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ISOMER AND ISOTOPE SHIFTS IN SPHERICAL NUCLEI ON THE BASIS OF THE THEORY OF
FINITE FERMI SYSTEMS
L. Dautov, R. Kasymbalinov, D. Kaipov, M. Kadykenov
To cite this version:
L. Dautov, R. Kasymbalinov, D. Kaipov, M. Kadykenov. ISOMER AND ISOTOPE SHIFTS IN SPHERICAL NUCLEI ON THE BASIS OF THE THEORY OF FINITE FERMI SYSTEMS. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-141-C1-142. �10.1051/jphyscol:1980136�. �jpa-00219705�
JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au n " 1 , Tome 41, janvier 1980, page C 1
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141ISOMER AND ISOTOPE SHIFTS IN SPHERICAL NUCLEI ON THE BASIS OF M E THEORY OF FINITE FERMI SYSTEMS
L.M. Dautov, K.N. Kasymbalinov, D.K. Kaipov and M.M. Kadykenov
Institute of NucZear Physics of the Kazakh Academy of Sciences, ALMA-ATA, USSR.
Massbauer isomer s h i f t a s well as an i s o t o p e s h i f t i n t h e s p e c t r a of one and t h e same element a r e caused by t h e change of mean square charge r a d i u s of nucleus.
When nucleus excited on MZTssbauer l e v e l s as well a s i n t h e case of a d d i t i o n of a neutron p a i r t o nucleus weak change of nuclear charge d i s t r i b u t i o n should be ex- pected s i n c e i t s t o t a l charge remains un- changed. Theref ore it i s advisable t o con- s i d e r changes of charge r a d i i i n both ca-
oase of a d d i t i o n of nucleon p a i r t o them, have been c a r r i e d out i n t h i s paper.Super- l u i d i t y of n u c l e i and c o n t r i b u t i o n of a l l t h e s u b s h e l l s of core t o A (r2) have been taken i n t o account. The s e n s i t i v i t y of cal- c u l a t e d parameters A (r 2 ) t o t h e choice of nucleon i n t e r a c t i o n constants has been elu- cidated. The present approach i n t h e case of isomer s h i f t s of M8ssbauer t r a n s i t i o n s i s described i n d e t a i l i n /4/.Por i s o t o p e s h i f t s
s e s i n t h e framework of one t h e same ap-
proach. A
(
= $ 2 + 1 ) ( p g 2-
pfA),where j A
-
t h e angular momentum of single- Numerous d a t a from d i f f e r e n t experi- p a r t i c l e s t a t e , A-
t h e number of nucleons ments on changes of nuclear charge d i s t r i - T,
l!%2-
diagonal matrix elements of butions i n i s o t o p e s a r e a v a i l a b l e a t Pre- correspondent isotopes. We have used m i l s - s e n t .They a r e e l a s t i c e l e c t r o n s c a t t e r i n gon nuclei, i s o t o p e s h i f t s of X-ray K-lines, o p t i c a l i s o t o p e s h i f t s and experiments with muonic atoms.From t h e s e methods t h e f i r s t and t h e second ones should be consi- dered a s t h e most r e l i a b l e . AS t o t h e t h e - o r e t i c a l c a l c u l a t i o n s of i s o t o p e ef f e c t s a s a t i s f a c t o r y agreement with experiment have been obtained f o r heavy n u c l e i / l , 2 / and u n s a t i s f a c t o r y r e s u l t s f o r l i g h t ones /3/ i n t h e first c a l o u l a t i o n s on t h e ba- sis of t h e Theory of F i n i t e Permi-Systems (TFPs). MBssbauer parameters A ( r 2
>
calcu-l a t e d i n t h e framework of t h i s approach /I/ haven't been c o n s i s t e n t with experi- mental d a t a i n some c a s e s (119~n,131~e).
I n t h e r e s u l t a n opinion has been form- ed t h a t IFFS i s not a b l e t o desoribe para- meters 4 (r2) of a l l t h e n u c l e i with ac- ceptable accuracy.le consider t h a t calcu- l a t i o n s according t o TFFS without ap- proximation should be c a r r i e d out i n or-
son scheme of l e v e l s . O s c i l l a t i o n wave fun- c t i o n s have been renormalized ~(p~-+v)OA(fim The p r o b a b i l i t i e s of l e v e l s ' f i l l i n g by nu- cleon p a i r s have been obtained accord- i n g t o standard s u p e r f l u i d n u c l e a r model.
A l l c a l c u l a t i o n s have been o w f l e d out on e l e c t r o n i c machine BESB6-6.We have used two s e t s of c o n s t a n t s i n t h e c a l c u l a t i o n s :
*) fPP,fPn,f= -1; fPP- pn-fPn i n i n in" ex-f ex- ex' -2,
fPP fpn-+ -I.
2) f f 0 ex=
I n t a b l e I t h e r e s u l t s of t h e c a l o u l a t i o n of Mssbauer % r a n s i t i o n s paramet ersd (r2) with t h e f i r s t s e t of constants and d a t a from srnalysis of t h e isomer shifts of IV(8ss- bauer s p e c t r a / 5 / a r e represented,lChe com- parison shows t h a t o u r r e s u l t s a r e i n sa- t i s f a c t o r y agreement with experimental ones f o r n u c l e i with strong pairing.Parameters
(r2) of t h e i s o t o p e &ins obtained i n our ca3oulations with t h e second s e t of c o n s t a n t s are given i n Table 11. In t h e d e r t o draw such a conclusion. oase of i s o t o p e s with f i l l e d proton a h e l l s
Calculations of parameters A <r2) of
o16-18
9 C a 40-42 9 S Z I ~ ~pb20k208 o u r ~ - ~ ~ ~ va- ,s p h e r i c a l n u c l e i i n t h e case of t h e i r ex- l u e s of
A
(r2)ae i n good ;a(greement fith o i t a t i o n on Msssbauer l e v e l s and i n t h e experimental data. Disorepancy between thisArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980136
C1-142 JOURNAL DE PHYSIQUE
c a l c u l a t i o n and experiments t a k e s place t i o n s with c i t e d above two s e t s of nuoleon f o r isotope p a i r Fe 5k56, t h a t associated i n t e r a c t i o n constants have shown high sen- with presence of deformation i n t h e s e iso- s i t i v i t y of A (r2) of t h e isomer s h i f t s topes. The r e s u l t s t e s t i f y t o e s s e n t i a l and r e l a t i v e l y high s t a b i l i t y of d<r2> of contribution of a11 t h e subshells of nuc- t h e isotope s h i f t s t o t h e changes of nuc- l e u s including t h e very i n t e r n a l ones t o l e o n i n t e r a c t i o n constant s.
t h e formation of b{r2) i n t h e isomer and For subsequent improvement of a charge isotope s h i f t s . It should be e s p e c i a l l y r a d i u s d e s c r i p t i o n i n t h e framework of underlined t h a t t h e contribution of core's t h e present approach it i s necessary t o
subshells has been dominating i n t h e form- define more precisely t h e nucleon i n t e r a c - a t i o n of
A
(r2) value.The i n c l u s i o n of su- t i o n constants. I n this sense it i s expe- p e r f l u i d i t y i n t h e consideration of nuclei dient t o t e s t s e l f consistent constants of with strong p a i r i n g has a n influence on nucleon i n t e r a c t i o n s obtained by quantum- t h e value and t h e s i g n ofh(r2).
Calcula- hydrodynamic method i n /6/.Nucleus
E ( k e ~ ) 23.8 37.2 35.5 39.6 81.0 165.8 21.7 82.3 73.0 77.3 279.2 This work
bi<r2) 103(fm2) 3.7 -103 3.2 2.7 59.0 25.0 31.0 9.3 7.1 5.2 6 8 Exp./5/
~ ( r ~ > l o ~ ( f r n ~ )
5.0 -24.7 4.4 3.0 15.7 11.811.2 25.3 20.7 17.5-
Isotope
A
(r2) e m 2 ) IsotopeA
(r2) (fm2)p a i r t h i s e-scat. o p t i c a l muonic P a i r this e-scat. o p t i c a l m o n i c
work /7/ s h i f t s atoms work /7/ s h i f t s atoms
/7/ /7/ /7/ /7/
References
/I/Belyakov, V. A., Sov. Phys. JETP. preprint of I n s t i t u t e of Nuclear Physics,
49 (1965) 833. Kaz.SSR (1978).
/2/Bunatyan, G. G. and Mikulinsky,M. A. ,Yad. /5/Dautov, L,M, ,Kadykenov ,M.M. ,I(sipov, D.K.,
Fie.1 (1965) 38. preprint P-8 of I n s t i t u t e of Nuclear Phy-
/3/Inopin,E.T. andGonchar,B.Ju.,inSbor. sics,Ka~.SSB(1976).
Vopr. Atom. Nauk i Tech.6 (1973) 54. /G/Khodel,V.A. ,Yad.Fiz.l9 (1974) 792.
/4/Dautov,L.M.Kadykenov,M.M. ,Kaipov,D.K., /7/Atomio Data and Nuclear Data Tables '$01.14 N 5-6 (1974).
