THE STRUCTURE OF 6Li AND ITS COULOMB FORM FACTORS

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THE STRUCTURE OF 6Li AND ITS COULOMB FORM FACTORS

Kuniharu Kubodera

To cite this version:

Kuniharu Kubodera. THE STRUCTURE OF 6Li AND ITS COULOMB FORM FACTORS. Jour-

nal de Physique Colloques, 1971, 32 (C5), pp.C5b-269-C5b-270. �10.1051/jphyscol:19715144�. �jpa-

00214723�

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Kuniharu Kubodera

S e r v i c e de Physique Théorique

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C.E.N. S a c l a y

Nous é t u d i o n s l e 6 ~ i dans l e c a d r e ( 1 ) du modèle de Hartree-Fock s u r des f o n c t i o n s d'onde d ' e s s a i p r o j e t é e s e t ( 2 ) du modèle en couches avec c o r r e l a t i o n . Les f a c t e u r s de forme coulombiens, é l a s t i q u e e t i n é l a s t i q u e , s o n t c a l c u l é s e t comparks avec l e s données expé- r i m e n t a l e s .

The 6 ~ i n u c l e u s h a s been s t u d i e d w i t h i n t h e framework of ( 1 ) t h e p r o j e c t e d Hartree-Fock mode1 and ( 2 ) t h e s h e l l model w i t h c o n f i g u r a t i o n mixing. The e l a s t i c and i n e l a s t i c Coulomb form f a c t o r s a r e c a l c u l a t e d and compared w i t h t h e e x p e r i m e n t a l d a t a .

R e c e n t l y s e v e r a l p r e c i s e measurements have t h a n a r e g i v e n by experiment. The a n a l y s i s of t h e been p e r f ormed of t h e Coulomb f orm f a c t o r s of 6 ~ i PHF wavefunctions i n terms of t h e shell-mode1 w i t h r e s u l t s d i f f e r i n g c o n s i d e r a b l y from t h e pre- b a s i s r e v e a l s t h a t t h e y c o n t a i n i n d e e d a p p r e c i a b l e v i o u s ones.

[

1

]

[4] amounts of e x c i t e d c o n f i g u r a t i o n s and a l s o t h a t

The C O f crm f a c t o r i n t h e t h e e x c i t a t i o n s c o r r e s p o n d i n g t o c o r e p o l a r i z a t i o n e l a s t i c e l e c t r o n s c a t t e r i n g and t h e C2 form f a c t o r a r e t h e most i m p o r t a n t .

i n t h e i n e l a s t i c s c a t t e r i n g t o t h e f i r s t e x c i t e d One may q u e s t i o n , however, t o what e x t e n t t h e s t a t e g i v e n by t h e s e new d a t a a r e shown i n Fig. 1 above f e a t u r e s depend on a s p e c i f i c assumption of and F i g . 2 , r e s p e c t i v e l y . The r e s p e c t i v e r m s r a d i u s t h e PHF model. The problem of t h e s p u r i o u s motion and B ( c ~ ) deduced from them a r e 2.54 fm and 25.1 a l s o remains t o be i n v e s t i g a t e d . Thus a more s y s - e2fm4. The C O form f a c t o r can be e x p l a i n e d f a i r l y t e m a t i c s t u d y of t h e e x c i t e d c o n f i g u r a t i o n s seems w e l l by modifying t h e r a d i a l behavior of t h e s i n g l e - v e r y d e s i r a b l e . The h a r m o n i c - o s c i l l a t o r s h e l l

p a r t i c l e ( s . p . ) o r b i t s w i t h o u t changing t h e s i m p l e mode1 w i t h c o n f i g u r a t i o n mixing p r o v i d e s a conve- shell-mode1 c o n f i g u r a t i o n , ( o s ) ~ ( o P ) ~ . [5] I t i s n i e n t framework f o r t h i s purpose. A c a l c u l a t i o n i n i m p o s s i b l e , however, t o e x p l a i n t h e C2 form f a c t o r which a l 1 p o s s i b l e c o n f i g u r a t i o n s up t o 21iw a r e

by t h i s method. i n c l u d e d h a s been performed by t h e p r e s e n t a u t h o r .

The p r o j e c t e d Hartree-Fock (PHF) method o f f e r s [8] The s p u r i o u s motion has been c o m p l e t e l y e l i m i - a c o n v e n i e n t way t o t a k e account of t h e e f f e c t of n a t e d . The r e s u l t s p e r t i n e n t t o t h e e l e c t r o n - s c a t - e x c i t e d c o n f i g u r a t i o n s . [6] A d e t a i l e d c a l c u l a t i o n t e r i n g experiment a r e reproduced i n F i g s . l , 2 and of t h e form f a c t o r s on t h e b a s i s of t h e PHF method Table 1 . I t i s found t h a t t h e 4Hw and h i g h e r c o n f i - has been made by Suzuki and t h i s a u t h o r . [ 7 ] Two g u r a t i o n s make an i m p o r t a n t c o n t r i b u t i o n t o t h e t y p e s of t r i a l s . p . o r b i t s were i n v e s t i g a t e d : ( 1 ) C2 form f a c t o r . An extended c a l c u l a t i o n i s now i n t h e deformed o r b i t s w i t h m a j o r - s h e l l mixing and ( 2 ) p r o g r e s s .

t h e "molecular" o r b i t s , which a r e a l i n e a r combina- BIBLIOGRAPHIE

t i o n of t h e s . p . o r b i t s around t h e a-and t h e deute-

[

11 S u e l z l e ( L . f e t a l . , Phys.Rev. 1967,

162,

992 r o n - c l u s t e r s

.

The l a t t e r p e r m i t s t h e i n t r o d u c t i o n

[2] Eigenbrod ( F . ) , Z.Naturforsch.1968,

a,

1 6 / 1 of p a r i t y - m i x i n g i n t o t h e t r i a l wavefunctions and

[ 3 ] Hutchen (R.) and Caplan (H.), Nucl-Phys. 1969,

a l s o t h e i n v e s t i g a t i o n of t h e importance of p o l a r i -

A127, 417 z a t i o n of t h e a-d s t r u c t u r e . With t h e above t r i a l

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9 [4] Neuhausen ( R . ) , Z. Phys. 1969,

220,

456

f u n c t i o n s

,

t h e energy v a r i a t i o n and t h e ~ & - f i t t i n g

[ 5 ] Radhakant ( S . ) and Ullah ( N . ) , Nucl.Phys. 1969,

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of t h e form f a c t o r s have been performed. The r e s u l t s

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66, 677 a r e shown i n Figs.l.2and Table 1. The o v e r a l l beha-

[ 6 ] Bouten ( M . ) e t a l . , Nucl.Phys. 1967,

m,

105;

v i o r of both t h e CO and C2 form f a c t o r s c a n be

Phys. L e t t e r s , 1968,

B,

191 r e a s o n a b l y reproduced a l t h o u g h t h e c a l c u l a t e d v a l u e s

[7] Suzuki (Y.) and Kubodera (K.), Prog.Theor .Phys.

of t h e r m s r a d i u s and t h e ~ ( ~ 2 ) ' s a r e s t i l l s r n a l l e r

1970,

44,

617

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19715144

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K. KUBODERA

[ 8 ] Kubodera ( K . )

,

p r e p r i n t ( D P ~ - T A I / ~ ~ , s a C l a y ) s u b m i t t e d t o Phys. k t t e r s .

T a b l e 1

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The r m s r a d i u s and t h e B(c~) c a l c u l a t e d w i t h t h e u s e of t h e w a v e f u n c t i o n s g i v e n (a) by t h e

2 .

e n e r g y v a r i a t i o n o r ( b ) by t h e

x

- f i t t i n g of t h e form f a c t o r s .

F i g . 1

-

The e l a s t i c form f a c t o r .

- -

Def ormed-orbit model

2kfu S h e l l Mode1 - - - M o l e c u l a r - o r b i t model

F i g . 2

-

The i n e l a s t i c form f a c t o r Deformed-orbit model

-

- -

M o l e c u l a r - o r b i t model

S h e l l model w i t h 2kfu e x c i t a t i o n s