SCIENTIFIC ABSTRACT DAVYDOV, A.S. - DAVYDOV, A.S.

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• Collection: Scientific Abstracts
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• Document Creation Date: January 3, 2017
• Document Release Date: July 28, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT


Sep/Oct
Spectra, Absorption
"Theory of the Absorption Spebtra of Some Poly-
atomic Molecules," A. S.Marylov, Phys Inst,
Acad Soi Ukrainian ME, 1 3/4 PP
"Tz At Nauk SM, Ser Piz" Vol Xn, No
P -44Y -5,
ftisting methods of calculating energy states
of polqatomio molecules are meatiefactory.
Three methods are usually used: (l) valence
bonds, (2) molecular orbits, and (3) anti-
symmetrical molecular orbits. DwAor dancrIlMs
.aww method base& an antleymostrioal vays-
1qA9T86
USM/ft"Ics (Conta) ft.P/Oot
functions. Gives synopsis of ble paper and
alecussion VMoh ensued.

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the crptal, unepoWized with the rk-c.vK-tor p~ralkl to the
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by the unequal %patsalcwicntationvianioctrtnt;t-nuAt. in thr
crystal; equal ork-niation wouk] cau%e ouly a thift of thc
testux. Th6 rrult contradirts the concituion of Ift-Ornusn
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type of naphthalene or anthnicene. tmutitiort~ mitt only
littireen the pound bAair And the uplwf at )qjwj-t "ICe u1
the corrgy zone of the eiritrif state. N. Thon

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Frawn that vKktd state the CkMrm can POSO to tile Son-
wilconalatent gate Jr. with i '- of 0.107 e,v.. and
tb~Dcc to of the optical " . ad tht
PWANO lut;. In a Ileum. and in coa-
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OVA the disiorm. loom at the Palates Is FM dOwful
hm lis =t N. 7%w

DA.VYN)V.I A. S.
I

DAVYDOV. A. S.
PA 56/49T103
NOT 48
Wh*'F*QtioIiS'*
bhthemsi~ics,"Applied
'Calculatiug-.tb~.Nouorthog0qftI QLMlity of Wave
Amations bj thd Moleddlarm Orbit Metbo&," A. S.
Ziev State U,
'Dav7doir, Chdii~ of TY40retiqal Phy'
~3 31~ vp.
."Zhur Piz-Xhim" Vol XXIIP No 11
ts
Develp h Rimple for=la with-which, given ree4i
determijaed:bv the mqleoular-orbit method wlthoii~
.domputation of - the ove?~Iapplng integrals of'tbe
wave ftaotla6s, valixes, be:obtained with cal-
Aulation of theae,'Int is. Slibmitted, 24, Feb, 48.

Dfvydovs A* Be
'25363
Otvet At S. Davydova Na,Pisbpio A..Bly*enfelbda 1r4c.Po Povodu Statbi
A. S. DavydovaA-Vychisleide Nizaldkh ElektroiuVkh Urovnoy Molekuly
Naftalina>>~ 44Zhi-nale Eksperim, I Teoret Fiziki.3'> 1948., vyp. 77
Zhrnal Eksperim. I Tooret. Fizild., 1948, VYP. 7, s 671-72
SO:-,LETOPIS NO. 30, 1948

DAVYDOV., A.S. DOC PHYSICOMATH SCI
Dissertation: "Theory of Light Absorption by Molecular Crystals."
26 Sep 49 -.
Physics Inst imeni F.N, lobedevt Aftd Sci USSR
So Vecheryaya Moskva
Sum 71

UWR/Physioe~ Feb 49
Absorption, Molecular
Crystallography
"The Molecular Theory ef Plero-ohrolem,7 A. S. Davydav,
Inst of PhyB, Ukrainian SSR, 7 PP
"Zhur Eks-ner i Teoret Piz" Vol =, No 'P
Att-e7ts to construct molecular theory of pleochrolon
or ~Otec
,ular crystals. Assumes energy states of
indivIdual. moleeulee are knovn. Investigates alter-
:4.,IDn of energy spectrum -when m6lecules combine Int--j
11
,rystal of any symmetry. Shove it Is possible that
n*w "Crystalline" absorption bands may appear, which
vanish when crystal is melted. Shove, using cryst~ils
USSR/Physics (Contd) Peb 49
cmtaining two and four molecules in a single
62~ystalline nucleus as an example, that the frequenp
of absorbed- light will depend on the directions
of~
propagation and pole-rization. Submitted 5 Jut'48
4
2,
.............

I
I
DAVYDOV., A. S.

DAVY-DOVj, A. S.
1A 165TioB

Tbettry of Itambesseass of walsed" aryoula. -A,- S.
I%vZIIT-. limit. AW. Sank S.S.S.M.. -'4r- Fig. 13.
t 151). cf. V.A. 44, 43'.Me.-In lool. crymak 2 t)1"
of excitatio" am possible: (1) k%ding to excilon warv*
throughout the crystal; (2) Leading to localized states. Ito
the becond CaLw the abwM1ion band don toot show the i,i-
fluence of the mcurturr of the tTptal, and it, palaritalinn k
Cive" by the oNeotAti-st of the mol.; ix. the i4bnipti4mi k
the %4tur a, in %olo, The hooior-Avikv t, ubprot K -A.
Its the fit-41 rair there Lre w-%vml mrxigly r"arized lksmI4
v%hich cAn be "vrtl hoin vAlco%. or the unit qvil, Zoeli
~L%t'ij4ji,jqj IrAdi to -innot honltw~vrwr whrn e%rit-,o- m-w-,l
to 4iot% with lmlivr tich-Cl. of ah-
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A.7

The Committee an Stalin Prizes (Of tb-- Council of Walsters WSR) in the fields or
science and Inventiow announces that the folloving scientific works, popular ricien-
tific books, and textbooks have been vibnatted for coupetition for Stalin Prizes for
the years 1952 and 1953. (2T2!!MYa rpultura, Moscow, No. 22-40) 20 F*b - 3 Apr 1954)
Nam
Title of Work
rcednated by
Davydov, A. S.
Prikhot1kov A. F.
Obreimov) I. V.
Research in the field of
the snectrosocopy of
moleciLlar crystals
Academy of Sciences,
Ukrainian SSR
SOII W-30604s 7 JulY .1954

DAVYDOVy A. S.
USSR/Physics Dispersion of light
FD-hq0
Card 1/1 Pub. 146-7/18
Author Davydov, A. S.
Title Theory of absorption, dispersion and scattering of light by solutions
Periodical Zhur. eksp. i teor. fiz., 24, 197-209, F(-%-b 1953
Abstract Obtain general formulas determining the shape of the curves of absorp-
tion, dispersion and scattering of light and their dependence in tempera-
ture and the other parwwters characterizing the oscillations of the
atoms of the solvent and their interaction vith the dissolved molecules
in various energy states. 3 references, including 1 foreign.
Institute Physics Institute, Acad. Sci Ukrainian 13SR
Submitted September 16, 1952

t I~f t -yclt-, Itimb -Cloven
M= A
min-TribDi 1110, 94L~ of Olt& iho
.-orlbo
solv~i atoms, Tho -p-ml b
phot
vj
ir

-,7,, j7
Title-
%brxM
Date-**

DAVTDOV, A.S.
7be-ory of ligbt absorption and dispersion in solutions. Pt.2.
Nauk sap.Kviv.un. 14 no.80-13 155. (MA 9:10)
(Solutions--Optical properties)

V)
U&WOptics - Physical Optics, 11-5
Abet Journalt Beferat Zhur - Fizika, No 12, 1956, 35749
Author: Agranovid, V. M., Pavydov, A.. S.
MmUtution: 116ne
Title: absorption and Luminescence Spectra;of Polyatmic Molecules
Original
Periodical: Nauk. zap. Uivalk. uo-t., 1955, 14) No 8, 15-20
Abstract: Starting with the idea that the polyatomic molecule can be considered
to some approximation as a complex system, obeying statistical laws,
a determination was -A of the shape of the absorption bands and of
the JI~aorescence bands of bomplicated molecules, characterized by
not too strong an interaction between the electronic and oscillatory
states (Neporent,, B. S.,, Eksperim. i teor. fiziki, 1951., 21., 172).
It is obbn that the levehim vdrror-sy=etry law should hold for
such molecules.
Card 1/1

Chemistry.- Crystals B-5
Abs Jour ReferatZhur-'r Khimiya, No 2, 1957, 3593
Author -Da
_Davydov A.S,,'Lubchonko A,F,.
Title i ~za tan'of the Dispersion Curves of Molecular
Crystals to t6calized Excitations
Orig Pub Ukr. fiz. zh-i 1956, 1, No :P-, m-ilg
Abstract On the basis of previously.obtained results (RZhKhim,
l!)561 67745.~ 67746) were calculated the configurations
of aispersion~.curves, (DC)'o:r molecular crystals in the
region of localized excitations, at different tempera-
tures. At hiF
,h temperatures DC have a configuration -anaim.
locous to tAiat of DC of thefree molecule on taking into
account the Doeppler,effect. On decrease of temperature
DC be(iomes.as,,yrLinetrical.in-i7elation to straight line exr
tending through maximzu of absorption band, perpendicu-
larly to tho f!requency,axiso At low temperatures, when
the absorption:s'pectrum, separates. into a system of lines,
Card 1/2 34

kit Mcs,
vau
t
gin
fFOrewLrmrl laah a 110T4 the eilt,
au )it VIS B.),--` #j,~i & ~nd 24 at
;tl smir aT . and ex:
of juplinexote c~ re-
Meg .
018 levelvez. a cmtul
;t 01 th4
uta
arx-dar ar M a 3
(fir 1, 0.0 1 1 ZAS cQTTr
dlumwlf"~t' 0 d luminucr"C",
tut~m Ora cl
vi It-ith. 91
witla tie Cu
to
ll~n ~j -, 074.
-ftction
C (for
jigtt andlul AtjtS_-13( I vaiucs for D
'~.gcltgtit IF D tht av- q. ,I,d, wern
For Vllrt I.
0 m :i--
6'. - M - I 'nes.
re5p., q,.r, .t,3 !k -IV the wai
at d 7.2
>
I d to D~!'
I-C
Prom Vltsl~ '1*`
1D tic
w ot Itsuroc~CCOCC of Luml tN-
_,jtans, al

USSR / optics &9 t~ K
Abs jour: Referat Zhur-Fizika, 1957, No 4, 10364
Author : Davydov, &k.
Inst : Not Given
Title :Theory of Absorption and Dispersion of Light by So,utions. II.
Orig Fab: Nauk zap. Kiivsk. un-t,, 1956, 14,, No 8) 5-13
Abstract: Unlike the preceding work by the author (Referat Mur.-Fizilm, 1955,
1521), it is assu d that at the instant of excitation of the im-
purity molecule the change in the forces of interaction with the
solvent leads to both a shift in the equilibrium positions for the
vibrations of the solvent atoms, as well as to a change in the fre-
quencies of vibrations themselves. General formulas are obtained
for the coefficient of absorption and for t,~e index of refraction.
It is shown that if there is no change in the equilibrium positions
of the solvent atoms upcm excitation of the impurity molecule, the
dispersion and index of absorption curves of the impurity molecules,
Card 1/2

USSR/Ruclear Physics Nuclear Reactions. C-5
Abs Jour : Ref Zhur - Fizika, No 4, 1957, 8788
Author : Dg-vvdov, A.S., Filippov, G.F.
StIr
Inst : Moscow F.-University,
Title : Concerning the.Problem of Scattering Lengths of Slow
Neutrons on Deuterons.
Orig Pub : Zh. eksperim. i teor, fiziki, 1956, 31, No 2, 34o-341-
Abstract : Scattering of slow neutrons on deuterons is fully deter-
mined by two scattering lengths 4 and a correspon-
;342,n st-
a142
ding respectively to two possibI p sof the
system. According to the experimental data two variants
of the values of the scattering length are possible.
A qualitative estimpte made by the authors, based on the
Pauli principle, favors orte of the variants, namely a3/2
= 6.2 x lo-3 cm, and a,/. =-o.8 x 1o-3 cm.
Card 1/1

DAVYDOV, A. S.f and FILIPPOV, G. F.
--------
"Coll-sative &citation of Oven-Even Atomic Nuclei
paper included in the program of the All-Union Conf. on Nuclear Reactions in 1"Iedium
and low Energy Physics, Moscow, 19-2? Nov. 1957.
Moscow State University.

AGRANOVICH, V. M. D;kVYW.V, A. S. (Acad. ~Ici. Ul~ &R. 11
"Optical 1,Mel of Nucleons-Nuclei Interaction in the Resonance
Region of the Compound Nucleus,"
paper submitted at the All-Union Conf. on Nuclear Reactions in kledium and Low
!%,ergy Physics, Moscow, 19-27 Eov 1957.

Z1,
It sshba. VkmUO
-b
backg-la4l. if
vith-timopticEj and tbeaant-tX-i
vi=tbim. The bad-groond. cuatmus dcpmd
Zily on iftx~m,- A airiiiitm the crystal str-=lum
grester thAi The mr.-pbontu cnira )~,. lbuz the displLce-
mint of thit barklFotind Stu. vitli mp-.lct to ul e 7im of
-,ronj -b-anna Irmsimm der-cuds c istntially on lhe -Amcl ure
the
br~-andray frequei6ts cf tbi. I;aullv vibratons, interaction
uitl, one vibmtlan hm-ach car lted to the sim-ult2imms
apptu=-L'a of Rve,al ba4zVmal rimx. If A* < i, -1c
of tbl. sat8kcs iu oue-di.q=sionall claills oln La
certmu ~=A cigimidew Rb 11te &risudw~y '.mqumck--.j, On
the 4);.thcT hamd,~ 3.4likoen6oial C2,,,
lau .1nays- - ji~', w imemi'dhAe vaLm of
vibra t~m fratu=.6*. f Therrfbre~ the sbilzing of the Wrk.
grouid max, in thil ~;pwLm oftbl~ mol. crys~ can-wt t~--
compred witlilbu vibrations lotiml Imm Ram4n e4sp~-mkia
Atlit ~Qlow- ~OOdwjan i'3-fwr=ml lly:

56. 4., ~ '?411,r,2
A LPTHOR DAVY-WOV. A S., FILTWOV, oj.
nteraction
TITLE _jo~~manof~n;rti& oi: a System of Particles in I'
(Moment inartaii sistemy vzaimod*ystvLWusIrhikh chastJ.P, Russian)
Pa.IODC.1,AL Zhurnal Eksperivic, it Terorato Fiziki, L957# vol 32,9 lit 4,, pp 826 - 836
(U.S.S.R.)
ABSTRACT The paper under review investigates the problem ofthe cutoff of the
collective motions in a system consisting of N particles in interaction
with each other*
Card 112
A system consisting of three particles of *~!al masses. - In this
chapter,, the authors Investigate three particles without spin and of
equal masses m. these particles being in interaction with each other
by eentral forces of any arbitrary kind. By introducing new coordinatsaj,
the authors of the:0qper under review go over to the center-of-mass
system, The paper u~dor - ,'~ew follows the computations step by steps
For the followir4; magnitAidosk explicit expressions are given. - poten-
tial energy, of the systim-ppp)irater of the total angular momentum of
the entire system., Hamilton" operator of the entire system, The opera.
ters of the square of-the total angular momentum and of its projectum,
commute with the total Hamiltonian. For this reason, the magnitude cor-
responding to these operators are integrals of this motiono The syatem
of equations as obtained in the paper under review is then a good appro-
ximation, if (a) the three-particlea system is symmetrical about sin axis

56-447/~5;2
AUTHOR
_PAIYDOVZ A.S., IELINICHENKO, D.M.
TiTi~ On t'he secona Approximation in the Problem of the Scattexi ng of Slow
NeutronsIBy Coupled, Protons
(0 vtorom priblizhenii v zadache rasseyaniya medlennykh neytronev guye-
zannymi protonami. Russian)
PERIODICAL Zhurnal Eksperim. i. Teoret. Fiziki, 1957, Vol 32, Nr 4, pp 94a. - 94'~
(U.S.S.R,,)
ABSTRXT First or all the paper u der review refers to some relevant previously
'~
proceeds to investagate the convergence of the
published papers. Then
second approximation in the problem of the scattering or a tilow 0)
natron by a proton situated in the formation of a molecule of the mass
M. First of all, the paper under review puts down a formula for the
scattering matrix Tba.for neutrons of the energy zero., - the accuracy
of this formula includes the second approximation. In the theory devised
by Schwinger-Lippmann, the second approximation diverges at the censide-
ration of the scattering of a neutron by a harmonically bound proten.
The author of the p"r points out a bringing about of convergence which,
"*'- his spimion, is not justified from &mathematical point of view. But
-is above-mentioned second approximation converges always then, when the
wave functions of the read molecules (instead of the wave functions of
idealized systems) are used. In a real molecule the high excited states
correspond to the decaying system. The cerrospmnding expression is writ-
Card 1/2 ton in its explicit form in.the paper under review. Even if the energy

56-4-50/52---
AUTHOn:- -DAV-iDOV A.S., FILIPPOV,G.F.
TITLE3 The QualraNle Moments and the Zero Oscillations on the Surface
of the Axially-symmetrio Nuclei. (Kvadzupol'nyy9 momenty i
nulevn,e kolebaniya poverkhnosti aksiallno-simmetrichaskikh yader,
Rue8ian).
PERIODICAL: Zhurnal Eksperim. i Teoret. Fiziki$ 1957, Vol 32, Kr 4s PP 945 - 947
(U.S.S.R.)
ABSTRACTt For the! purpose of simplification the authors here investigate
even-even atomic nuclei. In the generalized model of the nucleus
the nucleons located outside the nucleus are described by means of
the one-particle approximation, and the nucleons within the complete-
ly filled-up shells (nucleus trunk) are noticeable on!.,,, by their
collective properties. As collective coordinates the authors hisre
selected the threo EULER angles as well as the variables B and r,
which characterize the deviation of the nucleus from the spherical
shape. In adiabatic approximation investigation of the motion of the
outer nucleons in the field of a nucleus trunk with fixed shape can
be carried out. The energy of the interaction of the outer nucleons
with the nucleus trunk (which are averaged over the state of
motion< V - ABeoer of the nucleons) will depend upon the
coordinates B and and will play the part of an additional
Card 1/2

56-6-2;/56
a
AUTHOR AGRANOVICBjV.M.,,DA )OVJA.S ISAUWN
TITLZ Optical Model of Interaction!"ITetween Nuoleons and Nuclei
in the Resonance Region of the Compound Nu-'aleus.
(Opticheskaya modelO wzaimodeybtviya nuklonov s yadrami
v oblastl rezonansov sostavnogo yadra.- Russiaai)
PERIODICAL Zhurnal Ek-sperim. i Teoxet. Fiziki 19579 Vol 32, Nr 6,
pp 14?9-1436 (U.S.S.R.)
ABSTRACT The energy dependence of the real part and -the imaginary
part of the effective potential is investigated here by
taking account of all components of the compound nucleus.
For the pmrpose of not complicating the problem by taking
account ojE' COULOUB55 interaction, the authors here in-
vestigate only the interaction between one neutron and
one nucleon.
The dependence of the real paxt of the o2tical potential,
upon enerLj: At first the formula for the real part of
this potential is given. Next, the authors determine the
energy dependence of the relative motion of the mean value
of the real part of the optical potential. The authors are
interested here in the domain of energies which correspond
to the resonances of the cross sections of the nuclear
reactions. At energies of the relative motion I >- 30 UeV
CARD 1/3

ASSOCILTIM
PRZSSNM- D BY:
BUMMI.T71M.-
MILABLE:
CA" 3/5
Op*l-oal Hodal. of In"erac'.0-on between Bucleons and buclei
in the RDucnamcs Regton. oAl tho Oompound Hucleus.
56-6-20/56
not givign.
-
17-8. 1956
Library of Co4gress.

The Rotation Bands of Even-Evgn Axially-Symmetrio Huolei,
56-2-42/47
the relations -1) - J(J + 1064
P -----A-- A 2f2
(JA wo . (%,r + (1 /2) tI I + J (J+1)/64 4 +J(J+1)/66 +
+(1/2)6 2(t _1)2 . The present. statement gives the results
of the solution of this system of equations for the case
01. A diagram illustrates the dependence of
FV(J)/hwo upon the parameter 5. At 6 ~2,5 the oollecti-
ire spectrum of the collective excitations of the even-
even nuclei decomposes into a system of rotation-vibration
bands. A table compares the theoretical values of the
excitation energy of the first and second rotation band
of the exoited states of some nuclei with the qxperimental
values. The same table contains the values of -the
parameters tta and 5 which were used in the course of
theso computations. A second table contains the ratios of
CARI) 2/3 the energies of the first and second rotation state.

AU THORS Dav7dov, Asset Filippov, G.F* 56-3-25/59
-------------------
TITLE: Collective Excitation of Bven-Even Atomic Nuclei.
(Kollek,tivnyye vokbazhdaniya chetno-chetnykh atomnykh yader)
PERIODICAL: Zhurnal Eksperim. i Teoret. Fiziki, 1957, Vol- 33, NT 3,
PP- 723-729 (USSR)
A.*BSTRACT: The collective oxcitition of the levels of axial-symmetrical
even-even nuclei is theoretically treated by means of the in-
creased Bohr nuclear model. It is shown that the collective ex-
citation of such nuclei is characterized by 2 types: a) excitation
which is accompani d by only a small vatiation of the nuclear
quadrupole moment I b) excitation which is connected with an
important variation of the nuclear quadrupole moment. The ex-
oitatiOU mentioned at b) occurs especially in the case of nuclei
which do not deviate to a great extent from the spherical form.
In the case of nuclei deviating to a great extent from the apbarical
fwwl;6~e form mentioned at b) does not play say role in the
ease of transitions with small energies variations. For the first
4 - 5 excited states of the auolei
128
116
72
76
134
Cdi14
Pt 192
Pd 106 th
e
i
x
S
es
e
e
nerg
0
Sn
t Ge
t Ba
,
9
,
P
t
of the excited states as well as the inherent spin values are com-
Card 1/2 pared to the experimentally found values and in general a good

21M PHMB I BOOK EUTAITATION SOV/1588
Davydov., Aleksandr Sergeyevich
Teoriya. atonnogo -jadra (Theory of the Atomio Nuoleus) Moscow.,
,Fi=mtg:Lz, 1958, 611-p, 12,000 copies printed.
Ed,: Ifeje* Zhabotinskij~; Tech* Bd,,.* Mrashova,, N., Ya,
PURPOSE: This book is intended to serve as a,text for indepen4fant
study by individuals with a sufficient knowlefte,of.theoretical
physics, but the USSR MLn:Lmtry*of Higher Education also permits
its use as a textbook for students in State universities,
COVERAM This book presents a revised.and enlarged edition of
lectures delivered by this author at the ", Los Depailment of
'Moscow State University ix4 Lomonosov, The text analyzes pinb-
lems in nuclear theory relating to phenomena occurAring at vaergy
levels up to 100 Nev. But.,,syeoial attentica is given to the
nuclear shell model, the genera-lized nu6lear model, and problems
Card 1/14

DAVYIK)Vp A. S. and FILIPOVp G. F.
"LlUat RortAtionnel Do@ Boya= Pair-Pairs."
Repart presented at the Intl. Congress for Nuclear Interactions (Lmr Inergy)
and ftelear Structure, Paris,, T-12 JUly 1958.

,.S. and FILIPPOV, G. F.
DAVYDOV..~ A
--Moscow State University.
"Rotational States in Even Atomic Nuclei." Nuclear Physics, V. 8jp~(1958)
(North-Holland Publishigg Co., Amsterdam) ep. :137-A.1f.
Abst:ract: A theory of the energy states and the electromagnetic transitions between
them is developed for neuclei which do not posses axial symmetry. It is shown that
viol%tion of axial symmetry does not significantly change the rotational states of
axial nucikei and leads to the appearance of new energy states. The reduced pro-
babilities for Et and 141 transitions between various rotational statA,,s are computed.

HUNCARY/Nuclear rhysias - Structureand Properties of Nuclei C-
Abs Jour : Ref Zhur Fizika, No 3, 196o, 5329
Author : Daylidov, A.S., Filippov, S.F.
Inst : Moscow State University.
Title : Collective Excited States of Even-Even Atomic Nuclei
Orig Pub : Acta phys. Acad. scient. hung., 1958, 9, No 1-2, 169-
176
Abstract : The energy of collective excited states is calculated under
the assumption that the nuclei have an axial syrmietry.
Conditions are obtained under which the collective excit'l-
tions can be separated into rotational and vibrationa .
See also Referat Zhur Fizika. 1958, No 6, 12634
Card 1/1

The Collective Interaction of Odd Non-Spherical Nuclei SOV56-34-6-31/51
irreducible representations of the rotation group. The second
part of this paper reports on the collective excitations of
the odd non-spherical nuclei. A table compares the theoretical
values of the energy necessary for the excitation of the first
and second vibration-rotation bands of the excited states
of the odd nuclei (which were obtained in this paper) with
the corresponding experimental data., Comparing the spectrum
of the collective excitations of the odd nuclei with the
spectrum of the collective excitations of the even-even
nuclei-some conclusions concerning the parameters used in the
calculations are obtained. There are 1 figure, 1 table, and
8 references, 3 of which are Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (moscow state University)
SUBMITTED: January 24, 1958
Card 2/1')

21 (0)
AUTHORS: Davydov, A. S., Filippov, 0. F. SOV/56-35-2-18/60
TITLE: Rotation States of Nonaxial Nuclei (Vrashchatelinyye
sostoyaniya neakeiallnykh yader)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1958,
vol 35, Nr 29 pp 440-447 kUSSR)
ABSTRACT: In previous papers by the same authors (Refs 1 - 4) the energy
levels of nonspherical nuclei were investigated on the basis
of a generalized model of a nucleus according to Bohr and
Mottelson (Bor, Mottellson) (Refs 5 and 6) for collective
excitation without disturbing axial symmetry. In the present
paper a theory of energy states and of the transitionsamong
them is worked out for nuclei without axial symmetry. It is
shown thatp though in the case of a disturbance of axial
symmetry the rotation spectra in even-even nuclei change
only relatively slightly (compared,to those of axially
symmetric nuclei), new rotation states (with J - 2, 3, 4---,)
o0cur. In the case of slight deviations from axial symmetry
these levels are considerably higher and are undisturbed;
in the case of major deviations from axial symmetry it is
Card 1/2 found that part of these additional levels is considerably

Rotation States of Nonaxial Nuclei SOV156-35-2-16160
reduced. Thus, the ratio of two excited levels (1. level -
spin - 2) fromooto 2. In the second part of this paper the
authors-investigate the probability of electromagnetic
transitions between the rotation levels of non-axially
symmetric nuclei. A comparison between theory and experiment
shows that the so-called y-vibrational energy levels of
even-even nuclei must be looked upon as rotation leVelB.
The same appears to be true for several nuclei with a spin
sequence of Oy 29 2~ 3. There are I figure, 3 tables) and
24 reforenoeal 6 of which are Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow State
University)
SUBMITTED: March 17, 1958
Card 2/2

21(0), 24(5) SOV/56-35-3-21/61
AUTHORSt Davydov, A. S.,.Pilippov, 0. F.
TITLE: Magnetic Transitions Between Collective Excited States of Even-
Even Nuclei (Magnitnyye perekhody mezhdu kollektivnymi
vozbuzhdennymi sostoyaniyami chetno-chetnykh yader)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1958,
Vol 35, Nr 3, pp 703-7o6 (ussR)
ABSTRACT: The present paper is partly based on a previous work (Ref 1)
in which the authors calculated the probability for electric
quadrupole transitions between rotational states of non-axial
even-even nuclei; it was found that a number of energetic
states of non-axial nuclei. can be well explained by assuming
that they refer to rotational states. In the present paper the
authors calculate the probability of magnetic dipole transi-
tions between rotational states with the spins 2 2 Such
levels are observed in the case of the nuclei Se76 ; Te 122
188 186 192
Os , 08 , Pt etc. As already shown by reference 1, it is
Card 1/4 possible, by knowing the ratio between the second 2+-level and

SOV/56-35-3-21/61
Magnetic Transitions Between Collective Excited States of Even-Even Nuclei
the first, to determine the parameter r- and the ratio of the
reduced probabilities for transitions. In the present paper the
reduced probability of an M1 transition between 2 2 states
as well as the ratio between this transition and an E2 transi-
tion between the same states is calculated. The values obtained
agree well with experimental results (Ref 3). For the intensity
ratios of magnetic dipole- and electric quadrupole transitions
the general formula T(MJ)/U'(E,J+1),-,, [25(2J+1)/A 2/3 (I~W)M'avl 2
(according to reference 5) applies. For A,-30 and to-1100 keV
the ratio is ri 104, for heavy nuclei at twu rJ 1 MeV it is r-4 10.
For the ratio investigated by the authors the formula
T(Ml)/T(E2) - (0,03k 2)-l . B~Mlt 22 -.&1
,j was derived, where
k - (E22 - E B(E2; 22 - 21
21)/JLo. For the ratio of reduced transition prob-
abilities (magnetic dipole -4P electric quadrupole) it holds
that B(Mli 22 - 21 6ogRN~', it is, therefore, independent
B(E2; 221- 2)
Card 2/4 (eZR0 of t and (Rcr nuclear radius)

SOV/56-35-3-21/61
Magnetic Transitions Between Collective Excited States of Even-Even Nuclei
The numerical results foreA. - 5,05-10- 24erg/G, g R ' 0,4, and
R 0- 1,2 Al/3.10- 13 am are:
Nucleus E22-E 21 [keV] T(Ml)/T(E2) Percentage of E2 transition
(experimental - Ref 3)
Be' 16 643 9,8.10-2 98 + 1
Te 122 693 119.10-2 92 + 4
186 -3
Os 627 6,5.10 99 � 1
05 188 480 1,04. 10-2 - 99,6
There are 1 table and 4 references, I of which is Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow State University)
SUBMITTED: April 3, 1958
Card 3/4

24(5) SOV/56-35-6-27/44
AUTHORS: Davydovp A. S., Lubchenko. A. F.
TITLE: in Cryptals in the Region of Exciton
Absorption (Elektromagnitn e volny v kristalle v oblasti
eksitonnogo pogloshcheniyaF
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheakoy fiziki, 1958,
Vol 35, Nr 6, pp 1499-1507 (USSR)
ABSTRACT: Pekar (Ref 1), Ginzburg (Ref 2) and Agyranovich and Rukhadze
(Ref 3) investigated the propagation of light waves in the case
of spatial dispersion. They showed that in frequency ranges
near the exciton absorption band, waves with the same frequency,
propagation direction, and polarization may have different re-
fraction indices. Only the transparency domain was investi-
gated in this connection. A reduction of the amplitudes of
electromagnetic oscillations during their passage through met-
ter is a consequence of 1) scattering of the wave and b) of
energy transfer from the wave to particle motion (genuine
absorption). In the present paper only glanuine absorption at
crystal temperatures near absolute zero is investigated, name-
ly for a frequency range that coincides with the exciton ab-
Card 1/3 sorption band. Because of the connection between genuine ab-

SOV/56-35-6-27/44
Electromagnetic Waves in Crystals in the ReGion of Exciton Absorption
sorption and the' innermolecular excitations and oscillations
of the molecule, the absorption band broadens also at tempera-
tures near OOK. Davyd ov (Ref 4) showed that an excitation in
molecule crystals by light waves occurs in two different ways:
a) as 11 localized excitation and b) as an exciton excitation.
The absorption bands according to a) have nearly a Gaussian
distribution and are independent of crystal structure, those
according to b) depend essentially on crystal structure. Thus,
investigation of the band structure of exciton absorption of-
fers a possibility of investigating crystal structure, of the
dependence of the energy of the exciton state on the wave vec-
tor of the exciton, and of exciton interaction with lattice
oscillations. Davydov (Ref 5) as well as Davydov and 3~ashba
(Ref 6) developed a theory of the structure of light absorption
bands by basing on the example of a onedimensional crystal
and on a more general case, without, however, considering the
dependence on refraction- and absorption coefficients. In the
present paper the authors develop a theory that furnishes re-
fraction index and absorption coefficient in absorption bands
corresponding to exciton excitations. They operate with the
Card 2/3 model of the pure molecule crystal, in which molecules are able

SOV/56-35-6-27/44
Electromagnetic Waves in Crystals in the Region of Exciton Absorption
to perform only translation- and rotation oscillations of a
certain (average) value. It is shown that knowledge of the
structure of the absorption band may be instrumental in de-
termining the sign of the effeative exciton mass. Furthermore,
the conditions are given which lead to a zero refraction in-
dex at the short wave side of the excitation band. Electro-
magnetic waves of these frequencies are totally reflected,
they penetrate only very little into the crystal surface.
This total reflection is found to vanish with rising tempera-
ture. There are 3 figures and 8 Soviet references.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow state University)
SUBMITTED: June 26, 1958
Card 3/3

0guyDaIji ffs.
21 (7), 21 (8)
AUTHOIJ: Rudakov.. V. P. -2,125
TITLE: IX All-Union Confer=)i; on Nuclear Spectraoc'-.:-Py
(IX Vsesnyuznoye soveshchaniye pc yaderrcy spsktrrisk:~pii)
PERIODICAL: Atomnaya energiya, 1959v Vol 7, Nr 'i - PP 76-73 (US60
ABSTRACT; The IX All-Union ConferenQe wau held from Jarvi:a.-y 26 to
Pabnzarj 2, 1959 at i(harikov. lka-a than X,OO participants heard
100 lecturea, the most importpxt vf vihi~;h (lez-11; with the
following fields., Nuclear Theory, General probleins cf 11--decay.
A. S. Dav-vd MGU): Theoretical 'classffi~-at.:toa ---f lorr-enerKy
excited nuclear st.ates. L. K. Peke7~. Darfo:nneOl nu'~'Ri. B. L.
Birbrair, L. K. Paker, L. A. Sliv (L-M): !z70.;.1arUPr.'.La
oscillations of defoTmed nuclei.. Ye. V. InDpin, V. Yi- Gcacbarv
S. P. Taytko (IMYTI)t Calculation c.f the ft-values wit'l-I matrix
elements foro-trarsit-Jons by mearns of t~e eenera)ize%1- nu~ilear
model. S. T. Belyayev (IAE): ConE;iaerr-tion c-f pair- correlation
in nuclei. A. B. Migdall (IAE): T-he application of the super-
conductivity model to nuzlei for the p-=pDee of ctalculating
their moments of inertiv. P. E. Namirovskiy (IAE).- Frutiem,, of
the neutron stp.~iility of rradle.". Ya. A. Omorodinski~ (IAE): The
Card 1/3 present stage in the theox.-7 of (I deco-V. V. V. Vladimirskiy,

IX. All-Union Conference on Nuclear Spectroacopy SOV/89-7-1-18/26
V. K. Grigorlyev, V. A. Yergak,.cv, Yu. V. Trebukhovskiy (ITEF):
Measurement of the angul.ar correlation 'hetween electron and
neutrino in the decay of the nwitron. V. 1.1. Lcbe.:3hev, V. A.
Nazarenko, L. I. Rusinov (LIVI); Nsasurement of the carelation
between the transversal election polar ".Z ELt. ion and ci-TculaT
polaxization of ~-qu=ta occurring lin the decay of
S e-4 6and Co 60. Decay Schemes. p-radiation of Nuolei. Y-a. P.
Anufri,yev, A. K. Vallter, Yu. V. Gonchar, Ye. G. Kopaaeyts,
A. N. L'vov, P. 14. Tutakin, S. P. Tsy+,k-c, P. V. Sorokin, A. S.
Deyneko, 1. Ya. Malakhov, A. Ya. Taranov ( Piz ik-c.--tekhnicheak- y
Kharlkovskiy inatitut (Fhysico-technical Institute, Kharkov)):
I _a 4,
11-11(p,,d, .4x40(P,',t) ar
The Si Ne2O(p,.-).. 3 ~Plv'
reactions. D. G. Alkhazov,, A. P. Grinberg, G. M. Gus.-Inskiy,
M. Kh. Lemberg, V. V. Rozbdeatverrilej~r, K. N. Yerokhine. of the
Laningradskiy fizikc.-tekhnicheskiy institut (Leningrad Physico-
technical Institute); Investigation of the Coulomb excitat,4.on
of the lower levels of some nuclei during their bombardmer '11, by
multiply charged ions (C,, N, 0. and No). A. V. Kalyamin, A. N.
hurim, V. 11. Pokro,,rskiy, V. A. Yakovlev (RIAN); New isotopes
Card 2/3

IX. All-Union Conference on 1-furlear Spectrosculy SOV/89- -1-1,3/2-1-
'161 153 57
Tu Ho HO -=d Ho B. S. Dzholepov, V. A.
Sergiyenko (LGU): Decoy sobemas of come neut-c-n-deficient
isotopes, set up on 'the basis cf measuxeiaen-,s of the coinai-
den,-.e of the inte=E~L c-mversion electrv-nE;. i"pectro-=:---opy
E'ngineering. 13. 3, Dzhelepcv, R. B. V. G. Nedovesov,
V. G. Chumin (RIA-11): oc-spec,tzometer with doubIe fo,:;using.
S. A. Baranov, V. ~. Beruchko, A. 0. Zelerdcov, A. P. Malev,
G. Ya. Shchopkin (IAE). Improved --speetvMa ter. I. F.
Barchuk, G. V. Belykh, V. I. Golyshkin., V. A. X:ivt,.zn (irAN
UkrSSR) : Magnetin. spectrograph for hea-vy ohaxred particles.
The representatives of the Ministerstyo radiotekhnIcheskoy
promyshlennos-ti (Ministry cS the Radlo-engineering Industry)
gave a report about IIeW Multipliers. The Conference was
closed Iby B. 3. Dzhelepc.v,. Who stressed the fact tbat nuclear
tables and reference works ought to la pablishea mnzch more
quickly in order to be of waal usa to the --e-xparimentsr.
Card 3/3

24(5)
AUTHOR. Da~vjdov, A. S. SOT./48-23-7-3/31

TITLE: Collective_______8tates of Atomic Nuclei (Kollektivnyye vozb-
Excited
uzhdennyye sostoyaniya atomnykh yader)
PERIODICAL: Izvestiya Akademii nauk SSSR. Seriya fizioheakayat 1959t
Vol 23, Nr 7t P.P 792-611 (USSR)
ABSTRACT: The introduction of the present paper points out that the ex-
cited state of many nuclei can be approximated by a division
into a single-nucleon excitation and a collective excitation.
This division is only usable for evena-even nuclei since there
the energy of thesingle-nucleon excitation in the order of
magnitfide of 1-5-2 Mev is many times larger than that of the
collective excitation. The collective excitation is character-
ized by the high probability of quadrupole transitions caused
by the collective motion of a large number of nucleons. The
former assumption that all nuclei possessed a spherical sym-
metry proved to be--wrongv and it became clear that many nuclei
are non-spherical. The collective motion of non-spherical
nuolei,is divided in-to an internal excitation causing an
oscillation of the surface, and a rotary motion of the nuclei
Card 1/4 which does not change the internal state of the nucleus.

Collective Excited States of Atomic Nuclei . . SOV/48-23-7-3/31
The existence of a rotary excitation of low energy is
characteristic of a non-spherical nucleus; three ranges in
the.periodic system of elements are indicated by formula
(1,1), in which the nuclei have a rotational spectrum. Table 1
indicates the first excited levels of some even-even nuclei,
and the values of the nonsphericity parameters P. The approxi-
mation of these nuclei by an ellipsoid is dealt with, the
equation (1,4) for the rotational spectrum of axisymmetric
even-even nuclei is given, and the interval rule(1,5) is put
forward for the energy levels of these nuclei. Examples of
these levels are,shown in figure 19 and at the end of the
introduction, the papers of a number of non-Russian and of the
following-Russian authors axe indicated as references for~the
subsequent chapters: G. P. Filippov, V. S. Rosto:vskiy,
D. A. Zaikin, B. Ti; Geylikman. The second part of the present
paper investigates,the rotational levels of non-axial nuclei.
In this connection, a diagram (Fig 2)*sbows the dependence of
the energy of the rotational levels of even-even muclei on
the parameter of non-axiality 1. The spin quantum numbers are
investigated for the determination of the rotational state,
Card 2/4 and formula (2,1) is indicated in this connection, which

Collective Excited States-of Atomic Nuclei -SOV/48-23-7-3/31
considers the non-axiality of the nuclei. The small deviations
of the experimental values from the theoretical ones in
figure, 2 are calculated by formula (2,2) considering the
coupling of the rotational energy with the internal excitation.
Further, the energy levels of various non-axial muclei are
investigated, and the level scheme.(Fig 3) is shown. The third
part investigates electromagnetic transitions between rotation-
al states of non-axial nuclei. At first, the wave functions
of these nuclei are obtained, then the probability of electro-
magnetic transitions is investigated; table 2 comprises the
reduced probabilities of electric quadrupole transitions.
This table shows that there are three types of this kind of
transitions, and they'are dealt with in detail. Table 3 com-
prises the ratios of the reduced probabilitles of quadrupole
transitions of different nuclei, and compares the experimental
with the theoretical values. Besides, this chapter inveotiga-
tes the ratios of the reduced probOilities of the transitions
to levels with spin 2, and in particular the ratios of the
reduced probabilities of quadrupole-transitions cf wolfram.
The fourth chapter deals with rules for the intensity of
Card 3/4 P-transitione to different rotational states of Ithe even-even

Collective Excited States of Atomic Nuclei SOV/46-23-7-3/31
daughter nuclei. At first, the corresponding.theory is
developedp then the ralios of the reduced probabilities in the
disin:fp,gration Of R018b are calculated- the excitation of the
rat k8i opal levela of the nu*alei of'OsI100 in the P-decsy of
Rel~ and in the K-capture decay of IrI90 is investigated,
table 6 showing the ratios-of fte reduced probabilities.
ChaPter 5 deals with equilibrium forms of even-even nuclei,
wid two diagrams.(Fig 4) show the energy of '-t2e basic state,
of the even-even nuclei as a function of y. In the summary,
it is ascertaineid.that the theory of the-rotational excited
states is in an initial stage of development, that the limits
of the applicability of the adiabatic approximation have not
been investigatod in this direction, and that for the solution
of these problems the intensity of the y-transitions must be
investigated theoretically and experimentally. There are 4
figures, 6 tables, and 36 references, 15 of which are Soviet.
Card 4/4

21(8)
AUTHORS: Davydov, A. S.f Zaik-'- D. A. SOV/56-36-~1-31/62
TITLE: On the k0scillations of the Surfaces of an Atomic Nucleus
(0 1'- kolebaniyakh poverkhnosti atomnogo yaclra)
PERIODICAL: Zhuxnal ekspeximentaltnoy i teoreticheskoy fiziki, 1959p,
Vol 36, Nr 1, pp 233-237 (USSR)
ABSTRACT: The authors investigate the stability of a nucleus with
respect to the variation of the value rcorresponding to
equilil)rium for the minimum of potential energy. On the simple
model 4f the anislotropic harmonic oscillator field for the
individual nucleons, the following is shownt The energy of the
first excited state, which corresponds to the r-oscillations,
is nearly of the same order of magnitude as the energy of the
single-nucleon excitation. The reduced probability of the
reduced quadrupole transitions to levels corresponding to.the
r-oscillations is some hundred times lower than the correspondibg,
probability of transition to the first rotation level of an
axially-symmetric nucleus. According to the authors' opinion,
these results confirm the high stability of the shape of the
nucleus with respect to r-oscillations. The first part of this
Card 1/4 paper deals with the potential energy of the surface oscillations

On the roscillations of the Surfaces of an SOV/56-36-1-31/62
Atomic Nucleus
of the nucleus. The nucleons with the mass m are assumed to
move in a potential of the type
2 3 2
V (m&j /2) 1- 1 (yk/R Here it holds that
k k
R R exp (T- (210)k) , where /3 and
k I k) ~k =T754'7f ~cos
rdetermine'the shape of the nucleus. Besides, it holds that
R1R2R3 ~ R3, so that 29 k = 0 holds. The energy of each nu .cleon
depends on 3 quantum numbers nk. For each filled shell it holds
that 'E n - Of and the total ener&y of the nucleons which
sk sk ~k
fill several shells (magic nucleus), can be written down as
EM + (1/2)D _0 (r, + (3/2)), where D>O
s
denotes the elasticity of the nucleus with respect to
/3-oscillations. The minimum energy of the nuclei with filled
Card 2/4 shells corresponds to the spherical shape of the nucleus. In

On the r-Oacillations of the Surfaces of an SOV156-36-1-31162
Atomic Nucleus
the second chapter the r-oscillations of the surface of an
atomic nucleus are calculated. The Sohr6dinger (Shredinger)-
equation for the determination of the energy of these
oscillations is explicitly written down. The solutionD 6f
this equation are to be found in form of periodic even
functions (with the period 2)r/3) of) " The authors confine
themselves to dealing with the first four terms in the
corresponding expansion in series. Expressions are written
down for the difference between the ground state and the
first excited r-oacillation level. The authors investigate
especially the filling of a shell with H = 5. The third and
last chapter of the present paper deals with the excitation
probability of the oscillations. An eXDression is written
down for the tra - Con probability of th~ nucleus from the
ground state to the firsteccited poscillation state under the
action of an electromagnetic field. The reduced probability of
the first r- oscillation state is some hundred times smaller
than the! corresponding excitation -probability of the first
rotational 'state of the rracleus. There are 6 references,
Card 3/4 3 of which are Soviet.

On the r-Oscillations of the Surfaces of an SOV/56-36-1-31/62
Atomic Nucleus
ASSOCIATION: Fizicheakiy institut im. P. N. Lebedeva Akademii nauk SSSR
(Physics Institute imeni P. N. Lebedev of the Academy of
Sciences, USSR)
SUBMITTED: July 10, 1958
Card 4/4

2,T(1-)*24(5)
AUTHORS: Davydov, A, Sop Filippov, Go F, sov/56-36-5-30/76
TITLE% On the Problem--of the Shape of Even-even Nuclei
('K voprosu.o fdrme chetnb-chetnykh yader')
PERIODICAL; Zhurnal eksperimental"noy; i. teorstioh~,skoy fizikt, 1959,
Vol 36) -Nr 5? PP 14P-1502 ' (USSR)
ABSTRACT: In: the"present very, detailed paper a. nonspherical nuclear
model i s investigated. ~irat*j, the pr Oblem of non-sphericity
is discussod by..way pf an intr.b.duction and discussed on the
basis of the n-amero .us works alri.-iay ydblished an'd deal#&, with
this field and phenomena connected with it.-Among other things
it is shown-that the majo"rity of the properties of the first
excited,states.,of.even-even nuclei may be well explained by the
assumption that-ilie fincleus-hai the-shapeof!Ltriaxial ellipsoid
when in e quilibAum.. (Bohr),,' -,'T"he authors, investigs~ted- the
possibility of,
a deviation of the equilibrium shape of a
.
nucleus from axial symmetry bry means'of a new methods which is
based on a generalization of Bohr's method (Ref 2). A model is
investigated in-which the nucleus consists of a core of
Card 1,112 8everal.nualeons and 2 equivalent external nucleons in a

On the Problem of the Shape of Even-even Nuclei SOV/56-36-5-30/76
with a certain j-value. According to Bohr the ellipsoidal
shape of the nucleus may be-characterize.d by the two parameters
and the authors derive formulas representing nuclear
energy. a funotions, of fl and,,r . The two figures show nualear
energy as a funotion-of.r and I with J - 2 and J - 4 at
various:l-values. It is shown that in the ground state of the
nucleus a nonaxial shape of the nucleus with.j> 3/2
corresponds.to the-energy minimum. Several experimental data
are given which are in keeping with t#e authors' theory. There
are 2 figures and 10 references, 3 of-which,are Sov.iet. -
ASSOCIATION: Moskovskiy,go.sudarstvennyy universitet,(Hosc.ow State:University)
SUBMITTED: November 20., 1958
Cara --2/2

24(5)
AUTHOR: Davydov, A. S. SOV/56-36-5-41/76
--- - ---------------
TITLE: Rotational States of Non-axial Odd Nuclei (Vrashohatellnyye
so3toYa4WL.neaksialInYkh nechetnykh yaderP
PMODICAL: Zhurnal eksperimental'noy i teoretiobeakoy fizik~ 1959,
Vol 36, Nr 5, PP 1555-1559 CUSSR)
ABSTUCT: In an earlier paper (Ref 11,the author, in collaboration with
G. F. Filippov, already showed that many properties of the first
excited states ok even-even nuclei, as e.g. the spin sequence of
excited states, their energies, and electromagnetic transition
probabilities, may be explained well by -the assumption that the
equilibrium shape of the nucleus may in first approximation be
considered to be a triaxial ellipsoid, which, according to Bohr,
may be characterized by the parameters /3&nd y-Cr-shows deviation
from axial symmetry). Car-Iain connections exist between these
parameterso B. T. Geylikman (Ref 3), D. A. Zaikin (Ref 4P, as
as well as the author and Filippov (Ref 5) already investigated
the possibility of a disturbance of the axial symmetry of the
equilibrium shape. In the present investigation the author
Card 113 analyzos the rotational states of odd nuclei on the assumption

Rotational States of blon-axial Odd 14uolei . 3OV/56-36-5-41/76
that the shape of the nucleus is characterized by fixed
equilibrium values of the parameters /3andr-, and that the odd
nucleon is in a state with a fixed value of the total momentum
j a 1/2. In the first part of this -Paper equations are derived
for the energy of the rotational levels of an odd nucleus with
fixed ~3 and K~ and for the case in which the external nucleon is
in the state J a V2. The equations obtained were numerically
evaluated by G. I. Marchuk and A. 1. Vaskin, the energy values
are given in tablesI and 2 for the spins 5/2, 7/2, and 9/2 for
various r-values between 0 and*17/6. The energy 6 of the rotational
states may be represented as a f=otion of r'9 0 1~-- r4 1)/39 i.e.
f(I? *-' r~,- In the second part of the paper theoretical
re ts are shortly com~lrqd given wilb the values obtained
experimentally for the T 8%nucleus (Dzhelepov,'Peker) (Ref 81~.
The left part of figure 2 shows the energy levels of this nucleus
determined experimentally, the right part shows those calculated
with 27 0, Agreement appears -to be satisfactory. The author
thanIts.G. 1. Marahuk and A. 1. Vaskin. for the numerical
computation of energy values. There are 1 figure, 2 tables, and
Card Z/3 8 refes-encesp-5 of'which are Soviet.

Rotational States of Ron-axi&I Odd Ruclei MY/56-36-5-41/76
ASSWIA'PrOKr lUzicheakiy institut im. P. N. Lebedev& Akademii nauk SSSR
(Physiou-Inatitute imeni P. N. Lebedev of the Academy of
Sciences, USSR)
SUBNTrMt December 7, 1958
Card 313

24(5)
AUTHORS: Davydov, A. S., Rostovskiy, V. S. SOV/56-36-6-24/66
TITLE: Transition Probabilities Between the Levels of the Rotation
Bands of Nonaxial-Nuclei (Veroyatnosti perekhodov mezhdu
urovnyami irrashohatellnoy pdosy neaksiallnykh yader)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheakoy Tiziki, 1959t
Vol 36, Nr 69 RP 1788-1796 (USSR)
ABSTRACT: It in the aim of the present paper to calculate the energies
and irave functions of the rotational states (J:~!tO of non-
axial nuclei and to derive the reduced probabilities for
E2 transitions between these states. Davydov and Filippov
(Refs 1-3) have already investigated the rotational states
of even-even nuclei on the-assumption that the equilibrium
form of the nucleus may be represented by a triaxial
ellipsoid. They found analytical expressions for the energies
of the levels with the spine 2, 39 5, and calculated the
transition probabilities between these levels. The results
obtained by these investigations are discussed. In the present
paper the author gives the results of numerical computations
of the level energies (spins 4p 6, and 6) for various values
Card 1/3 of the parameter 1, which characterizes the deviation of the

Transition Probabilities Between the Levels of the SOV/56-36-6-24/66
Rotation Bands of Nonaxial Nuclei
nucleus from the axially-symmetric shape. Calculation of the
wave functions of these excited states and of the transition
probabilities between them (quadrupole transitions in the
rotational band) are very detailed and are discussed in the
following. Table 2 shows the coefficients of the wave func-
tions for spine 4 and 6 in the case of y-values between 0 and
300. Tablo 3 shows the probabilities for the electric
quadrupole transitions between some rotational states of
even-even nuclei again for 9 y-values between 0 and 30*. It
is found thatthese transitions may be subdivided into 3 tYPes:
1) Such# the probabilities of which (in e2Q2/16n units) are
of lihe order of magnitude I - cascade transitions of the type
3 -'22, 42 a- 3, 42 -o,22. 2) Transitions between levels of the
ground rotational band and "anomalous" rotational levels of
another spin, e.g. 3 - 21, 41 - 22, 42 --o-21, 61 -* 42.
3) Transitions between levels of the same spin; e.g. 22 -9-21,
42-~1-41, In part 3 of the paper the conditions at which the
rotational states of the nuclei can be described are investiga-
ted by means of approximation wave functions. The here
Card 2/3 derived approximation formulas for the determination of the

Transition Probabilities Between the Levels of the BOV/56-36-6-24/66
Rotation Bands of Xonaxial Nuclei
E2 transition probabilities between rotational states of the
nucleus deviate only little from those for axially symmetric
nuclei. Comparisons with experimental results show that, if
the nuclear shape deviates from the axially symmetric shape,
the interval rule 1 : 3.3 : 7 : 12 observed in the rotational
band of axial nuclei is infringed. Thus, for 7 - 300 the
ratio 1 . 2.67 : 5 : 8 holds. Tables 4 and 5 contain further
red ced probabilitiesp viz for various transitions in
ONO and H22/1'321 for a number of other nuclei (comparison
between calculated and measured values). There are I figure,
5 tables, and 15 references, 4 of which are Soviet.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet (Moscow State Univer-
sity)
SUBMITTED: December 16, 1958
Card 3/3

21(a)
AUTHOR: Davydciy
SOV/56-37-1-22/64
TITLE: The Rules of Intensities of the P-Transitions for Different
Rotational States of the Even-even Daughter Nucleus
(Pravila intensivnostay dlya P-perekhodov na ra2lichnyye
vrashchatellnyye sostoyaniya dochernego chetno-chetnogo yadra)
PERIODICAL-. Zhurnal okeperimentallnoy i tooreticheakoy fiziki, 1959,
Vol 37, Nr Iffl, PP 137-142 (USSR)
ABSTRACT: As the relative energies of all rotational levels and their
wave functions can be definitely determined for any nucleus
if the ratio of energies of two levels (which have the spins 2)
is known, the relative probabilities of the P-decayp can
be estimated from a given state of the parent nucleus into
various rotational states of the nonaxial nucleus. Such re-
lative probabilities of the P-decays are calculated in the
present paper. Tbe author finds out at first the ratio of
the squaies of the modules of the matrix elements which
determine the P-decay into various rotational levels. An even-
even nucleus results from the P-decay of an odd-odd parent
Card 1/3 nucleus with integral spin. The P-decay is characterized by

SOV/56-37-1-22/64
,The Rules of Intensities of the P-Transitiona for Different Rotational-States
of the Even-even Daughter Nucleus
the moment L which is carried off by an electron and an
anti-neutrino. The operator can be assigned to such
a P-deoay, p denoting the projection of the momant.L.onto a
certain marked direction. For investigating the.excitation of
the rotational states of the daughtei nucleus in the P-decay,
it is convenient to express the moment 7n by the multi-
Lp
pole operators which are defined in thq coordinate
U
system connected with the nucleus. Such a transition is re-
presented by the transformation
L
Lp DVII (0i). Subsequently, expressions are written
down for the final states of the even-even daughter nucleus
(in adiabatic approximation), for the wave function of the
initial state of the parent nucleuap for the reduoed-prombility
corresponding to a P-transition with the moment L, and for
the ratio of the reduced probabilities. In the next part,
these theoretical results are comDared with the experime4t.
Card 2/3 A formula for the ratio of the values Tf n for 2 P-transitions

BOV/56-37-1-22/64
The Rules of Intensities of the P-Transitions for Different Rotational
States of the Even-.even Daughter Nucleus
with an initial state of the parent nucleus to various rota-
tional states of the daughter nucleus is uritten down.
7 denotes the half life, and fn the integral, taken over the
energy, of the distributi.Qn function of the electrons for
a given type of The results found are then applied to
189"y*238 and to the p-decay. of Eu154. Final-
the decay of Re ) HP
ly, the excitation of Ve -rotational levels of the OS190 Claus
in-the P-decay of Re19 and in the K-capture decay of IrT98
are investigated. There are 3 figures, 2 tables, and 10
references, 6 of which are Soviet.
ASSOCIATION: FizicheskJy-institut im. P.'N. Lebedeva Akademii nauk SSSH
(Institute of Physics imeni P. N. Lebedev of the Academy
of Sciences, USSR)
SUBMITTED: January- 13, 1959
Card,-3/3

DAVYDOVI A.S.
"Collective Ebmited States of Nuclei"
report sulmitted for the 12nd USSR, Conference on ffittlear Reactions at Low and
Intemediate Eaergies., Moscow., 21-28 July 1960.

S/048/60/024/007/003/011
B019/tO60
AUTHOR: Davydov, A. S.
TITLE: The Rotational Energy of Even Even and Odd Atomic Nuclei
PERIODICAL: Izvestiya Akademii nauk SSSR. Seriya fizicheskaya, 1960,
Vol. 24, No. 7, PP. 820-832 .
TEXT: This is the reproduction of a lecture delivered at the 10th All-
Union Conferenoe_Qn Nuilear Spectroscopy held in Moscow from January 19
to 27, 1960. In introduotion,the author discusses the theory of nonaxial
nuclei which had been developed by A. S. Davydov and G. F. FiliDDOV
(Ref. 2) as well as A. S. Davydov and V.-S. Rostovskiy (Ref. 3), and* which/
is based on three simplifying assumptione. Firstly, the internal state is -
not altered by the nuclear rotation; secondly, the three principal moments
of inertia of the nucleus are dependent on a parameter which determines the
deviation of the nuclear from the axially symmetric shapej thirdly, the
probability of electromagnetic transitions between the rotational states
is calculated on the premise of the electric charge being homogeneously
distributed in the nuclear volumes With assumptions the theory of rotational
Card 1/4

The Rotational Energy of Even - Even and Odd B/048/60/024/007/003/011
Atomic Nuclei B019/BO60
states of nonaxial even-even nuclei becomes very simple and can be easily
compared with experimental results. In the first part of this article,
a comparison is made between the results derived from the theory of rota-
tional states of nonaxial nuclei and those obtained from experiments. Here
the author refers to papers by American and Canadian physicists and
thoroughly discusses the comparison between theoretical and experimental
results made by To. P. Gri-zo-r'vev and M. P. Avotina (Ref. 7). This paper
also supplied the dependence, illustrated in Fig. 2, of the rotational
levels on the parameter of nonaxiality for 15 atomic nuclei. The deviations,,/ .
of the theoretical values from the experimental ones are greatest in the
case of Mg24, Gd154, and Hg198 nuclei. The second part of this article
deals with the further development of the theory of rotational states of
nonaxial even-even nuo lei. Formula (3) which has been formulated by the
British physicist Donald for the moments of inertia is then discussed, and
a-paper by Davydov, 1C.._S. Rabotnov,,and A. A. Chaban (Ref. 8) is mentioned.
Mention is made of the current assumption that the moments of inertia in
nuclei have values lying between those that are obtained with the hydro-
dynamic nuclear model and the model of a rotating solid body. The third
Card 2/4

The Rotational Energy of Even - Even and Odd S/048/60/024/007/003/011
Atomic Nuclei B019/BO60
part offors a,theory of the rotational states of odd nuclei, which starts
from the Hamilton operator (5) proposed by Bohr and Mottelson, and the
extension of the theory to nonaxial odd nuclei, made by Davidson (New York)
is discuosed. The author then refers to one of his own rapers (Ref. 11),
in which he studied the effect of coupling between nuclear rotation and
the motion of outer nucleons. D. F. Zaretskiy and A. V. Shut1ko (Ref. 12)
attempted to introduce an additional interaction of nucleon spin 4ith
nuclear rotation. The author obtains formula (9) for the enerU3~-levels,
I'-
which reveals that the interaction of outer nucleons with rotation gives
rise to a shift and to a splitting of the rotational levels of the core
of the nucleus. It is found that in nonaxial odd nuclei the core of the
nucleus has the shape of a triaxial ellipsoid. In the fourth part, the
author discusses the theoretical calculation of the equilibrium shapes
of nuclei, and makesfurther reference to several papers. Some configure-
tions calculated by Filippov are cited,.which correspond to nonaxial
nuclear forms and from uhich the conclusion is drawn that a correlation
in the motion of the outer nucleons gives rise to nonaxial nuclear forms
Card 3/4

The Rotational Energy of Even - Even and Odd S/048/60/024/007/003/011
Atomic Nuclei B019/BO60
in some cases. B. T. Geylikman (Ref. 16) and D. I. Zaikin (Ref. 17) are
mentioned. There are 6 figures, 1 table, and 17 references: 13 Soviet,
2 Canadian, 1 US, and 1 Danish. V/
ASSOCIATION: Moskovsk.iy gos. universitet im. M. V. Lomonosova
(Moscow State University imeni M. V. Lomonosov)
Card 4/4

83741
S/056 60/038/004/034/046
BO YB056
AUTHORS: Davydov, A. Rabotnov, N. S., Chaban, A. A.
TITLE. Rotational Energy and Moments of Inertia of Nonaxial Nuclei
PERIODICA.L: Zhurna.1 eksperimentallnoy i teoreticheskoy fiziki, 1960,
Vol. 38, No. 4, PP- 1311 - 1315
TEXT: A, S, Davydo'v., G. P. Filippov, and V. S. Rostovaki developed a
theory of the rotational states of nonaxial nuclei (Refs. 1,2). They
showed that the ratios of the energies of all rotational levels to the
energy of the first excited spin-2 level,can be uniquely determined if
the corresponding ratios for the second excited spin-2 level are known
from the experiment. It was further found that the relative probabilities
of electric quadrupole transitions between rotational levels may also be
determined from these ratios. These results were obtained on the assump-
tions that a) the inner state of the nucleus does not change during its
rotation (adiabatic approximation), and b) the main moments of inertia
of the nucleus can be expressed by the parameters A and 1:
Card 1/3

83
~ ~7
Rotational Energy anti Moments of Inertia of S/0 6 60/038/004/034/048
Nonaxial Nuclei Boo67BfCO56
Ii Asin.2(y - 2ai/3), 1 -.1,20. This formula corresponds to the hydro-
dynamic nuclear model. The authors therefore described this approxima-
tion as hydrodynamic. The authors now investigate the question as to
the manner in which these results change if the simplifying assumptions
are abandoned. The rotational states of nonaxial nuclei with arbitrary
(three) main moments of inertia are investigated in adiabatic approxima-
tion. It is shown that in general the rotational energy ratio may be ex-
pressed by two prrameters: by f, the energy ratio of two spin-2 levels,
and by 'q, a parameter depending on the character of the collective mo-
tions causing nuclear rotation; E (2)/E1 (2) > 1 , a, t a /E3(2).
~ - 2 f 2 3 1
In the following, the energies of all rotational states are expressed
by the dimensionless E: E - E/E,(2). Thus, the following relations hold
for the spin-2 and spin-3 states as, e.g., EW - I + E1(5) - 4 + f,
E2(5) = 1 + 4~. The energies of other rotational levels cannot be given
as functions ofj alone, but they are functions of and 71. For the
sPin-4 and spin 6 states, the corresponding formulas are given. With
Card 2/3

83741
Rotational Energy and Moments of Inertia of S/056 60/038/004/034/048
Boo6 B056
Nonaxial Nuclei
formula (5) the foll owing-inequalitias are given forf and
J'(3 - f ):!~-54~-43k -1 , Q