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DIRECT VS. COMPOUND PROCESSES
PRODUCTION AND DE-EXCITATION OF HIGH ANGULAR MOMENTUM STATES
H. Morinaga
To cite this version:
H. Morinaga. DIRECT VS. COMPOUND PROCESSES PRODUCTION AND DE-EXCITATION OF
HIGH ANGULAR MOMENTUM STATES. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-
103-C5-110. �10.1051/jphyscol:1972508�. �jpa-00215110�
JOURNAL DE PHYSIQUE Colloque C5, supplifment au no 8-9, Tome 33, AoGt-Septembre 1972, page 65-103
DIRECT VS. COMPOUND PROCESSES
PRODUCTION AND DE-EXCITATION OF HIGH ANGULAR MOMENTUM STATES
H . MORINAGA
Technische U n i v e r s i t L t
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On d i s c u t e l e s c a r a c t g r i s t i q u e s d e s r e a c t i o n s i n d u i t e s p a r d e s i o n s l o u r d s s a n s p a r a l l b l i s m e d i r e c t avec l e s r e a c t i o n s i n d u i t e s par d e s p r o j e c t i l e s 16gers. La forme d e s noyaux hautement e x c i t e s e s t d i s c u t e e B c e s u j e t , En o u t r e , on p r g s e n t e d e s exemples d'ap- p l i c a t i o n en s p e c t r o s c o p i e n u c l e a i r e d e s r e a c t i o n s i n d u i t e s p a r d e s i o n s lourds.A 3 s t r a c t
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S p e c i f i c f e a t u r e s of heavy i o n r e a c t i o n s , which have not d i r e c t p a r a l l e l i s m i n t h e r e a c t i o n s w i t h l i g h t p r o j e c t i l e s i s d i s c u s s e d . I n t h i s c o n n e c t i o n , t h e s h a p e of nu- c l e i a t high e x c i t a t i o n i s d i s c u s s e d . Also examples of t h e use of heavy i o n r e a c t i o n s f o r n u c l e a r spectroscopy a r e given.Reactionsbetween heavy n u c l e i , o r more p r e c i s e l y , between complex n u c l e i r e v e a l many i n - t e r e s t i n g f e a t u r e s and r e c e n t l y very much a t t e n t i o n h a s been p a i d t o t h e s t u d y of t h e s o - c a l l e d heavy i o n r e a c t i o n s from v a r i o u s p o i n t s of view. A c t u a l l y , t h e h i s t o r y of a c c e l e r a t i o n of heavy i o n s i s n o t s o new. For example, very high energy 12C i o n s had been a c c e l e r a t e d by cosmic r a y p h y s i c i s t s i n Chica- go a l r e a d y twenty y e a r s ago [I
1 .
S t r a n g e l y enough, not much a t t e n t i o n was p a i d t o t h e beam except f o r c a l i b r a t i o n of n u c l e a r emulsions. Probably, we were not s o well prepared t o b e i n t e r e s t e d i n such e x t r e - me novelty.The reason why one i s i n t e r e s t e d i n heavy i o n p h y s i c s s o much seems t o be due t o t h e f a c t t h a t we have now c e r t a i n ways t o look a t t h e phenomena.
One can a t l e a s t c l a s s i f y phenomena w e l l enough t o o r g a n i z e s e s s i o n s . - l i k e Coulomb e x c i t a t i o n , one nu- c l e o n t r a n s f e r , two nucleon t r a n s f e r , e l a s t i c s c a t t e - r i n g , o p t i c a l model parameters, and s o on. Those con-
r i n g with heavy i o n r e a c t i o n s . The e x t e n s i o n of a concept developed i n nucleon-nuclear c o l l i s i o n t o heavy i o n c o l l i s i o n o f t e n seems r a t h e r t r i c k y and problematic, a t y p i c a l example is probably t h e op- t i c a l p o t e n t i a l i n heavy i o n collisions.How f a r can one push c e r t a i n c o n c e p t s and how f a r c a n one p a r a m e t r i z e a phenomenon without b e i n g t o o much
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c r i t i c i z e d i s a l r e a d y a bold experiment.
S i n c e I am n o t an e x p e r t i n n e i t h e r of t h o s e e s t a b l i s h e d d i r e c t i o n s , I should r a t h e r not review t h e development of t h o s e main l i n e s which, I am s u r e , most of you a r e a l r e a d y f a m i l i a r w i t h , but r a t h e r l i k e t o look a t two problems connected with t h e heavy i o n r e a c t i o n s i n which I have my own problems and t h e n , f i n a l l y , j u s t i n o r d e r n o t t o b e a snob, I ' d l i k e t o show you t h e u s e f u l n e s s of heavy i o n r e a c t i o n s a s a s p e c t r o s c o p i c t o o l : an example t h a t one can u s e a t o o l even without under- s t a n d i n g t h e p r e c i s e f u n c t i o n i n g of t h i s t o o l .
I1 - DIRECT PROCESSES e e p t s a r e w e l l d e f i n e d and one can a t l e a s t t a l k a-
bout v a r i o u s parameters and t h e i n t e r p l a y between T y p i c a l d i r e c t p r o c e s s e s a r e t h e e l a s t i c
v a r i o u s mechanisms. s c a t t e r i n g , t h e Coulomb e x c i t a t i o n a m f ~ t r a n s f e r
Indeed, t h e f a c e of heavy i o n r e a c t i o n s r e a c t i o n s , They a r e by now w e l l parametrized i n t h e i s very many-sided. We c a n s e e almost every "phy-
s t a n d a r d way a s u s e d i n l i g h t i o n physics.
sics1' developed with l i g h t e r p r o j e c t i l e a l s o occur-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972508
H . MORINAGA
T h e r e a r e , h o w e v e r , t w o new p r o c e s s e s w h i c h are more c h a r a c t e r i s t i c o f h e a v y i o n c o l l i - s i o n s b u t n o t so w e l l s t u d i e d , a n d I s h o u l d l i k e t o d r a w y o u r a t t e n t i o n on them. T h e f i r s t i s what we m i g h t C a l l t h e s c a t t e r i n g v i b r a t i o n a l s t a t e a n d c o r r e s p o n d s t o t h e g i a n t r e s o n a n c e i n n u c l e o n - n u - c l e a r c o l l i s i o n s .
I f t w o h e a v y i o n s c o l l i d e e a c h o t h e r a n d i f we a s s u m e t h a t t h e v i s c o s i t y of n u c l e a r m a t t e r i s s m a l l , t h e r e i s a c h a n c e t h a t t h e compound s y s - tern comes back t o t h e i n c i d e n t c h a n n e l a n d c a u s e s e l a s t i c s c a t t e r i n g . W e c a n i m m e d i a t e l y g u e s s t h a t
t i o n s " [ 4 ] . P a r a l l e l t o t h e s h e l l model t h e o r y o f n u c l e a r r e a c t i o n s we a s s u m e t h e c o l l e c t i v e p o t e n - t i a l t o b e n o t a s i m p l e h a r m o n i c o s c i ' l a t o r b u t a f i n i t e w e l l
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n a t u r a l l y t h e c o o r d i n a t e s a r e n o t x , y , z o f t h e p a r t i c l e b u t c o l l e c t i v e c o o r d i n a t e s ( a ) a n d t h e q u a n t a a r e b o s o n s . Now, p e r m a n e n ti
o s c i l l a t i o n s are n o t a l l o w e d and c o r r e s p o n d i n g t o t h e s c a t t e r i n g n u c l e o n s t a t e , t h e s c a t t e r i n g v i b r a - t i o n a l s t a t e s a p p e a r . R e f i n e m e n t o f t h e t h e o r y i n - c l u d i n g i n t e r a c t i o n o f t h o s e b o s o n s w i l l l e a d t o t h e s p l i t t i n g o f t h e s i m p l e s c a t t e r i n g v i b r a t i o n a l s t a t e s t o t h e doorway s t a t e s .
s u c h compound e l a s t i c c h a n n e l i s s m a l l b u t i n c e r -
I t would b e v e r y i n t e r e s t i n g i f t h e w i d t h t a i n c a s e s i t may n o t b e i g n o r e d . T h e g r a z i n g c o l l i -
o f t h o s e i n t e r m e d i a t e r e s o n a n c e s c o u l d b e e s t i m a t e d . s i o n o f t w o h e a v y i o n s may b e r e g a r d e d i n t h i s way
B u t i t w i l l n o t b e s o e a s y . W e c o u l d , h o w e v e r , s i n c e t h e d e p e n d e n t i m a g i n a r y o p t i c a l p o t e n t i a l
l o o k a t e x p e r i m e n t a l r e s u l t s a n d see i f t h e r e arc a b o v e h a s some c r i t i c a l L e x p e c t e d t o be small.
a n y phenomena which may b e t l i e i n d i c a t i o n o f s u c h A c t u a l l y , t h e most i n t e r e s t i n g c a s e i n
t h e h e a v y i o n c o l l i s i o n s s u c h as 1 2 c - 1 2 c o r 1 6 0 - 1 6 0 o c c u r s f o r low a n g u l a r momentum c o l l i s i o n s . A d e s c r i p t i o n f o r s u c h a c o l l i s i o n o p p o s i t e t o t h e o p t i c a l model, w h e r e t h e e x i t c h a n n e l ( i n w h i c h w e l l d e f i n e d s e p a r a t e p a r t i c l e s t r a v e l t o w a r d s e a c h o t h e r ) i s d e s c r i b e d e x a c t l y , is t o c o n s i d e r t h e t o t a l s y s t e m . T h e l a t t e r d e s c r i b e s b e t t e r t h e s i t i t a - t i o n when t h e s y s t e m i s a m a l g a m a t e d a l t h o u g h t h e a s y m p t o t i c b e h a v i o r i s less p r a c t i c a l l y d e f i n e d .
W c a n u n d e r s t a n d s u c h c o n s i d e r a t i c n s s o m e - e what a n a l o g o u s t o t h e u n i f i e d t h e o r y o f n u c l e a r r e a c t i o n s o f n u c l e o n - n u c l e a r c o l l i s i o n s , w h i c h i s d e v e l o p e d by B l o c h , F e s h b a c h a n d o t h e r s [ 2 , 3
1
a n d c a l l e d u s u a l l y t h e s h e l l model t h e o r y o f n u c l e a r r e a c t i o n s . I n t h i s t h e o r y b o t h bound s t a t e s a n d s c a t - t e r i n g s t a t e s o f s i n g l e n u c l e o n s i n a f i n i t e w e l l are c o n s i d e r e d a n d b o t h bound l e v e l s a n d s c a t t e r i n g l e v e l s are o b t a i n e d a f t e r t h e i n c l u s i o n o f r e s i d u a l i n t e r a c t i o n s . T h e r e s u l t i s t h e a p p e a r a n c e o f t h e doorway s t a t e s or i n t e r m e d i a t e s t r u c t u r e w h i c h g i v e f i n e s t r u c t u r e t o t h e g i a n t r e s o n a n c e , n a m e l y a s i n g l e n u c l e o n s c a t t e r i n g s t a t e . I n t h i s d e s c r i p - t i o n a s t a t e i s e x p a n d e d a c c o r d i n g t o t h e d e s c e n d i n g o r d e r o f s i m p l i c i t y as l p , 2 p - l h , 3p-2h,...
a n dSO on.
I t i s o b v i o v ~ s t h a t s u c h an expansion i s i n - c o n v e n i e n t f o r t h e d e s c r i p t i o n of h e a v y i o n c o l l i - s i o n o r f i s s i o n phenomena. I t would b e b e s t to start w i t h j u s t a n o p p o s i t e d e s c r i p t i o n which we m i g h t c a l l " c o l l e c t i v e model t h e o r y o f n u c l e a r r e a c -
a n a r r o w doorway s t a t e . T h e most s u s p i c i o u s c a n d i - d a t e i s t h e o l d Bromley m o l e c u l a r s t a t e : a n a r r o w a n d low s p i n s t a t e w;lose o u t g o i n g c h a n n e l s show d e f i n i t e s i g r s o f c o r r e l a t i o n .
A n o t h e r p o s s i b i l i t y of i n v e s t i g a t i n g s u c h collective modes i n h i g h e x c i t a t i o n may b e c o n s i d e - r e d a g a i n f r o m t h e a n a l o g y t o t h e n u c l e o n - n u c l e a r c o l l i s i o n . T h e l o o s e c o u p l i n g i n t h e d e s c e n d i n g o r d e r o f h i e r a r c h y o f l p , 2 p - l h
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i s s e e n i n t h e e x i s t e n c e o f t h e pre-compound d e c a y i n t h e n u c l e o n - n u c l e a r c o l l i s i o n e v e n i n t h e r e g i o n s w h e r e t h e n a r - row r e s o n a n c e i n t h e i n g o i n g c h a n n e l i s a l r e a d y s m e a r e d o u t . I n t h e c a s e o f h e a v y i o n c o l l i s i o n t h e r e a r e d e f i n i t e l y i n d i c a t i o n s t h a t compound e l a s t i c i s h i g h e r t h a n t h c s t a t i s t i c a l v a l u e . B u t t h i s may b e& l e t o h i g h e r s p i n p a r t w i t h l o w w
.
A more i n t e - r e s t i n g o b s e r v a t i o n w o u l d b e t h a t of a pre-compound gamma d e c a y , w h i c h s h o u l d h a v e r a t h e r l a r g e c n h a n - c e m e n t if s u c h s c a t t e r i n g v i b r a t i o n a l s t a t c i s n o t i m m e d i a t e l y damped. C o m p a r i s o n o f (p,Y ),
(a,\')( 1 1 1 , ~ ) a t t h e same e x c i t a t i o n a n d same i n p u t angu- l a r momentum s h o u l d b e h i g h l y i n t e r e s t i n g .
T h e s e c o n d c a t e g o r y o f t h e p r o c e s s e s which was n o t much d i s c u s s e d i s a p r o c e s s i n which t w o i o n s t o u c h e a c h o t h e r b u t d o n o t f o r m compound n u c l e u s . T h e s u p e r h i g h e n e r g y r e a c t i o n w i t h m u l t i GeV is n a t u r a l l y o n e e x a m p l e b u t also e v e n a t l o w e n e r g i e s h i g h a n g u l a r momentum h i n d e r s t h e s y s t e m t o f o r m compound n u c l e u s . W e s h a l l d i s c u s s t h i s p r o c e s s t o g e t h e r w i t h t h e compound n u c l e u s f o r m a - t i o n i n t h e n e x t s e c t i o n .
DIRECT VS. COMPOUND PROCESSES
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C5-105I 1 1
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COMPOUND PROCESSEST h e r e i s n o d o u b t t h a t t h e o r d i n a r y t y p e o f compound n u c l e u s c a n be f o r m e d b y t h e c o l l i s i o n o f h e a v y n u c l e i . I n d e e d , u n d e r t y p i c a l c o n d i t i o n s
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a b s v e b a r r i e r b u t n o t t o o h i g h e n e r g y-
t h e main p r o c e s s i s f o u n d t o b e t h e compound n u c l e u s f o r m a - t i o n a n d s u c c e s s i v e e v a p o r a t i o n of p r o t o n s , neu- t r o n s a n d a l p h a s . T h e b r a n c h i n g r a t i o s i n t h e e v a - p o r a t i o n p r o c e s s may d i f f e r f r o m t h e case o f reac- t i o n w i t h l i g h t p r o j e c t i l e s . B u t t h e y are p r o p e r l y a c c o u n t e d f o r by s o l e l y t a k i n g i n t o a c c o u n t t h e h i g h e r i n p u t a n g u l a r momentum.A s e r i o u s d e v i a t i o n f r o m t h e n o r m a l com- pound n u c l e a r f o r m a t i o n c r o s s s e c t i o n
f o r m u l a h a p p e n s a t h i g h e r i n c i d e n t e n e r g y . T h e com- pound n u c l e u s f o r m a t i o n c r o s s s e c t i o n d e c r e a s e s se- r i o u s l y b e c a u s e o f t h e f a c t t h a t t h e h i g h a n g u l a r pomentum c o l l i s i o n c a n n o t l e a d t o t h e f o r m a t i o n o f t h e compound n u c l e u s . T h e r a t i o o f m e a s u r e d compound c r a s s s e c t i o n t o t h e v a l u e ( 1 ) i s a v e r y i n t e r e s t i n g q u a n t i t y . I s h a l l d i s c u s s i t somewhat more i n de- t a i l i n t h e n e x t s e c t i o n .
b u t r a t h e r a g a i n f r o m t h e s t a b i l i t y c a l c u l a t i o n o f t h e t o t a l s y s t e m .
T h e s t a b i l i t y c a l c u l a t i o n of a r o t a t i n g l i q u i d d r o p h a s b e e n a c l a s s i c a l a s t r o p h y s i c a l p r o - blem. T h e o b l a t e s h a p e o f t h e s u n may b e c a l c u l a t e d by t a k i n g i n t o a c c o u n t t h r e e e n e r g i e s
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s u r f a c e e n e r g y , r o t a t i o n a l e n e r g y a n d t h e g r a v i t a t i o n a l e n e r g y . S u c h e q u i l i b r i u m s h a p e c a l c u l a t i o n may b e t r a n s f o r m e d f o r d i s c u s s i n g t h e r o t a t i n g n u c l e i j u s t by c h a n g i n g p a r a m e t e r s a n d c h a n g i n g t h e s i g n o f t h e g r a v i t a t i o n a l e n e r g y .T h e c a l c u l a t i o n was d o n e t e n y e a r s a g o by C o h e n , P l a s i l a n d S w i a t e c k i [ 5 ] . - They f o u n d t h a t f o r s l o w r o t a t i o n , a l l s t a r s , l i g h t n u c l e i , a n d h e a v y n u c l e i p r e f e r o b l a t e s h a p e b u t when t h e a n g u - l a r momentum i s i n c r e a s e d , t h i s s h a p e becomes un- a t a b l e a n d , i n h e a v y n u c l e i g o e s o v e r t o f i s s i o n . S t a r s , a n d l i g h t n u c l e i , however, g o f i r s t o v e r t o r o t a t i n g e l l i p s o i d t h e n l a t e r t o f i s s i o n . R e c e n t l y , a v e r y i n t e r e s t i n g e x p e r i m e n t t o see t h e l i m i t o f t h e a n g u l a r momentum was r e p o r t e d by P U h l h o f e r a n d Diamond [6]. T h e g e n e r a l b e h a v i o u r i s r e p r o d u c e d a l t h o u g h 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 i s s m a l l e r . We c o u l d t h i n k o f v a r i o u s r e a s o n s b u t o n e o f them nlav b c t h e f a c t t h a t t h e t h e o r e t i c a l v a l u e u s e s t h e T h e c o n s i d e r a t i o n s g i v e n i n t h e p r e v i o u s
s u r f a c e t e n s i o n p a r a m e t e r o b t a i n e d f r o m t h e g r o u n d s e c t i o n l e t u s s u s p e c t t h a t t h e r e m u s t b e some p r e -
s t a t e w h i c h c o u l d b e l a r g e r t h a n t h e v a l u e f o r t h e compound phenomena i n h e a v y i o n r e a c t i o n s . How d o
h o t n u c l e u s . A l s o i t h a s b e e n n o t i c e d i n a o h o t o - t h e s e phenomena show op i s a n i n t e r e s t i n g s u b j e c t
f i s s i o n s t u d y t h a t t h e s u r f a c e t e n s i o n s h o u l d b e o f s p e c u l a t i o n ? E x c e p t f o r a v e r y h i g h e n e r g y c o l l i -
t a k e n s m a l l e r , i n o r d e r t o a c c o u n t f o r l o w e r p h o t o - s i o n , t h e c o l l i s i o n i s most l i k e l y t o b e a d i a b a t i c ,
f i s s l o n t h r e s h o l d s o f l i g h t e r n u c l e i t h a n t h e t h e o - s i n c e t h e v e l o c i t y of nucleons a t t h e F e r m i s u r f a c e
r e t i c a l e s t i m a t e s [7
1.
i s s t i l l much f a s t e r t h a n t h e m u t u a l v e l o c i t y o f i o n s a t t h e c o l l i s i o n . T h i s w i l l a s s u r e t h e ccms- t a n c y o f t h e d e n s i t y o f n u c l e a r m a t t e r , t h a t i s , t h e r a t h e r w e l l d e f i n e d i n s t a n t a n e o u s s h a p e w i t h c o n s - t a n t volume. T h e r e f o r e , i t i s e x p e c t e d t h a t a t f i r s t t h e n u c l e u s i s moving r a t h e r l i k e a n amceba, w h i c h w i l l e n h a n c e t h e e m i s s i o n p r o b a b i l i t y o f l a r g e r o b j e c t t h a n a - p a r t i c l e s . A l s o t h e r e may b e e f f e c t s o n t h e e f f e c t i v e Coulomb b a r r i e r f o r p r o t o n a n d a l p h a p a r t i c l e s .
I V
-
THE COHEN-PLASIL-SWIATECKI CALCULATIONHow b i g t h e cross s e c t i o n i s f o r f o r m i n g a compound n u c l e u s i n h i g h e r e n e r g y c o l l i s i o n s w h e r e t h e h i g h a n g u l a r momentum h i n d e r s t h e f o r m a t i o n , may b e d i s c u s s e d n o t f r o m t h e o p t i c a l model a p p r o a c h
An u n s a t i s f y i n g a s p e c t o f t h e C.P.S. cal- c u l a t i o n f o r n u c l e i i s t h e f a c t t h a t i t i s a comple- t e l y c l a s s i c a l c a l c u l a t i o n . T h e r e f o r e , a t l o w e r f r e - q u e n c i e s o n e g e t s r o t a t i o n a r o u n d t h e symmetry a x i s which i s t r i c k y t o i n t e r p r e t e i n quantum m e c h a n i c s . How f a r we c a n u s e t h e a n a l o g y b e t w e e n t h e r o t a t i o n
of t h e s u n a n d t h e s t a r becomes p r o b l e m a t i c . T h e o n l y way t o u n d e r s t a n d t h e a n g u l a r mmmentum a r o u n d t h e symmetry a x i s i s t o g i v e t h e a n g u l a r momentum t o t h e s i n g l e p a r t i c l e s r a t h e r t h a n t h e t o t a l r o t a - t i o n , w h i c h i s m e a n i n g l e s s i f t h e r e i s symmetry a r o u n d t h e a n g u l a r momentum a x i s .
T h i s p r o b l e m i s a c t u a l l y n o t f i c t i t i o u s b u t l i e s v e r y c l o s e t o o u r e x p e r i m e n t a l l a b o r a t o r i e s . We h a v e s e e n a s e r i o u s d i s t u r b a n c e t o t h e r o t a t i o n a l
C5-105 H. MORINAGA
ground s t a t e band of r a r e e a r t h n u c l e i a t I = 14 t o 2 0
[€!I.
R e c e n t l y , t h e r e was a s m a l l m e e t i n g i n Stockholm, where t h k s phenomenon was t h o r o u g h l y d i s c u s s e d . The i n t e r p r e t a t i o n is n o t u n i q u e and t h e r e a r e two l i n e s of t h e o r i e s , namely, one i s t o assume b r e a k i n g of one p a i r [9] and t h e o t h e r a s s u - mes t o t a l d i s a p p e a r a n c e of t h e p a t r i n g c o r r e l a t i o n[lo].
Anyway, i t seems t o u s t h a t a f t e r a n g u l a r mo- mentum o f 14 o r 2 0 , t h e p a i r g e t s broken. T h i s pha- se t r a n s i t i o n , however, d o e s n o t c o r r e s p o n d t o any p h a s e t r a n s i t i o n i n t h e c l a s s i c a l c a l c u l a t i o n a n d s h o u l d t a k e p l a c e b e f o r e t h e c l a s s i c a l phase t r a n - s i t i o n . Kumar c a l c u l a t e s 3 andP
a s a f u n c t i o n of I a n d o b s e r v e s a s u d d e n i n c r e a s e ofP
a t t h e t r a n - s i t i o n ( I=
1 4 ) and a t t h i s p o i n t5
d e c r c a s e s 1111.
T h i s s u g g e s t s a t r a n s i t i o n from a p r o l a t e t o a more o b l a t e shape. I f i t g o e s i m m e d i a t e l y t o t h e o b l a t e s t a r , i t i s s t i l l a problem. Experiment t o s e e t h e Y r a s t s t r u c t u r e and t h e gamma t r a n s i t i o n s i n t h i s r e g i o n s h o u l d b e e x t r e m e l y i n t e r e s t i n g .
V
-
HIGH SPIN STATES IN LIGHT NUCLEIJ u s t f o r comparison, t h e p r o p e r t i e s of h i g h s p i n s t a t e s i n l i g h t n u c l e i is i n t e r e s t i n g a n d i n s t r u c t i v e . A c a s e w e l l s t u d i e d b o t h e x p e r i - m e n t a l l y and t h e o r e t i c a l l y , i s t h e ground s t a t e band of 2 0 ~ e
.
Although t h e r e e x i s t s some d i s c r e - pancy of t h e o p i n i o n i n t h e c a s e o f t h e s t r u c t u r e of t h e 8' s t a t e [ 1 2 ] , we might t e n t a t i v e l y t a k e t h e l o w e s t 8' as a member of t h e ground band. Both t h e - o r e t i c a l l y and e x p e r i m e n t a l l y , E2 t r a n s i t i o n pro- b a b i l i t i e s d e c r e a s e C o n s i d e r a b l y a s t h e s p i n i s i n c r e a s e d . And a c c o r d i n g t o t h e c a l c a l a t i o n of Arima [ 1 3 ] , t h e d e f o r m a t i o n deduced from t h e E2 t r a n s i t i o n p r o b a b i l i t y assuming a c i g a r s h a p e de- c r e a s e s i n t h e h i g h e r member of t h e band, which i s o p p o s i t e t o what i s e x p e c t e d from e n e r g y spa- c i n g s t h a t show t h e i n c r e a s e of moment of i n e r t i a . I t i s s i m i l a r t o t h e tendency i n heavy n u c l e i and s u g g e s t s t h a t t h e r e a r e some s i m i l a r p h y s i c s b e h i n d t h e s i t u a t i o n s a l t h o u g h i n l i g h t n u c l e i we c a n n o t t a l k a b o u t t h e p a i r i n g c o r r e l a t i o n .I t i s i n t e r e s t i n g , i n t h e c a s e of
ON^,
t o l o o k a t t h e m i c r o s c o p i c a l wave f u n c t i o n . The l o - wer s t a t e s
o+,
2 + , 4+ c o n t a i n l a r g e m i x t u r e of s , d , which is e s s e n t i a l f o r a c i g a r s h a p e d e f o r m a t i o n . B u t h i g h e r s p i n s t a t e s c o n t a i n no s componentswhosei n t e r f e r e n c e i s e s s e n t i a l t o c a u s e t h e d e f o r m a t i o n . F o r example, t h e 8+ s t a t e i s a c o m p l e t e l y s t r e t c h e d s t a t e w i t h o u t s , which means t h a t t h e a n g u l a r mo- mentum i s a l i g n e d t o t h e Z a x i s . T h a t i s , t h e angu- l a r momentum i s a l o n g t h e symmetry a x i s and t h i s i s a pancake h i g h a n g u l a r momentum s t a t e b u t no c o l l e c - t i v e r o t a t i o n . T h i s s i t u a t i o n c a u s e s t h e r e d u c t i o n of t h e E2 t r a n s i t i o n p r o b a b i l i t y .
VI
-
NUCLEAR RINGR o t a t i n g s t a r s , h i g h e r s p i n s t a t e s i n heavy n u c l e i and a l s o h i g h s p i n s t a t e s i n l i g h t n u c l e i s u g g e s t t h e need t o c o n s i d e r m o b l a t e object where a n g u l a r momentum i s p a r a l l e l t o t h e SYmmetry a x i s . A l s ~ t h e q u a l i t a t i v e s u c c e s s of t h e C.P.S.
c a l c u l a t i o n shows t h a t a t c e r t a i n h i g h a n g u l a r mo- mentum t h e n u c l e i may h a v e a sun shape. How t h e t r a n s i t i o n from one s t r u c t u r e t o a n o t h e r t a k e s p l a - c e may b e c o m p l i c a t e d . T h e r e f o r e , we might f i r s t t r y t o d e s c r i b e a h i g h s p i n o b l a t e s t a t e ( n o t r o t a - t i o n a l - b u t r o t a t i n g i n a c l a s s i c a l s e n s e ) . I n N i l s s o n ' s scheme we t a k e t h e o b l a t e s i d e and we t a - k e a t h r e e d i m e n s i o n a l p l o t (E,6,m)
.
Then i f we l o o k a t t h e diagram of (E,m) f o r f i x e d n e g a t i v e6 i t w i l l be a s shown i n F i g . 1
.
F i g ? . The Nilsson diagram
The e x t r e m e c a s e of l a r g e d e f o r m a t i o n i s l i k e Fig.2
.
Now i f t h e r e is a n a t y p e c o r r e l a t i o n weDIRSCT VS. COMPOUND PROCESSES
. . .
C5-107Fig.a : E - m d i a g r a m f o r a r i n g .
i e x p e c t t h a t t h e e x t r e m e c a s e w i l l become a " n u c l e a r r i n g 1 ' whose t h i c k n e s s is t h c t h i c k n e s s o f t h e a l p h a p a r t i c l e . T h e n u c l e a r p o t e n t i a l i s n o t a n y more t h e h a r m o n i c o s c i l l a t o r ( F i g . 3 1 , b u t i t i s a r i n g . b r t h e I$ d i r e c t i o n we must a l l o w t h e p a r t i c l e s t o b e i n d i f f e r e n t m s t a t e .
I
F I G : N u c l e a r p o t e n t i a l V ( r , z,+) o f a ring-.
-
I n t h e K i l s s o n quantum number (N,nZ,A) t h e s t a t e s a r e ( 0 , 0 , 0 1 4 ( 1 , 0 , 1 ) 4 ( 2 , 0 , 2 ) ~
. . .
c o r r e s p o n d i n g4 4 4
t o t h e c h a i n ( 0 , 0 , 0 ) ( 1 , 1 , 0 ) ( 2 , 2 , 0 )
. . . .
Ofc o u r s e , t h e i n c l u s i o n o f t h e r e s i d u a l i n t e r a c t i o n w i l l c a u s e t h e p a r t i c l e t o l o c a l i z e . I t s l i m i t i s t h e c h a i n o f a l p h a s . F o r a l a r g e number o f a l p h a p a r t i c l e s t h e s t r u c t u r e i s n o t much d i f f e r e n t f r o m
a c h a i n except t i m t b o t h e n d s of t h e c h a i n a r e c o n n e c t e d t o make a r i n g (we o m i t t h e Coulomb e n e r g y ) . T h e e n e r g y i s somewhat l o w e r t h a n t h a t of t h e c h a i n d u e t o t h i s c o n n e c t i o n .
S u c h r i n g s a r e n o t c o m p l e t e l y a j o k e . A s much a s 'I3e i s a c h a i n ( t h e s m a l l e s t c h a i n ) 1 2 c g r o u n d s t a t e i s c o n s i d e r e d t o b c a r i n g ( t h e smal- l e s t r i n g ) . R e c e n t H a r t r c e Fock c a l c u l a t i o n s s u g g e s t i t [14
1.
T h e 6 . 0 6 MeV 1 6 0 s t a t e i s p r o b a b l y t h e n e x t r i n g [15]. T h e c h a i n l i e s much h i g h e r ( N 1 6 MeV).T h o s e d a t a s u g g e s t t h a t t h e r e a r e d i f f e r e n c e s o f 5 ~ 1 0 MeV b c t w e e n c h a i n and r i n g . ; I n c i d e n t a l l y , s u c h a n u c l e a r r i n g w i t h f i x e d l e n g t h i s c l a s s i c a l - l y s t a b l e .
Of c o u r s e , s u c h a n e x t r e m e s t r u c t u r e would n o t show u p i n t h e e x p e r i m e n t s o e a s i l y a n d i f t h e r e i s a n y c h a n c e t o s e e i t , i t w i l l b c i n l i g h t n u c l e i . 2 0 ~ e , 2 4 ~ g a r e t h e n e x t c a n d i d a t e s a n d t h e c h a i n may l i e some 1 0 - 2 0 M e V h i g h . B u t t h o s e e n e r g y r a n g e s a r e a l r e a d y b e i n g l o o k e d a t e x t e n s i v e l y .
Such r i n g s are e x p e c t e d t o h a v e more a l p h a t y p e s t r u c t u r e , j u s t l i k e c h a i n s , t h a n s p h e r e s , be- c a u s e t h e r e a r e more s u r f a c e s . I s h o u l d a l s o m e n t i o n t h a t f o r a r i n g , t h e
e-s
f o r c e s h o u l d become h a r d l y i m p o r t a r - t b e c a u s e of t h e s h a p e o f t h e n u c l e a r p o t e n - t i a l . So, b e t t e r p a i r i n g o r q u a r t e t i n g i s e x p e c t e d . Then t h c r i n g c a n h a v e a n y a n g u l a r momentum w h i l e f o r a r i n g S z 0,
1.-
Ce.
L o o k i n g f o r s u c h a r i n g a t A - 2 0 must b e a v e r y i n t e r e s t i n g e x p e r i m e n t .VII
-
NUCLEAR SPECTROSCOPY WITH HEAVY ION REACTIONSHeavy i o n r e a c t i o n s g i v e u n i q u e o p p o r t u - n i t y f o r n u c l e a r s p c c t r o s c o p y . T h e m u l t i p o l e Coulomb e x c i t a t i o n g i v e s u s o p p o r t u n i t y t o r e a c h v e r y h i g h s p i n s t a t e s . T r a n s f e r r e a c t i o n s h a v e b e e n u s e d ex- t e n s i v e l y d u e t o t h e i r s e l e c t i v e c h a r a c t e r . T h o s e r c a c t i o n s a r e b e i n g u n d e r s t o o d r a t h e r q u i c k l y . B u t I s h a l l n o t t a l k a b t thcm s i n c e t h e r e i s a t a l k by G e o r g e M o r i s s o n .
Somewhat more i n t e r e s t i n g i s t h e a v a i l a - b i l i t y o f compound r e a c t i o n f o r some s p e c i f i c s p e c - t r o s c o p i c a l p u r p o s e . An i n t e r e s t i n g e x a m p l e h a s b e e n f o , l n d by t h e S a c l a y g r o u p [ 1 6 ] . They o b s e r v e d h i g h
2 4
e n e r g y r e s i d u a l s t a t e s i n M g by 1 6 0 ( 1 2 ~ , a ) 2 4 ~ g
C5-108 H. MORINAGA
r e a c t i o n a n d f r o m t h e a n a l y s i s o f e x c i t a t i o n f u n c - One c a n m e a s u r e t h e f o l l o w i n g p r o p e r t i e s t i o n t h e y w e r e s u c c e s s f u l t o show t h a t t h e y a r e o f t h o s e r a y s :
s t a t i s t i c a l a l p h a s t o h i g h s p i n s t a t e s whose i n t e n -
1. E x c i t a t i o n f u n c t i o n s s i t i e s are f i t by Ifausex-Feschbach a n a l y s i s , T h e
2. C r o s s bombardment ~ r o u e r t i e s
. .
a n a l y s i s l e a d s t o t h e d i s c o v e r y o f t h e l o w e s t 10'
3. C o m p a r i s o n w i t h t h e y - r a y s f o l l o w i n g a c t i v i - a n d p r o b a b l y 1 2 ~ states a f t e r a d j u s t i n g t h e p a r a -
ties p r o d u c e d by t h e beam m e t e r s t o known 8- i n t e n s i t i e s .
4 . T h e s h a p e of t h e l i n e o f t h e D o p p l e r - s h i f t T h e gamma s p e c t r o s c o p y o f t h e h e a v y i o n 5. A n g u l a r d i s t r i b u t i o n
c o l l i s i o n i s , a c c o r d i n g t o my o p i n i o n , o n e o f t h e 6. L i f e t i m e w i t h p u l s e d beam
m o s t f r u i t f u l d o m a i n s o f a p p l i c a t i o n o f h e a v y i o n 7. L i f e t i m e w i t h t h e r e c o i l d i s t a n c e methods a c c e l e r a t o r s . Compared w i t h i t s p o w e r f u l n e s s t h e 8 . P o l a r i z a t i o n
f i e m d i s n o t s o much e x p l o i t e d
.
T h e r e f o r e , X s h o u l d 9. y-Y c o i n c i d e n c el i k e t o a c c o u n t f o r t h i s f i e l d b r i e f l y w i t h some 10. C h a r g e d p a r t i c l e - y c o i n c i d e n c : e e x a m p l e s f r o m o u r l a b o r a t o r y i n Miinchen. 11. C o i n c i d e n c e w i t h n e u t r o n s .
No m a t t e r what t a r g e t o n e i r r a d i a t e s w i t h
T h e m e a s u r e m e n t s a r e u s u a l l y d o n e w i t h w h a t e v e r beam, o n e g e t s y - r a y s . They are t h e Coulomb
h i g h r e s o l u t i o n gcrmar~ium d i o d e s a n d t h e h e a v y i o n e x c i t a t i o n s o f b o t h t h e t a r g e t a n d beam, y - r a y s
i s a d v a n t a g e o u s b e c a u s e o f t h e s m a l l n e u t r o n y i e l d . f o l l o w i n g t r a n s f e r r e a c t i o n a n d Y - r a y s f o l l o w i n g
t h e e v a p o r a t i o n o f l i g h t p a r t i c l e s ( p , n , a ) f r o m S u c h r i c h n e s s o f t h e h e a v y i o n Y - s p e c t r o s - t h e compound n u c l e u s . I n a h e a v y n u c l e u s , t h e main c o p y g i v e s u s o p p o r t u n i t y t o d o v e r y much s p e c t r o s - mode i s t h e n e u t r o n e v a p o r a t i o n a n d t y p i c a l l y o n e c o p i c a l work w i t h i t . U s u a l l y w i t h h e a v y i o n s we sees t h e Y r a s t l i n e u p t o some t r a n s i t i o n p o i n t . F o r Can s t u d y t h e Yrast s i d e , t h a t i s t h e h i g h s p i n d e f o r m e d r a r e e a r t h even-even n u c l e i t h e r o t a t i o n a l s i d e b e t t e r , b u t t h e o p p o r t u n i t y i s n o t l i m i t e d t o band i s s e e n t o some 20' or s o , t h e n a f t e r t h a t we t h e h i g h s p i n s t a t e s .
d o n o t see much. F o r l i g h t e r n u c l e i t h e c o m p e t i t i o n A s a n e x a m p l e , I s h a l l s ? ~ o w you o u r re- Of t h e p or a e m i s s i o n is s t r o n g or d o m i n a n t , b u t c e n t work o n t h e l e v e l scheme o f 4 8 ~ [16]. T h e t h i s t e n d e n c y a l r e a d y s t a r t s a r o u n d t h e r a r e e a r t h n u c l e u s 4 8 may be r e a c h e d by v a r i o u s m e t h o d s a n d ~ r e g i o n b e c a u s e t h e c o l l i s i o n of a h e a v y i o n u s u a l l y i n t h e last decade t h e r e are many spcctroscopical l e a d s t o t h e v e r y n e u t r o n d e f i c i e n t s i d e . w o r k s u s i n g p a r t i c l e s p e c t r o s c o p y . Much work
DIRECT VS. COMPOUND PROCESSES
...
C5-109u s i r i g m a g n e t i c s p e c t r o m e t e r i s a v a i l a b l e f o r o b s e r v i n g t h e l e v e l s i n t h i s odd-
3 3
o d d n u c l e u s . They a r e ( H e , p )
,
( H e , d ) ( p , n ) coun- ter r a t i o m e a s u r e m e n t s , ( p , t ) r e a c t i o n on 5 0 ~ r , w h e r e a n a l o g u e states o f 4 8 ~ are o b s e r v e d , ( d , a ) a n d a l s o d e c a y of 4 8 ~ r.
B u t t i l l h a l f a y e a r a g o when w e l o o k e d a t t h e Y s p e c t r a i n t h i s n u c l e u s on- l y t h r e e l o w e r l e v e l s h a d known s p i n p a r i t y . F i g . 4 i n d i c a t e s o u r y - d e c a y r e s u l t s . H e r e t h e r e a c t i o n employed was 4 0 ~ a ( ' 0 ~ , ~ p ) 4 8 ~ r e a c t i o n a t 2 5 MeV 'OB e n e r g y . O r i g i n a l l y e x p e r i m e n t was p l a n n e d f o r f i n d i n g g r o u n d b a n d s o f 4 8 ~ a a n d t h e r u n n i n g t i m ewas a b o u t 2 0 h o u r s f o r t h e y-y c o i n c i d e n c e w h i c h y i e l d e d m o s t i m p o r t a n t i n f o r m a t i o n . Of c o u r s e , t h e i n f o r m a t i o n f r o m p a r t i c l e s p e c t r o s c o p y was f u l l y u s e d . But i t i s s u r p r i s i n g t o know, how e f f i c i e n t t h e h e a v y i o n r e a c t i o n y s p e c t r o s c o p y is. A l s o t h e e n e r g y v a l u e s a r e much more p r e c i s e l y d e t e r m i n e d by t h e y - s p e c t r o s c o p y .
F o r d o i n g s u c h gamma s p e c t r o s c o p y i t i s n o t t o o i m p o r t a n t t o know t h e s t r a n g e r e a c t i o n m e - c h a n i s m s , B u t r a t h e r t h e f a c t t h a t we see s t r u c t u r e of n u c l e i s o w e l l , w i l l l e a d t o t h e n e x t s t e p w h e r e new i n t e r e s t i n g phenomena w i l l show up.
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K. RLEULER (Bonn) H. MORINAGA (Munich)
I would l i k e t o d r a w some a t t e n t i o n on a re- Not c o m p l e t e l y y e t , B u t t h e d i v e r s i o n i s t o c e n t work o f P r o f e s s o r s S t e p h e n s a n d Diamond become o b l a t e , s i n c e a p a r t o f t h e a n g u l a r mo-
( B e r k e l e y ) : l c v e l s s c h e m e s o f h e a v i e r e v e n - odd n u c l e i a r c s u c c e s s f u l l y i n t e r p r e t e d by a s s u m i n g a h i g h s p i n ( 1 3 / 2 ) s i n g l e - p a r t i c l e s t a t e c o u p l e d t o a r o t a t i n g c o r e . Viould s u c h a s t r u c t u r e c o r r e s p o n d t o y o u r i d e a s ? One m i g h t a s s u m e t h a t e v e n 2 o r more s i n g l e - p a r t i - c l e s t a t e s would c o n t r i b u t e t o t h e l a r g e a n g u - l a r momentum i n t h e c r i t i c a l r e g i o n .
mentum i s d e c o u p l e d from t h e r o t a t i n g c o r e . G, RIPKA ( S a c l a y )
I h a t e t o s o u n d p h i l o s o p h i c , b u t I h a v e s e e n r e c e n t l y s o many c u r v e s p l o t t i n g moments o f i n e r t i a or e x c i t a t i o n e n e r g i e s i n t e r m s o f a n - g u l a r momentum, o r i t s s q u a r e o r of t h e f r e - q u e n c y
...
t h a t I wonder : f r a n k l y , what d o e s i t m a t t e r what you p l o t ? Does anybody r e a l l yC5-110 H. MORINAGA
c a r e i f t h e c u r v e b u c k l e s up o r n o t ? Why n o t a n o t h e r ? s i m p l y c a l c u l a t e t h e d i s t o r t i o n and ( o r ) p h a s e H. MORINAGA (Munich)
c h a n g e s i n t h e n u c l e u s a n d s e e i f t h e spec- I d o n ' t t h i n k t h a t any p a r t i c u l a r f a n c y p l o t t r u m a g r e e s w i ~ e x p e r i m e n t ? I s t h e r e any phy-
h a s v e r y deep t h e o r e t i c a l meaning.
s i c s f a v o r i n g one p a r a m e t r i z a t i o n r a t h e r t h a n
