.
1. Leningrndskiy gosudarstvenriF
(Light--Scattering)

SOBOLEV, V.V.
Hydrogen lines in promineAces spectra. Astron.zhur. 39 no-4.632-
642 Jl-Ag 162. (MIRA 15.-?)
1. Leningradskiy gosudarstvennyy universitet.
(Sun-Frominences-Spectra)

S-()BOIEV, V.V.; IVANGV, V.V.
Intensity of-hydrogen smission lines in steLlar spectra.
Uch.zap.LGU no-307:3-17 162. (MIRA 15:9)
(Stars--Spectra)

GORBATSKIY, V.G.; MININ, I.N.; ; AMBARTSUMYANp V.A., red.; BUSTEL'
E,R... red.; SEVERNYY, A.B., red.; SOBOLKV V V red.;
KULIKOV., G.S., red.; AESELIROD, I. ., tekhn. re .
[Nonatable stars] Nestatsionarnye zvezdy. Moskva Fizmatgiz,
1963. 355 P. (kRA 16:4)
(Stars, Variable)

KAPLM4, Samuil Aronovich; FIKELINEH'., Solomon Borisovich;
AMBARTSUMYAN, V.A., red.; MUSTEL', red.; MTMYY,
A.B., red.; SOBOLEV, V.V., red.; 17ULIKOV, G.S., red.;
AKSEL I ROD) I. red.
[Interstellar medium] Mezhzvezdnaia sreda. Moskva, Fiz-
matgiz, 1963. 531 p. (MIRA 17;2)

ACCeSStOff NRt M4003731 8/0293/63/001/W2/0227/0234
AUTHOR: Minin, 1, N*i Sobolev, V. V.
TITLE: Light scattering In & spherical atmaybere.
SOURCE: Kossicheskiye Looledovaniya, v. 1, no. 2. 1963, 227-234
TOPTC TAGS: atmospheric light scattering,.spherical atuosphere,*planet&171
atmosphere, atmospheric layer curvature, light scattering, light reflection,
outgoing radiation, atmospheric pbsorptLon,.atmospheric: optical thickness,
planet reflected light, homogeneous aphere'luminescence.
ABSTRACT: The article Is continuation of the authors' previous work on
the scattering of light inaa planetary atmosphere which acepunts for the
curvature of atmospheriu layers (V.- V. Sobolev, I. N. Minin. Sbe "Iskusstvask-..
ny*ye Sputniki Zemli,'! vy* p. 14. Izd vo ANSSSR, 1962, str. 7). In the
present article, the-case of a constant atmospheric absorption coefficient
is considered. An analytical solution is obtained for the basic equation
determining the mean iiit-enaity of the diffused radiation, J, at a point iii
1/3 the atmosphere,.aubject to boundary conditions,' Theme conditions assum
that there "iota no diffused radiation incident upon the atmophore frM
Cwd

ACCESSION NR: AP4003731
the outside, and they account for the reflection of light from the planet's
surface. The expression for the quantity J of a homogeneous sphere is
derived for the optical thickness of the atmospherej'which is large in
comparison to the planet dimensions. The result Is similar totbut simpler
than that obtained by R..G. Giovanelli and J. T. Jefferies (Procs Ays.
Soc., 69, No. 11, 1077.1956). From the kno0ledge of J, the ratio B of the
radiation coefficient to the,absorption cQefficient can be derived for any I
point., The intensity of radiation leaving tho.stmosphere is then-expressed
to
i3e.
0
I f
where T is the range along a ray of light between apoint in the atmosphere
@and the observer T is the total path traveled by the ray in the atmosphere#,
and %* is the ii6ality.of.rodlation due to retleatton from the planatto
surfpce. The integral of the.equation in written'&* 11 + A to i!hore I to
the.4ntensiL-7 duo to first order scattering and I represents higher I
2/3
Card

ACCESSION NRt AP4003731
orders. For the case when the atmosphere can be approximated by a homogeneous
pphere and the observer to at a far field, the coordinates of any point are
iasily expressed in terms of TI, and an explicit expression for I is found*
This expression in further simplified by assuming an atmosphere with larse '
radius. The resulting expression for 11 closely approximate the total intensity
of scattered light for-small vall of X , the albedo, of the scattering particle*
or for small values of'C , the angle between the direction of liSht'-ingident 04
the planet and the ray directed toward the observer. It is further pointed out
that entirely different@ expressions 4re found for 11 when the stmosptftri to
assumed to consist of.plane a" parallel layers. Wigs art* has: Wiormlas
and 3 figures.
ASSOC1#1ON: Mona
SUBMITTEDt 20Feb63 DATE ACQ: 26Dec63 INCL: 00-
SUB CODEz AS 190 REr iOV: .001 armt 001
3/3
Card

ACCEMION MR: AN30012DS 81901 SOV00011 75/0004/0004
MTOWS Sobolevo V. (Corresponding Mwbers Acaftw of Balances USSR)
TIUM Space the laboratory of motlern p1waics
WJ=t Pravda, 24 Jun 63a po 4,p cola. 4.6
TOPIC TAGS: The atudar of universev possibilities of p4ting the astrophysical
observatories in space
7=.- MWW diffemt sciences am Presently concerned.vith the study of the
univerbe) the newst of these Is space astrophysics', product of the marriage
of astroVWslca, and rocketry and. the solution to the problem of placing an
observer mUlde this terrestrial atmosphere. Sobolev staites that the UV spectra
of stars Itill surface temperatures of 10,,000 -to 20,,000 degrees have been cbm
tained by means of rocket-borne instruments; It is felt that It Vould be a
signIfiewrb advance if the UV spectra of hat stare vith low luminosity, the
"utite dmarfa,," could also be obtained. The fllgbU of Wbovakly and
Tereahkova have brought science closer to a new advancess the day is approachina
when Uera_ vill be astropby"cal abservatorles in a3pace, and astrammers vM
land ca the planets of the solar ftatem.
C SPAO, - Itan no* 19
UM AM 2U=63

L 13-192-65 EWT(I)/FCO(w)/BbS/ES(v~r-in-M/ASD/ESP-3/APGC/SSD-
ACCESSION NR,- AP3001243 33/63/040/003/0496/0503:
3/00
AUTHOR: Minin, I.N.; Sobolev, V.V.
TITLEs Contribution to the theory of the scattering of li in planetary
atmospheres
SOURCE: Astronomicheskiy zhurnal, v. 40, no. 3, 1963, 496-563
TOPIC TAGS: planetary atmosphere, scattering of light, luminosity of planetary
atmosphere, twilight phenomena, terminator
ABSTRACT: This theoretical paper'examines the problem of the scattering of light
in a spherical atmosphere, continuing and extending the investigifion reported
in the authors' paper in "Iskusstvannyye'sputniki Zemli (Artificial Earth
satellites)", no. 14, Izd=.vo AN SSSR, Moscow, 1962, in wbLich the problem is
approximately reduced to a certain differential equation.- In the present paper
the problem is reduced to an integral equation. The solution of this problem is
essential for the study of the luminosity of a planet in the vicinity of the
terminator, i.e., that region of the planet in' which the altitude of the sun over
the horizon is low, also for the construction of a theory of twilight phenomena.
The integral equation for the source function is developed on the premise of
Card 1/3

T_ 11192_63
ACCESSION NRt AP3001243
isotropic scattering of the light. For the sake of simplicity, the planetary
atmosphere is imagined to consist of plane-parallel layers. However* it is
assumed that these layers, in a given locality, are illuninated by the solar
rays as though they were part of a spherical atmosphere. The reflection of the
light from the planetary surface is taken into,aceount. If it is assumed that
the atmospheric layers are illuminated by parallel solar rays at eaoh point,
then the equation obtained thereby yields the well-known equation of the theory
of the scattering of radiation in a planetary atmosphere. The integral.equations
obtained in the present paper will subsequently be numerically solved for various
cases. In particular, the authors inf-,@nd to examine in detail the case of a
gaseous atmosphere in which the absorption coefficient decreases exponentially
with elevation, also the case of a two-layer atmosphere.consisting of a lower
cloud-filled layer and an upper gaseous layer. The results of the calculation
will be applied to the study of the luminosity of the atmospheres of the Earth
and other planets when the sun is at v. low looal"altitude. Here the first-order
scattering will be taken into account exactly, the higher-order scattering
approximately. It is further intended to generalize the results of this study*
There are 46 numbered equations and 2 figures.
ASSOCIATIONs Astronomicheskaya observatoriya. Leningradskago gas. universiteta
Card ?'/3
17, - _7
MMWM@

;e no.,
a,7*

MININ, I. N.; SOHOLEV, V..-V.-,-
"Light scattering in the spherical atmosphere."
paper presented at the Atmospheric Radiation Symp, Leningrad, 5-12 Aug 64.

ACCESSION NR: AI?4043498 S/0293/64/002/004/0610/0618
AUTHOR: Minin, I. N., Sobolev, V. V.
TITLE: Light scattering in a spherical atmosphere. Part III
iSOURCE: Kosmicheskiye issledovaniya, v. 2, no. 4, 1964, 610-618
i TOPIC TAGS: planetary atmosphere, light scattering, atmospheric optics, atmospheric
absorption coefficient, planet brightness, planetary albedo
ABSTRACT- In this article, as in the previous parts of their study (Iskusstveany*ye
1, sputnild Zemli, No. 14, lzd-vo AIN SSSR, 1962, p. 7; Kosmicheskiye issledovaniya, 1,
No. 2, 227, 1963), the authors consider the problem of diffusion of radiation in a
planetary atmosphere illuminated by the sun's rays. The curvature of atmospheric
layers is taken into account. In the earlier studies the principal equations of the problem f
were derived and a solution was found for a case when the absorption coefficient for the
atmosphere is constant. Ia this third Dart of the study the assumption is made that the
absorption coefficient decreases exponentially with height. The problem is solved in the
first approximation and the following computations were made: 1. brightness of the
r-rat o s from e
planet near the terminator, and 2. brightness of the zenith during obse , I n th
Mor-T-L13

ACCESSION NR: AP4043498
earth's surface for different zenith distances of the sun. Table 2 in the original giver. ti,_
brightness of a planet near the terminator. Table 3 gives the values I and '6@ 1 (where I
is the intensity caused by first-order scattering in the case of a spherical indicatrix of
scattering and A I is the intensity caused by scattering of Wgher orders) as a function of
-n
solar zenith distance ',J) for different values of the optical thickness0of the ati osphere
The value AI is given for hvo values of the albedo of a planetary surface (A @= 0. 2 and A
0. 8). appro2dmately corresponding to summer and winter conditions. These data show that.
the relative role of higher-order scattering changes little with a change in solar zenith
distance. Table 4 gives the values of the total brightness of the zenith. A comparison of
computed and observed values of zenith brightness shows good agreement. The presented
theory of light scattering in a spherical atmosphere is rather approximate, but it can be
made more precise by taking into account a term neglected in one of the formulas or by
using an integral equation describing diffusion of radiation in a spherical atmosphere
derived earlier by the authors (Astron. zh., 40, No. 3, 496, 1963). The radiation trans-
port equation used does not take into account the refraction of radiation. However, re-
fraction apparently must be taken into account only in a study of first-order scattering for
angles close to 7r/2. In a study of higher-order scattering refraction probably can be
_k@
Z/3

ACCESSION NR: AP4043498
neglected, as it is neglected in the ordinary theory of light scattering in planetary atmOE@;
0
pheres. "The authors wish to thank Ye. B. Babkova and L. P. Savitskaya for comput-ationci
involved in this study. Orig. art. has 48 formulas and 4 tables.
ASSOCIATION: none
ENCL: 00
SUBMITTED: 31Jan64
SUB CODE: AA. OP NO REP SOV: 007 OTHER: 001
3/3

L 33594-66 EWT(m)/F.WP(t)/ET1 IJP(c) JD/RDVI
ACC NR: AR016201 SOURCE CODE: UR/0058/65/000/011/DO35/DO35
AUTHOR: Snhni ey, _3L,
TITLE: ExperimentaJ investigations of the energy band structure of crystals of group
A',-BVI, selenium., tellurium, and group PbS
Tq
SOURCE: Ref. zh. FLzika, Abs. 1ID268
REF SOURCE: Tr. Konis. po spektroakoDii. AN SSSR. t. 3, vYP- 1, 1964, 478-486
TOPIC TAGS: energy band structure, selenium, tellurium, lead compound, optic proper-
ty
II VI
ABSTRACT: The optical propqrties of single crystals of the A B were investigated
in the region of 1 - 6 ev. On the basis of the data obtained and those already
known, as well as the theoretical calculations of the energy band structure of the
crystals, models of' the band structures of the crystals under consideration are
proposed. [Translation of abstract]
SUB CODE: 20
1/1

ACCESSION NR: Ap4ol76)9 S/0033/64/041/001/0097/01O)l
AUTHOR: Sobolev, V.. V.
TITLE: An investigation of the atmosphere of Venus. 1.
SOURCE: Astronomicheskiy zhu@na), v. 41, no. 1, 1964, 97-103
TONC TAGS: Venus,-Venus atmosphere,.planet, luster curve, atmosphere light
scattering ;!, I
ABSTRACT- The article initiates a series of studies on the atmosphere of Venus.
From the planet's luster curve, the values for x ('Y) and N are found using the
latest advances in'the theory of light scattering. The expressions for these
values are derived and the quantities.h (X) and g (oQ are substituted. The
light scattering directrix x ('Y) was found o protrude noticeably, su-_;gesting
that light scattering is due to large particiles in the atmosphere. Sources of
possible inaccuracies include; measuring the planet's brightness when the scatter-
ing angles are smal.1; assuming that atmospheric strata are planopara liel although
their curvature maV show up when the phase angle@ art large; and assbming an at-
mosphere pattern ig which x (Y) and A are constant although actually these quanti-
ties vary with the'altitude. More accurate measurement of the optical properties
of the,@tmosphere requires finer observations and further theoretical efforts.
Card 2 V

ACCESSION NR: AM17619
"The author would like to thank M. L-@ Zvonareva for performing the calculations."
Orig. art. has: 4 6bles and 24 formulas.
ASSOCIATION: LENINGkAOSKIY GOSUDARSTVENNY*Y UNIVERSITET (Leningrad State
University)
SUB,MITTED: 27,lunO DATE@ACQ: Mar'@64 ENCL: 00
SU6:CODE: AA NO REF SOV; 005 OTHER:' 005
Card 2/2

ACCESSION NR: AP4022714
S/0020/64/155/002/0316/0319
AUTHOR: Sobolev, V. V. (Corresponding member)
TITLE: Radiation diffusion in a plane layer of a large optical thickness
SOURCE: AN SSSR. Doklady*, v. 155, no. 2, 1964, 316-319
TOPIC TAGS: radiation diffusion, radiative transfer, large optical thickness
layer, plane layer radiation diffusion, semi infinite medium radiation diffusion,
.radiation
ABSTRACT. The author discussed in previous publications (DAN, v. 120, no. 1, 1956;
v. 116, no. 1. 1957) the radiation diffusion in a semi-infinite medium, and in a
plane layer of finite optical thickness 't. . Now assume that t.,@ 1_,, the asympto-;,
tic solutions are sou:-,,ht for the quantity characteristic of the radiation field In
the layer. The integfal equation for the radiation diffusion in the layer is
.solved, and two special cases considered in debate: when the true absorption in
the layer is high, and when it is small. Asymptotic solutions for the Ambartsumyaa-
"The author is grateful to Vo V. Ivanvy for
Chandrasekhar functions are found.
useful discussion." Orig. art* has: 00 figures, 36 equations.
11-Card 1/2

ACCESSION NR; AP4022714
ASSOCIATIQI: Leningradakiy gosudarstvenny*y universitat im. A. As Zhdanava-
@(Lcningrad State University).
!SUIMITrED: 19Nov63 DATE ACQ: 08Apr64 ENCL: 0 0
SUB CODE: PH NO RKF Ws 007 OnMR: 001
i Card_ 2 /2

. @ (') i @ Ci j ""'ll @ ".if .
- I @ ) I
of radiaticn in nebulae of large oy,'JC;Li
Tru-3y 1@.strofiz. inst, ANT Kazakh. 'S'Sn' c:-.285-231 f65.
18: 6)

, - " I- - .1 , 1 ..2 1 .. ,

r7@8 1 f6 1 G;V "GD
C NR: AT6024379______
AC
AUTHOR: Sobolev, V. V.
R)IO000/6@ 105/0126
_MCE CODE: U 60/000/000/0
ORG: none
TITLE: Diffuse radiation in a gas
SOURCE: leoriya zvezdnykh spektrov (Theory of stellar spectra).
mo!icow, i7a-vo ritkuka, 1960'. 105-126
TOPIC TAGS; diffuse radiation, interstellar space, stellar atmosphere,,
radiation dispci-sion, absorption coefficient, emission coefficient,
ntegral equaLion, thermodynamic equilibrium
ABSTRACT- The theory of diffuse radiation in planetary nebulae, inlver-',
stellar space, and stellar and planetary atmospheres deals with
proceoses of rLdiation dispersion in elementary voluries. Denoting the
coefficients of radiation absorption and emission on the frequency v
from a spectral line with ov and EV 0 these coefficients can be deter-
mined by the integral equations
a e-,Vdy
'5v Ilk,
A (x + YP + a2
-00
Card 1/3

L 3821r@-66
ACC NR: AT6024379
where
V-VO AvE
X a@
AvD AVD
Av- and AvD are the natural and Doppler width of the line,, ko is the
ab@orption coefficient for one atom in the line's center when a = 0,
3
and n is the number of absorbing atoms in one cm The formula of the
absorntion coefficient becomes complicated when the Stark effect and
collisions are taken into consideration. The emission coefficient is
determined by the equation
where X is the probabil-1.Ly of reemission of the quantum from the lilnqt
0
after its absorption; c is the coefficient of true emission; Iv,*is tiie
V
intensity of emission, and w is a solid angle. The problem of diffus'.
radiation can be solved using the equation for radiation transfer a16
'the ray direction. The equation is transformed and adapted to cohereftV-
herent cases. In stellar atmospheres absorption and emission
and inco
occur not only in individual lines, but also in the continuous spectrumv
where a local thermodynamic equilibrium occurs. The equation syste
for diffuse radiation may be solved approximately and in exa*V@06
2/3
C.,d

L 33215-66
UG.Jng computers. The main functions of the equation system are com-
puted for various cases and are given in tabular form. Orig. art.
has: 72 formulas. [EG'j
SUB CODE: 03/ SUBM DATE: 17Mar66/ ORIG REF: 015/ OTH REF; 024
ATD PRESS,
Card 3 13

L 38214-66 EWT(l) GW/GD
ACC NR, A T-6 6-i4_;C6- SOURCE CODE: UR/oooo/ 6 6/ ooo/ooo /o-l- @Y/_6_iViF
1AUTHOR: Sobolev, V. V.
Vn%j; none
TITLE: Models of stellar atmospheres
SOURCE: Teoriya zvezdnykh spektrov (Theory of stellar spectra).
Moscow, Izd-vo Nauka
% 1966, 193-200
TOPIC TAGS: stellar atmosphere, effective temperature, gravity
acceleration, thermodynamic equilibrium, chemical compound, radiation
flux, absorption coefficient
ABSTRACT: A model of stellar atmosphere can be computed when the
effective temperature and the gravity acceleration are known. The
effective temperature can be determined from the measured brightness
and the radius of the star and the gravity acceleration from the mass,
using corresponding formulas. The model of the stellar atmosphere
depends upon many unknown physical conditions in the star. The compu-
tation therefore can be carried out using arbitrary assumpticns. Theusiml
assumptions are that: the stellar atmosphere is thin compared with its
radius; the energy source is located within the star and the radiation
energy passes only the atmosphere; a thermodynamic equilibrium with the
Card

L 38214-66
ACC NR% AT6024380
temperature exists in the atmosphere; the chemical composition of the
atmosphere is considered to be constant; and the absorption of radia-
.ive energy occurs in the range of the continuous spec trum. The 4
radiation flux in the atmosphere is considered to be equal to aTe wbere a
is the Boltzmann constant and Te is the ef fective tenperabire. These arbitrary ccnditons md&e the
computed result problematic. Formulas developed for solution of the
problem are transformed introducing real conditions and looking for
their accurate solution. A stellar atmospheric model can be solved
with high accuracy when the absorption coefficient does not depend upon
the frequency. The accuracy of the model depends upon the ratio AII/H
where 11 is the intensity of the radiation flux and AH its change from
one atmospheric layer to another. This ratio is associated with the
absorption coefficient, which is a complicated function of the fre-
quency, temperature, and the chemical compound. Orig, art. has:
25 formulas. .-I (EGI
I SUB CODE:
03/. SUBM DATE: lTMar66/
ATD PRESS:5'04,,V
Card 2/2

L 06254-67 EWT( m)/EWP@ 0 IJP( 6 JD/JG
ACC NR: ---- AP6031958--
AUTHOR: Kovtunenko, S. 1. S-obolev, V. V.-
ORGS none
TITIS: Reflection spectra of Ge, InSb, GaSb, InAs and G&F
SOURCEI Optika i spektroskopiya, V. no. 3, 1966, 322-324
TOPIC TAGS: reflection spectrum, germanium single crystal, indium compoundp gallium
compound, antimonide, arsenide, phosphide, semiconductor crystal
ABSTRAM The report dea-Is with the reflection spectra in the rangeof 1-6 eV of Go
and InSb dendrites, sDecular spalls of GaSb and InAs, and GaP wafers obtained by trare
port reactions. All ihe sDecimens had Darfe9t snecular surfaces 2 x 4 mm2 in area and
imDurities in the amount of the order of 101 C11,3. The data obtained were comoared
wilh earlier data and led to the following conclusions. In etched crystals, two in-
tensity of the shortwave component of the observed doublet is a-1ways much lower than
that of the longwave component, whereas in dendrites and spalls the intensities of
both comDonents of the doublet are ap roNimately equal, and the doublet maximum is
much more distinct than in etched samples. In the latter as well as in polished and
etched crystals, the relative intensity distribution between the maxima may change
from one sample to the nextp but the position of the maxi-a in the spectrum remains
unchanged. New findings made in the study include the observation of reflection peaks
.,.Cord-- 1/?--- UDC- .-535---1L2-:535-33S%6-0---

ACC NR. - AP60319-58
of 1.44 eV (InSb), 1.68 and 1.38 eV (InAs) and 4.77 eV (GaP), and a more accurate de-
termination (as compared to etched or polished crystals) of the spin-orbital splittin
of the valence band at point L. The 1.44 eV (InSb), 1.68 and 1.38 eV (InAs) peaks ar
attributed to L3
t-LI transitions, and the 4.77 and 3.76 eV (GaP) peaks, to
If" 15v r c and L3 1@ or A3 - A transitions. Authors are deeply grateful to
. Ma 0 9
V. . sl,@ N. m. I)emenkov, S. V. Isivinskiy, M. Ya. Dashevsk , I. I. Pt@an,
N. 1. Luzhna , A. 1. Koppel' and A. Ya. Nashellskiy for providing the specimens.
Orig. art. hast 3 figures and I table.
SUB CODEt 20/ SUBM DATE-' 15Jan66/ ORIG REF-' 003/ OTH REFs 008
i Ca,d 2/2

S/058/62/000/005/0117/119
A001/A101
AUTHORS: Gross, Ye. F., Sobolev, V. V.
TITLE: Investigation of the structure of absorption, emission and photo-
electric effect at the edge of CdSe crystal fundamental absorption
(Theses)
PERIODICAL: Rel'erativnyy zhurnal, Fizika, no. 5, 1962, 33, abstract 5V227
(V sb. "Fotoelektr. i optich. yavleniya v poluprovodnikakh",
Kiyev, AN USSR, 1959, 4o-42)
TEX".P:0 A fine structure is discovered at low temperatures, most complicated
at 4.2 K, in absorption and emission spectra of CdSe single crystals, as well as
in the spectral distribution of internal photoeffect. Absorption and emission
spectra are strongly polarized. Position of lines and bands in hbsorption and
emission spectra is constant for specimens being in free state, but varies very
strong1v in dependence upon strains and stresses in the specimen. Conblusions
are drawn on the observed bands in CdSe absorption spectra.
LAbstracter's note: Complete translation]
Card 1/1

CROSS, Ye.F.; SOBOLEV, V.V.
Fine structure of the main absorption edge of cadmium selenide
single crystals. Fiz. tver. tela 2 no-3:40@-413 Yar '60.
(MIRA 14:8)
1. Fiziko-tekhnicheskiy institut AN SSSR, Leningrad.
(Cadmium selenide--spectra)

? tq
81
S/020/60@113731/0 1/15/070
BO 1 4/BO I I
AUTHORS: Gross, Ye. F., Corresponding Member of the AS USSR,
Sobolev, V..,V.,
TITLE-, Photoluminescence Within the Edge of the Fundamental Absorp-
tion of Mixed CdSe - CdS Crystals
@k
PERIODICAL- Doklady Akademii nauk SS$Rq 1960, Vol. 133, No. 1,
pp. 56-59
TEXT: In their long introduction the authors discuss the complicated
structure of emission and absorption arising at low temperatures in a
number of crystals (CdS, CdSe, HgI 2' ZnS, and others) within the longwave
absorption edge. In the present paper, the authors study the photo-
luminescence of macrocrystalline CdSe-CdS solid solutions of CdSe single
crystals and of maorocrystalline CdSe- and CdS layers within their absorp-
tion edge. The emission and absorption spectra of CdSe single crystals are
analyzed in the first chapter. The great analogy with the spectra of
CdS single crystals is pointed out. The structure is discussed in greater
detail, andq among other things, the great differences existing between
Card 1/3 v

11
8 17
Photolumineacence within the Edge of the 5/020/6V133/01/15/070
Fundamental Absorption of Mixed BO14/BO11
CdSe - CdS Crystals
the bands of different crystals are described. The second chapter treats
pure macrocrystalline CdS- and CdSe layers. Agreement is found between
the emission and absorption lines of the CdS layers and thos 8 of the US
single crystals. The emission lines of US layers at T - 4-2 K exhibit
triplet structure, whereas the single crystals have a doublet structure.
According to the authors' results, the emission of CdSe layers has a
triplet structure. At T = 77-30K the emission of the CdS layers consists
of structureless bands, the CdS single crystals and pure CdSe layers have
a doublet structure. The third chapter deals with the macrocryBtalline
layers of mixed CdSe-CdS crystals. In the case of T = 4.20K, the Dhoto-
luminescence of all of the 20 samples under consideration has a s1ruature,
and the line spectrum consists of a few weak lines. On heating to 77-3 0K,
the emission intensity drops, the clearness of the structure and the in-
tensity of the shortwave lines of the edge emission likewise drop sharply2
while the intensities of the shortwave components of the doublet and
triplet structures rise. There are 3 figures and 18 references: 8 Sovietq
2 French, 3 German, 1 British@ and 4 American.
Card 2/3 LIK

-.roper, ; us o-.: binary sc.-aiconduc,ing compounds and Sencral izac
S. saidov (10 minutes).
Zxper:lm,antal investigation of the energetic structure of zones of
se@-.-Iconduczinq compounds. V. V. Sobolev (10 minutes).
TnVL.Stigation of the thermia] conductivity of doped gallium arsenide.
1. Aliev, G. G. Achmedli.
I I I -SboSe
Concerning zhe thermal conductivity of solid solutions 04 S52S3 - 3-
G. B. Abdulaev, A. A. Bashmnaliev.
(Presented by,M. I. Al.'ev--10 minutes).
:L-@;port presented at the 3--L. T-Tational Coz-Lffe-mance on Sezmi-cordvctor
Compounds, Kishinev, 16-21 Sept 191-,.",

SOBOLVEV3 V.V.
Possibility of obserV4 ng Bose-Einstein condensation ot excitons
_L -
in group AIIBVI crystals. Fiz. tver. tels. 5 no.10:3028-30370 0
163. (,-URA 16:11)
1. Institut i'iziki matematiki AN !,FDSR, lashinev.

L 18901-63 EWP(q)/EWT(m)/BDS
ACCESSION NR:- AP3oo6589
AUTHOR.- -Sobolev, V. V.
AFFTC RDW/JD
S/0020/63/151/006/1308/1319
TIME: Experimental study of1the band structure of hexagonal
crystals of seleniumvand tellurium [Presented by Academician
B. P. Konstantfn-ov,29 Exch :L9T3T-,
SOURCE: AN SSSR. Doklady*, v. 151, no. %@ 19639 1308-1310
TOPIC TAGS: Se, To, dichroism, crystal band structure, reflection
spectimmt crystal structure, crystallography, tellurium, selenium
ABSTRACT: Because of the similarity of the erystal structure of So
and To. the latter have a similar anisotropy of'optical, electrical
and other properties. Some references attribute the dichroism of
the edge-absorption to the doublet conductivity band, others to the
valency band. There are other discrepancies in interpretations of
the observed phenomena. Therefore, the author has investigated some'---
.optical properties of Se and Te crystals. The reflection spectra
were studied in the range from 1 to 6 ev. On the basis of these
studies, X-ray absorption data, as well as theoritical. computations,,---
Card 1/2

L 18901-63
ACCESSION NR: AP3006589
a scheme of the bands and the transition is suggested. Orig. art.
has: 4 figures.
ASSOCIATION: Institut fiziki i matematiki Akaderdi Nauk MSSR
(Institute of Physics and mathematica, Academy
of Sciences, YSSR),,
SUBMITTED: 2lMar63 DATE ACQ: 27Sep63 -ENCL-. 00
SUB CODE.-@, Ph. El NO REP SOV.- 007 OTHER: 010
2/2
Card

SOBOLLV9 V.V.
Complex structure of bands and excitons in cadnium selerlide
crystals. Dokl. At, SSSR 152 no.6.-1342-1345 0 163. (MIRA 16.11',f
1. Institut fiziki i matematiki AN Moldavskoy SSR#j Predstavieno
akademikom A.N. Tereninym.

ACCEMION NRs AMMOSS 3/0UV64/006M3/MW/M0
AUTHOIls Sobolev, To To
TITLEs Couplax structure in the valence band of crystals In the froup AI%V'
SOURGEs Fialka tyerdoeo tela, Y, 61, no* 3v 296ho 906-910
TOPIC TAGS: semiconductor band structure, spin orbital splitting, crystal
lattice derormations Brillouin zone, light absorption
ABSTRACT: The author has sought to find the valid Wlanation of structure in
the upper valence band of the investiCated crystals, which consists of three
subordinant bandso Two schema have been proposed for the origin,of these bandst
that of Birman,, in which the upper two banev are due chiefly to spin-orbital
splitting and the third to Um crystalline fJL91A, and that of Wield, In which
the upper two valence bands are due chief2y to the crystalline field,, and the thixd;
to spin-orbital aplittlage The aut1hor follows the lad of G. re, MID, (2=0 So
15D7s 1961) that during defamation the upper two valence bands In hsmgml
crystals may shift drAamrd relaUve to the 2wer conduction boa sithor almllarly
Cori. IA

ACCMION MR: AP4M9%8
(the Birman scheme) or dissimilarly (the HopfleU schms)s and be acamirm
absorption and reflection spectra in the region of fundamental absorption to
discover which view is correct* The position of the upper valance bands and of
the exciton lines of the first two exciton series'in crystals of CdSe and GdSO
after deformation, indicates a markedly different displacement of the upper two
valence bands, thus confirming Hopfield's view and contradicting Birmanla conclu-
sion. Discovery of ultraviolet absorption bands with triplet structure in CdSe
and CdTe, along with the known absorption band-in CdS,, leads the author to conclude
that- these bands may, be due to transitions t 1) between the th.-*ee upper valence
bands and the conduction band not in the cenioar of the Brillouin Sonep 2) between
the fourth valence band and the conduction band, or 3) between the valence bands
and the conduction band beyond the lowermost band. Data are ipaufficient to permit!,
proper selection of the best possibility. "In conclusion, I thank 6. Ye. Pikus for,;
valuable discussions and for making it possible to acquaint 110melf with his
computations before their publication," Orig* arte hass 2.figures and 2 tablese
A=IATIONs Institut fisiki i matematiki AN Moldo SMt# Kishinev (Institute of
Physics and Mathematics AN Holde SO)
Card 2/3

ACCESSION INRI AP4M$W
SUBMTED i MarO DM ACQs 3MAA
SuBcaul (RO 33 W SOV 006
ReLd 00
022
Cmw 3/3

ACCESSION NR: AP 4011487
AUMIOR: Sobolev, V.V.
TITLE: Exciton structure of cadmium selenide crystals
S/0051/64/016/001/0076/0084
SOURCE: Optika i spaktroskopiya, v.16, no.1, 1964, 76-84
TOPIC TAGS: fund"mental absorption, absorp'lon spectrum, exciton, exciton states,
free exciton, trapped exciton, cadmium sdenide, cadmium sulfide, zinc oxide, wurt-
zite
ABSTRACT: In a series of pervious experimental studies (V.V.Sobolev,Avtoreferat
kand.diss.,L,19G2; E.F.Gross,V.V.Sobolev,ZhTF 26,1622,1956; F7T,2,406,1960) there
were obtained the absorption spectra of cAdmium selenide single crystals. Measure-
ment at 4.20K using a high dispersion (6 A/mm) spectrograph and thin freely mounted
single crystals enabled the experimenters to record the fine structure in the re-
gion of the long wavelength edge of the fundamental absorption. The absorption spec-
tra of CdSe crystals were also recorded at 77.3, 160 and 290*K, for the most part
using single crystal plates 0.1 microns thick. The absorption lines at 4.20K, which
fall into three major gzoups , are tabulated. Two spectrograms are reproduced. On the
Card

ACC.NR: AP4011487
basis of the polarization behavior the continuous and line "edge" absorption of
CdSe may be divided into two parts. In the presentpaper the earlier experimental re-
sults are summarized, and discussed and analyzed from the standpoint of the excitoll
mechanism. The general conclusions arrived at on the baBds of analysis of the lines
detected in the region of the fundamental absorption edge are the following: 1) All
the absorption lines are very narrow; hence all three types of exciton states are
associated with non-localized excited states of the CdSe lattice. 2) All three types
of non-localized (free) excitons have the same energy level structure: the energy
gaps between the levels of one exciton are virtually repeated in the energy struc-
ture of the other two types of excitons. 3) The long wavelength and short wave-
length subgroups of lines in each of the three exciton groups can be associated with
the first and second excited states of the excitons, respectively. Some of the dis-
tinctive features of cadmium selenide crystals as compared with other wurtzite type
crystals of the same class are discussed. "I thank E.F.Gross for his interest in
the work." Orig.art.has: 3 formulas, 2 figures and 2 tables.
C,rd

L 217-32-65 ElFr (1)/F.WG (k)/T/EWA (h) Peb/Pz-6 ijP(c)/sS_n(c)As1)(a)-w5/SSD/
AFMD(t)/AFETR/FSD(c)/ESD(gs) AT
ACCESSION NR: AP4043391 8/0181/64/006/008/2537/2539
AUTHORI S012olev, V. V.1 Sy!rbu, Neiu.
TITLE: Band structure of gallium phos@hide
SOURCE: Fizika tverdogo tela, ve 6. no..8., 1964, 2@37-2539
.TOPIC TAGS: gallium compound,' band spectrum, doublet splitting,
conduction band, valence band, reflected radiation spectrum
ABSTRACT: The reflection spectrum of GaP at.290K had two peaks at
230 and 330 mg, thelatter a doublet consisting-of lines at 320 and
335 mg. The doublet peak at 3.7 ev corresponded. to direct interband'
transitions at the point L and the reflection peakat 5.4 ev cor-
responded to the p61nt X, which can beseen in the energy band
structure of GaP derived in the present paper (see'Fig. 1 of. Enclosure),
Herman's formula (J. Electronics, v. 1, 103, 1955) was used to cal-
culate. the energies of direct interband transitions and the separw-
Card 1/3

L 21732-65
ACCESSION NR. AP4043391
tion of the uppermost valence.band 'from -the second conduction ban1d
.at the point r. The conclusions of Gross et al. (PrTs, v. 3. 35430
1961) on the valence band structure of GaP are stated to.be incor-
rect. Orig. art. has: 2 figures.
ASSOCIATION: Institut f iziki i matematiki AN Mold SSR, -Kiahinev
(Xnstill-ute of Physics and Mathematicsi AN MoldSSR)
SUBMITTED: 23Jan64 ENCL: 01
SUB CODE: IC, OP NO REFISOVx .OTHER: 006
Card 2/3

L 21732-65
ACCESSION.NR: AP4043391
Card3/3

ACCESSION NR: AP4043392 S/0181/64/006/008/2539/2541
AUTHORS: Sobolev, V. V.; Andriyesh, A. M.; Sy*rbu, N. N.- Shumov,
S. D.
TITLE: Reflection spectra of crystals of groups 11-IV ani III-VI
SOURCE: Fizika tverdogo tela, v. 6, no. 8, 1964, 2539-2541
TOPIC TAGS: indium antimonide, cadmium alloy, group II element,
group iii element, group IV element, group VI element, reflected
radiation spectrum, band spectrum
ABSTRACT: This investigation was undertaken in connection with the
great interest which is attached to compounds of the CdSb and In Te
type. The energy structure of crystals of groups II--V and II1_3VI3
was investigated at 290K in the region 1-6 eV. The reflection spec-
tra of polished and etched crystals CdSb, ZnSb, 56% ZnSb-44% CdSb,
Cd4 Sb 3# Zn3Sb2, Zn4Sb 3' ln2Se3' In2Te 3' CdIn 2Se4 j Ga2Se 3' Ga 2Te 3'
Card 1/3

ACCESSION NR: AP4043392
GaSe, and GaTe were investigated. The similarities and differences
between the various spectra are briefly discussed. it -Lis c0ncbi-.-,e?1
that in view of the similarity of their reflection spectra, the
crystals CdSb, ZnSb, and Zn Sb , Zn Sb and Cd Sb have similar
3 2 4 V 4 3
energy-band structures and nearly equal transition energies@ The
general conclusion is that the compounds-of groups 11--V and III--Vi
are close to compounds of groups III--V and II--VI not only in
lattice structure but also in the type of bond and energy-band
structure. Orig. art. has: 1 figure.
ASSOCIATION: Institut fiziki i matematiki AN MoldSSR. Kishinev
(Institute of Physics and Mathematics, AN MoldSSR)
SUBMITTED: 23Jan64
f@k
SUB CODEj Ss NR REF SOV: 003
ENCL: 01
OTHERs 001
C,,d 1/3

ACCLWICN NIts AP4043392
INCU)SM 1 01
Ref lecUcn spectra -at T 2909K in the range of 1-6 dV; I - SnEbt 2 - OMP
3- 1"3
Card 3A

Ic
L'3-1085-65 EVIT(1)/EWT(m)/T/EWP(t)/EEG(b)-2/EWP(b) IJP(c)/SSD/A3D(a)-5/
ESD(gs)/ESD(t) JD
ACCESSION NR: AP4046631 S/0181/6'4/006/010/3124/3130
AUMOR: V.
ev"'V
TITLE: Energy band structure of als fgroups IV and III-V
SOURCEs Fizika tverdogo telat v. 6s @no. 10, 1964, 3124 3130
TOPIC TAGS: group IV element, group III alloy, group,V alloy, re-
flected radiation spectrum, energy band-structure, optic crystal
ABSTRACN, e ction spectra of sinqle@@_
-The Ruthors investigated th refle
I:Eqp, itnAs. nSb GaP, GaAs, and GaSb at 290K
in the range 1-6 eV. results yielded a larger numrm&b of re-
flection peaks than were previously obtained by the author and by
others. The band structure of the co ounds of groups III-_V is
MP
found to be very close to the band structure o*f crystals of group
IV, particularly germanium. The structures of the reflection spec-
tra of the crystals are explained on the basis of a scbeme for direct
Card 1/2
NONE&.

L 11085-6>
:ACCESSION NR: AP4046631
:interband transitions,at points L, X, and r, which were defined by
the author in his dissertation (State 2etical Institute, Leninqrad,@
1962). In addition, the spin-orbit splitting of the valence bands
at the points and L and of the transitions at the points r, L, and
;'X are determined. An arrangement is proposed for the location of
the extrema of the bands at the points -L, X, and r. The results
@are compared with experiment and with calculations by others, and
Some of the discrepancies are explained. Orig. art. has: 3 figures
:1 formula, and 2 tables.
!ASSOCIATION: Institut fiziki i matematiki AN MoldSSRI Kishinev
':,(-Inst�tute of Phys:Lcs Mathematics, AN MoldSSR)-
:SUBMITTED-.. 23LTan64
ENCL: 00
OTHER: 022
SUB CODE: SS, OP NR REF SOV. 007
Card 2/2

L EVVI (1 /j',/B';P(t')'1 T @Lp A- /'Rr'-'
ACC NR: AR60172LP4 SOURCE CODE: UR/00 58/65/000/012/--,0 "JI-DO 39
A'J'ILIHOR: Sobolev, V. V.
TITLE: Quantitative studies of exciton absorption in single
d- d i ox
of cuprous oxide, cadmium selenide, cadmium sulfide, a ea
@rvl --Yl -vl
SOURCE: Ref. zh. Fizilca, Abs. 12D326
REF SOURCE: Tr. Komis. po spelctroskopii. AN SSSR, t. 3, vYP. 1, 1564,,
487-494
TOPIC TAGS: exciton absorption, spectral distribution, crystal
absorption, absorption coefficient
fO3STPLACT: The spectral distribution of the exciton absorption
coefficient was obtained by the study of crystal absorption at low
temperatures. The contours of the lines were determined and the
U
oscillator strengths were computed. The theoretical and experimental
data were compared. (Translation of abstract] CKPI
SUB CODE: 20/ SUBM DATE: none/
pb
rcl

ACCESSION NR: AP4041384 S/0048/64/028/006/1090/1095
AUMIOR: Sobolev, V.V.
TITL6.- Optkcal invastigazions of the energy structure of bands In some crystals
,61-eport, Third Conference on Semiconductor Compounds hold in Kishinev 16-21 Sepl9'-4
133
SOURCE: AN OSSR. 1mvestlya. Serlya fizicheakaya, v,28, no.6, 1964, 1090.1095
TOPIC TAGS; reflected radiation spectrum, conduction band, silicon, germanium, in-
dium compound, gallium compound
ABSTRACT: The author has obtained the optical reflection spectra of crystalline St,
Ge and the six compounds of the type AIIIBV in which A is In or Ga.and B is .P, As
or Sb. The S1 and Ge spectra werti in good agreement with those of H.H.Phillip and
E.A.Taft (Phys.Rev.113,1002,1959; 120,37,1960) exqept for ihe Go reflection peak at:
3.35 eV, which was found to be much sharper than reported by Phillip and Taft. The
reflection spectra of the compounds were all very simiiar; each had one.intense
sharp peak between 200 and 400 millimicrons and a broad loss ititense maxinum be-
tween 400 and 800 odIlinicrons. The longer wavelength peak was absent In GaP and
double in GaSb and GaAs. Theme spectra are compared with results obtained by seve-
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ACCESSION NR: AP4041384
ral other workers. There is much agreement among the results of the different expez-
imentors, but there Is also considerable disagreement; further experiments to clazi@
fy this situation are now under way. The spectra are compared with calculated band,
structures and the features are tentatively identified. It is found that the X4-Xl
(X5-XIL) and I.3t-L, separations are approximately the same (2 to 2.2 eV1 in all the i
compounds investigated, and it is tentatively concluded that the lower conduction
band in crystals of the AIV and AIIIDV types shift by the same amount at the L and
X points. Earlier optical measurements on CdSe by the author and Ye.F.Gross are re-!
:viewed briefly. These data, together with experimental data on ZnSe, CdS, ZnS and
..ZnO from various sources are compared with theoretical band structures. It is con-
-cluded that the band scheme of J.J.Hopfild (J.Phys.Chen.S611do 10,1597,2960) in cor@
':rect fop the sulfides and selen1des and that of J.L.Birman (Phys.Rov.114,1490,19-50
for ZnO. "The author In deeply grateful to S.M.Ry*vklnp U.N.Nasledav, k.A.Gorynovs@l
B.T.Kolomiyto and V.U.Tuchkovich for kindly providing the crystals." C)r:Lg-.art.haaS;
13 figures and 2 tables.'
tASSOCIATION: Institut fisiki i watematiki Akadeuii nauk Mo1d88R (Institute of Phy-
and Mathematics, Acadeny of Sciences, Ko1dWR)1
StMU17TIM: 00
XMCLI 00
SUILCOM loppas NR RIF SOV: 012
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OMU: 023,

L 5017-66 r=WT(m)/EWP(t)/ENP(b) IJP(c) JD
ACC NR- AP5026322 UR/0368/65/003/004/0372/0374
535.33
AUTHOR: Sobolev, V. V.
TITLE: Energy structure of aluminum antimonide ones
. .......................
SOURCE: Zhurnal prikladnoy spektroskopil, v. 3, no. 4, 1965, 372-374
TOPIC TAGS: crystal surface, crystal optic property, crystal lattice energy, light reflection
coefficient, spectrum analysis, aluminum, antimonide
ABSTRACT: The recent intensive development of the theoretical structure of the energy zones
of crystals in the k-space and the establishment of a direct connection between the reflection
spectra'in the E,-Eg region and the structure of the zones led to a successful investigation of
crystal reflection spectra in the domain of self-absorption. The least studied of the M-V gro
of compounds seem to be the AlSb crystal. An energy level diagram for the AlSb crystal zon s
(shown in Fig. 1) has been proposed elsewhere. To check these theoretical predictions the pre.
sent author carried out reflection spectrum determinations shown bi Fig. 2 in good agreeme4
with the energy level diagram. Numerous studies of the influence of surface conditions on th6
crystal reflection spectra of Si, Ge, GaAs, GaSb, GaP, InAs, InSb, and InP indicate that the@
position of the maxima does not change in spite of possible large variations in the shape of th6
curves. "The author thanks M. S. Mirgalovskaya, and I. A. Strellnilvoya for Idndly supplying
the AM monocrystals, S. G. Kroitor for carrying out the measureRents, and M. Cardona add
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