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ISOSCALAR CHARACTER OF THE 5,845 MeV 1+
STATE IN 208 Pb
M. Fujiwara, Y. Fujita, I. Katayama, S. Morinobu, T. Yamazaki, H. Ikegami, S. Hayakawa
To cite this version:
M. Fujiwara, Y. Fujita, I. Katayama, S. Morinobu, T. Yamazaki, et al.. ISOSCALAR CHARACTER OF THE 5,845 MeV 1+ STATE IN 208 Pb. Journal de Physique Colloques, 1984, 45 (C4), pp.C4- 453-C4-457. �10.1051/jphyscol:1984434�. �jpa-00224100�
JOURNAL DE PHYSIQUE
Colloque C4, supplkment au n03, Tome 45, mars 1984 page C4-453
2 0 8
ISOSCALAR CHARACTER O F T H E 5 , 8 4 5 MeV '1 STATE IN Pb
M. Fujiwara, Y . F u j i t a , I. Katayama, S . Morinobu, T. Yamazaki, H. Ikegami and S . I . ~ a ~ a k a w a *
Research Center for Nuclear Physics, Osaka University, Osaka 567, Japan
*Ashikaga I n s t i t u t e o f Technology, Ashikaga 326, Japan
R~sume Un B t a t I+ de f o r t e i n t e n s l t e e t ayant une grande cornposante ~ ( h ~ ~ / ~ h ~ / ~ ) -1 a Q t 6 observe a 5,845 MeV dans l e "pb p a r l e s r 6 a c t l o n s ' p b ( p , p t ) e t
' ~ i ( d , 3 ~ e ) . Des c a l c u l s DWBA microscoplques d e s s e c t i o n s ef f i c a c e s ( p , p ' ) mon- t r e n t que c e t d t a t 1' e s t s u r t o u t de na-ture I s o s c a l a i r e . C e t t e conclusion e s t compatible avec l e grand f a c t e u r spectroscopique d e d u i t de l a r e a c t i o n (8, 3 ~ e ) .
A b s t r a c t A s t r o n g 1+ s t a t e which h a s a l a r g e component of t h e ~ ~ ( h ~ ~ / ~ h ~ / ~ ) -1 con- f i g u r a t i o n was found a t 5.845 MeV i n 2O8Pb f r m t h e r e a c t i o n s 2 0 8 ~ b ( p , p 8 ) and
2 0 9 ~ i ( d , 3 ~ e ) . Microscoic DWBA c a l c u l a t i o n s of ( p , p 8 ) c r o s s s e c t i o n s show t h a t t h e 1+ s t a t e h a s a predominant i s o s c a l a r n a t u r e . T h i s conclusion is c o n s i s t e n t with t h e l a r g e s p e c t r o s c o p i c f a c t o r deduced from t h e (d,3He) experiment.
The missing 1+ ( M l ) s t r e n g t h i n 208Pb has been a big p u z z l e f o r a long time.
T h e o r e t i c a l l y numerous c a l c u l a t i o n s have been r e p o r t e d about t h e e x c i t a t i o n e n e r g i e s and t h e p r o p e r t i e s of t h e 1+ s t a t e s l ) . Experimentally s e v e r a l s t a t e s i n 2 0 8 ~ b have been proposed t o be t h e 1+ s t a t e s i n t h e p a s t . However many of t h e s e proposed 1+ s t a t e s were shown t o have e i t h e r n e g a t i v e p a r i t i e s o r d i f f e r e n t s p i n s by l a t e r experiments2). This i n t e r e s t i n g h i s t o r y t o f i n d t h e 1+ s t a t e s i n 2 0 8 ~ b can be seen i n a review a r t i c l e by ~ a m a n 3 ) . By 1980, i t was believed t h a t t h e r e was only a group of fragmented 1+ s t a t e s a t t h e e x c i t a t i o n energy of around 7.5 M ~ v ~ ) , which t o g e t h e r has about o n e - f i f t h of t h e shell-model l i m i t of s t r e n g t h . I n a simple shell-model, two 1+ s t a t e s w i t h l a r g e B ( M ~ ) + v a l u e s , which a r e made of n(h11/2h9/2) -1 and v(i1;+2~11,2) c o n f i g u r a t i o n s , a r e expected a t n e a r l y t h e same e x c i t a t i o n energy of around 6 MeV. Due t o t h e e f f e c t of t h e r e p u l s i v e
r e s i d u a l i n t e r a c t i o n 5 ) , t h e each s t a t e s p l i t s i n t o t h e s t a t e s with a s m a l l M 1 s t r e n g t h ( i s o s c a l a r c h a r a c t e r ) and with a l a r g e M 1 s t r e n g t h ( i s o v e c t o r c h a r a c t e r ) , r e s p e c t i v e l y . I n more e l a b o r a t e shell-model c a l c u l a t i o n s r e p o r t e d by vergadosl) t h e i s o s c a l a r and i s o v e c t o r 1+ s t a t e s were p r e d i c t e d t o be a t 5.45 and 7.52 MeV, r e s p e c t i v e l y . Thus we may expect some 1+ s t r e n g t h i n t h e r e g i o n of t h e e x c i t a t i o n energy lower t h a n 7 MeV, even i f t h e r e a r e s i g n i f i c a n t quenching and/or fragmenta- t i o n of t h e M 1 s t r e n g t h i n 2 0 8 ~ b .
We have performed a c a r e f u l s e a r c h f o r 1+ s t a t e s a t t h e e x c i t a t i o n energy between 4 and 7 MeV by t h e r e a c t i o n s 2 0 8 ~ b ( ~ , ~ ' ) 2 0 8 ~ b and 2 0 9 ~ i (dI3He)208pb. I n t h e c a s e of t h e 2 0 9 ~ i ( d , 3 ~ e ) 2 0 8 ~ b r e a c t i o n , we can e x p e c t some proton p a r t i c l e - h o l e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984434
C4-454 JOURNAL DE PHYSIQUE
s t a t e s with a p a r t i c l e i n t h e lhg/2 o r b i t and a h o l e i n t h e 3 ~ 1 1 2 , 2d3/2, Ih11/21 o r 2d5/2 o r b i t s . Thus our scheme f o r f i n d i n g 1+ s t a t e s was f i r s t t o l o c a t e t h e s t a t e s with n(h11/2h9/2) -1 component by picking up t h e p r o t o n s i n t h e l h l l / 2 o r b i t , and t h e n t o a s s i g n t h e s p i n s from t h e shapes of proton angular d i s t r i b u t i o n s of t h e
( p , p l ) r e a c t i o n l e a d i n g t o t h e s t a t e s .
A s a s u c c e s s f u l r e s u l t of t h e s t u d y i n t h i s scheme, we r e c e n t l y found t h a t t h e 5.845 MeV s t a t e i n 2 0 8 ~ b i s a 1+ s t a t e which h a s a l a r g e n(h1;>2h9/2) cornponent6).
The experimental s e t u p and d a t a a n a l y s i s method have been given elsewhere6). This 1+ s t a t e a t 5.845 MeV has a l s o been found by means of (y ,y ' ) 7 ) , ( e , e 1 ) 8 ) , ( d , d l ) 9, and o t h e r ( p , p 1 ) 9 ) experiments. A high r e s o l u t i o n spectrum of t h e 208pb(p,p') r e a c t i o n a t 65 MeV is shown i n f i g . 1, which c l e a r l y shows t h e presence of t h e Ex = 5.845 MeV l e v e l .
0 -
CHANNEL NUMBER
Fiy.1. I n e l a s t i c proton s p e c t r u m of t h e 2 0 8 ~ i p , p ' ) r e a c t i o n a t O1,h-lo0.
The t r a n s i t i o n s t r e n g t h of t h e 5.845 MeV 1+ s t a t e o b t a i n e d from t h e ( y , y l ) experiment7) is ~ ( l 4 1 ) +=1.6?0.5 u;. and t h i s value and t h e energy l o c a t i o n a r e q u i t e c o s i s t e n t with t h e i n t e r p r e t a t i o n of t h e i s o s c a l a r 1+ s t a t e which has been p r e d i c t e d i n a simple TDA c a l c u l a t i o n s by v e r g a d o s l ) , and a l s o p r e d i c t e d i n a RPA c a l c u l a t i o n by Wambach e t a l . 1 )
However t h e ( e r e 1 ) experiment8) c l a i m s t h a t t h e measured ( e , e l ) form f a c t o r f o r t h e e x c i t a t i o n of t h i s 5.845 MeV s t a t e is c o n s i s t e n t with an i s o s c a l a r chara- c t e r but an " i s o v e c t o r i n t e r p r e t a t i o n " can n o t be d e f i n i t e l y excluded. I t was suggested t h a t t h e r e would be two p o s s i b l e c h o i c e s f o r t h e amplitudes of t h e simple two-state model wave f u n c t i o n of t h e following form,
\2088pb. 11,5.845 M e V > = a l n h 11/2 h 9/2 > + f3\vi13/2ill,2>, -1
where i n t h e e l e c t r o n s c a t t e r i n g , t h e v a l u e s of n=O.81 and f3=0.59 have been determined f o r t h e i s o s c a l a r c o n f i g u r a t i o n and t h o s e of n=0.16 a n d 8=-0.17 f o r t h e i s o v e c t o r one. The s i m p l i f i c a t i o n of t h e i s o s c a l a r 1+ wave f u n c t i o n by t h e two-state model is supported by t h e c a l c u l a t i o n of ~ e r ~ a d o s l ) , i n which t h e lowest
1+ s t a t e a t 5.45 MeV e x c i t a t i o n h a s extremely s m a l l admixtures of t h e o t h e r p a r t i c l e - h o l e s t a t e s . I t should be noted t h a t 2p-2h components a r e neglected i n t h e i s o v e c t o r 1+ wave f u n c t i o n i n t h e above e x p r e s s i o n because t h e 2p-2h s t a t e s can n o t be d i r e c t l y e x c i t e d v i a ( e , e t ) and ( p , p 8 ) r e a c t i o n s .
I n o r d e r t o examine t h e type of t h e wave f u n c t i o n of t h e 5.845 MeV 1+ s t a t e i n 2 0 8 ~ b , we c a r r i e d o u t t h e microscopic DWBA c a l c u l a t i o n s f o r t h e 65 MeV ( p , p t ) c r o s s s e c t i o n s . We used e x a c t l y t h e same wave f u n c t i o n s a s obtained by t h e ( e , e l ) experiment. The microscopic DWBA c a l c u l a t i o n s have been performed using t h e com- p u t e r code ~ ~ ~ ~ 7 4 1 0 ) which i n c l u d e s knock-out exchange amplitudes e x a c t l y . We used t h e M3Y i n t e r a c t i o n l l ) a s an e f f e c t i v e two-body i n t e r a c t i o n between t h e i n c i d e n t proton and a nucleon moving i n t h e n u c l e a r medium. S i n g l e - p a r t i c l e wave f u n c t i o n s were c a l c u l a t e d i n a Woods-Saxon w e l l of r a d i u s R = 1.25 ~ 1 / 3 f m , d i f f u s e n e s s a
= 0.6, and a s p i n - o r b i t f o r c e of 6 MeV. The 1hll/2 and lh9/2 p r o t o n s and l i l 3 / 2 and l i l l / 2 neutrons were assumed t o be bound by 9.37, 3.77, 8.9 and 3.0 MeV, r e s - p e c t i v e l y . The optical-model parameters f o r t h e i n c i d e n t and outgoing p r o t o n s were t h o s e d e r i v e d by Sakaguchi e t a l l 2 ) .
F i g . 2 . C o m p a r i s o n o f t h e m e a s u r e d i n e l a s t i c a n g u l a r d i s t r i b u t i o n f o r the 5.845 MeV li
s t a t e i n '08pb w i t h 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 . T h e s o l i d and d o t t e d c u r v e s s h o w t h e D W B a
c a l c u l a t i o n s w i t h t h e a s s u m p t i o n o f t h e i s o s c a l a r and i s o v e c t o r c o n f i g u r a t i o n s , r e s p e c t i v e l y . No r e n o r m a l i z a t i o n h a s b e e n made f o r t h e t h e o r e t i c a l c u r v e s .
The o b t a i n e d r e s u l t s a r e shown i n f i g . 2. A s can be seen i n t h e f i g u r e , t h e c a l c u l a t i o n with t h e assumption of t h e i s o s c a l a r c o n f i g u r a t i o n (a=0.81, B=0.59) g i v e s a f a i r l y good agreement with t h e experimental d a t a , b u t t h e c a l c u l a t i o n with t h e i s o v e c t o r assumption g i v e s a poor agreement, e s p e c i a l l y a t forward a n g l e s . Thus from t h e DWBA a n a l y s e s of t h e ( p , p l ) r e a c t i o n a t 65 MeV, it is suggested t h a t t h e i s o v e c t o r i n t e r p r e t a t i o n f o r t h e 5.845 MeV 1+ s t a t e i n 2 0 8 ~ b is excluded. A s i m i l a r c o n c l u s i o n t h a t t h e 5.845 MeV 1+ s t a t e h a s a predominant i s o s c a l a r n a t u r e h a s been a l s o given by ~ G l i c h group from t h e ( p , p t ) and ( d , d t ) experiments a t 45 M ~ v ~ ) ,
I t is very i n t e r e s t i n g t o n o t e t h a t t h e experimental s p e c t r o s c o p i c f a c t o r of t h e n (h11/2h9/2) proton component f o r t h e 5.845 MeV 1+ s t a t e o b t a i n e d from t h e -1 2 0 9 ~ i ( d , 3 ~ e ) 2 0 8 ~ b r e a c t i o n i s l a r g e r than 0.756), i . e . a so.87. This value of t h e s p e c t r o s c o p i c f a c t o r is q u i t e r e a s o n a b l e with t h e i s o s c a l a r i n t e r p r e t a t i o n f o r t h e
C4-456 J O U R N A L D E PHYSIQUE
5.845 MeV s t a t e . However t h e l a r g e proton component l e a d s t o t h e magnetic t r a n s i - t i o n s t r e n g t h , B ( M ~ ) 4 4 . 6 u$, i f one uses t h e b a r e M 1 o p e r a t o r . The r e s u l t e d l a r g e B(M1) v a l u e , t h u s , seems t o be i n c o n s i s t e n t with t h e experimental value of
%1.6 &.
Recently, Toki, Bertsch and ~ h a l 3 ) p o i n t e d o u t t h a t t h e discrepancy between t h e experimental B(M1) value and t h e value deduced from t h e s p e c t r o s c o p i c f a c t o r i n t h e (d,%e) pickup measurement may be removed i f one renormalize t h e s p i n moments i n t h e M 1 o p e r a t o r by a f a c t o r of c. This seems t o be i n agreement with t h e f a c t t h a t t h e observed magnetic and Gamow-Teller t r a n s i t i o n s a r e quenched by a f a c t o r of 2 - 3 compared w i t h simple shell-model calculation^^^! However, i n order t o g e t more d e f i n i t e conclusion about t h e quenching phenomenon of t h e 5.845 MeV 1+ s t a t e i n 2 0 8 ~ b , one should remember t h e f a c t t h a t we deduced t h e s p e c t r o s c o p i c f a c t o r under t h e assumption t h a t t h e l h l l / 2 proton o r b i t of t h e ground s t a t e i n 208pb was com- p l e t e l y occupied. T h i s assumption was necessary because o f t h e well-known ambiguity o f t h e a b s o l u t e v a l u e o f t h e DWBA c r o s s s e c t i o n s f o r ( d , 3 ~ e ) r e a c t i o n s ; f o r example, a 1% change o f t h e r a d i u s o f t h e l h l l l 2 proton o r b i t causes more than 20% change o f t h e calculated c r o s s s e c t i o n s .
Thus, t h e s p e c t r o s c o p i c f a c t o r f o r t h e 1' s t a t e from t h e ( d , 3 ~ e ) experiment should be c o r r e c t e d by t a k i n g i n t o account t h e occupation p r o b a b i l i t y of t h e l h l l / 2 o r b i t i n 208pb. which seems t o be i n t h e range above 0.86 i n 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 l 5 ) . I f we renormalize t h e s p e c t r o s c o p i c f a c t o r by a f a c t o r of 0.86 a s a lower l i m i t , we o b t a i n t h e v a l u e o f cr=d0.75x0.86 = 0.80. T h i s cr v a l u e l e a d s t o B ( M l ) +=1.8 u i i n c o n s i s t e n t w i t h t h e experimental observation.
Another p o i n t of c o n t e n t i o n r e g a r d i n g t h e M 1 s t r e n g t h i n 208pb i s t h e i s o - v e c t o r 1' s t a t e which is expected t o be s t r o n g l y e x c i t e d v i a both ( e , e r ) and ( p e p B ) experiments. In t h e p r e s e n t ( p , p ' ) experiment a t 65 MeV, t h e shape of t h e angular d i s t r i b u t i o n is expected t o show almost i d e n t i c a l phases f o r both t h e i s o v e c t o r 1'
Fig. 3. Comparison o f t h e measured i n e l a s t i c angular d i s t r i b u t i o n s f o r the 7.27-, 7.29-, 7.30-, 7.32-, 7.46-, and 7.49 MeV s t a t e s i n ' 0 8 p b w i t h t h e o r e t i c a l DWBA c a l c u l a t i o n s . The s o l i d curves a r e t h e micro- s c o p i c DWBA c a l c u l a t i o n s w i t h t h e assumption o f t h e i s o v e c t o r 1+ c o n f i g u r a t i o n . The dotted curves are t h e DWBA c a l c u l a t i o n s w i t h a c o l l e c t i v e 2' form f a c t o r . A l l t h e curves a r e renormalized a t forward angles.
t r a n s i t i o n and t h e L=2 c o l l e c t i v e t r a n s i t i o n i n t h e f o r w a r d a n g u l a r r e g i o n o f
l o 0 % 3 0 " ( s e e f i g . 3 ) . Due t o t h i s d i f f i c u l t y , we c o u l d n o t d i s t i n g u i s h 1+ s t a t e s from 2+ s t a t e s by means o f t h e e x p e r i m e n t a l c r o s s s e c t i o n s . However, a s shown i n f i g . 3 , s e v e r a l c a n d i d a t e s o f t h e s t a t e s w i t h J~ = 1' o r 2' have been o b s e r v e d i n t h e e n e r g y r e g i o n o f %7.5 MeV where t h e i s o v e c t o r 1 s t a t e + is e x p e c t e d t o e x i s t . I n o r d e r t o s e a r c h f o r t h e i s o v e c t o r I+ s t a t e s i n 2 0 8 ~ b , i t is most d e s i r a b l e t o p e r f o r m t h e h i g h e n e r g y and h i g h r e s o l u t i o n ( p , p l ) e x p e r i m e n t s o n 208pb a t f o r w a r d a n g l e s .
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