INTERMEDIATE STRUCTURE IN LIGHT ION REACTIONS

HAL Id: jpa-00216590

https://hal.archives-ouvertes.fr/jpa-00216590

Submitted on 1 Jan 1976

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

INTERMEDIATE STRUCTURE IN LIGHT ION

REACTIONS

H. Feshbach

To cite this version:

JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 11, Tome 37., Novembre 1976, page C5-177

INTERMEDIATE STRUCTURE IN LIGHT ION REACTIONS

H. Feshbach

Massachusetts Institute of Technology, Cambridge, Mass.

Résumé.- Une revue de la théorie et de l'expérimentation concernant la présence ou l'ab-sence de la résonance et de la structure intermédiaire observées dans les sections effi-caces de collision des ions légers est présentée.

Abstract.- A. review of the theory and experiment regarding the presence and absence of the resonance and intermediate structure presented in the cross-sections for the colli-sion of light ions is presented.

This paper will present a review of the inter-mediate structure and doorway states which have been discovered in the reactions induced by collision of the light ions 1 2C + 1 2C and 12C and 1 60 . An inter-pretation of the C + C data will be presented as well as arguments explaining the absence of in-termediate structure in the interaction of other light ions. It is found that the model proposed by Imanishi and Nogami [l] provides a qualitative un-derstanding of the data. This theory needs further development. A calculation of the total reaction cross-section is particularly required in response to the criticism that the potentials employed by Imanishi have imaginary terms which are too small. However as is pointed out below this does not neces-sarily mean that the resulting reaction cross-sec-tion will be too small because it is necessary to take into account the effects of the coupling of the incident channel to the other channels considered by Imanishi and Kondo, Matsuse and Abe [2] The reader is referred to several excellent review arti-cles by Bromley [3] , Cindro [4] , Siemssen [5] and Stokstad [6] which I found to be very helpful in the preparation of this paper.

12 12

We begin with the C + C system which provides the best and nearly unique examples of resonant structure in the collision of light nuclei. Fig. 1

i 2

c

•

l 2

c

2+ 6* 8* 4* 2* 4+ 8+2+4+ 0+ 8+4+6+

8 1 I I I I I III I III

-1 " r - v i e w I -1^

+

n 6 _ * II

5

4+

y

| 4 - ,* f.

J'

1

,

h 4*

/ \° V / 1-1 (0+)

?w ' c bi '" • o I 1 1 1 1 — i 1 3 4 5 6 7 8

Ee.m. (MeV)

F i g . l - The t o t a l gamma r a d i a t i o n yield in the 12C + 12C system. The l e v e l s a t the top of the f i gure a r e those predicted by Kondo e t a l . S i s d e f i -ned by

a = S/E exp [- (2irn + gE) ~\ where , ._ T) = Z,Z2e2/%v and g = 1/3 (mR3/2ZjZ2) '

shows the results of a measurement of the y-yield in 12 12

the C + C reaction as obtained and collected by Spinka et al. [7], The ordinate is the cross-section divided by the Sommerfeld factor to remove the ef-fects of the Coulomb barrier. This figure summarizes the experimental situation as of the time of the Maryland Conference. The three resonances between

H. FESHBACH

5 . 5 and 6.5 MeV were f i r s t s e e n by t h e Chalk R i v e r group [8] i n 1960 and 1961 w h i l e t h e resonances be- low were e s t a b l i s h e d c o n s i d e r a b l y l a t e r by P a t t e r s o n e t a l . [g] and by Stephens e t a l . [IO]. The s p i n s of a few of t h e l e v e l s had been determined. It i s im- p o r t a n t t o n o t e t h a t t h e w i d t h s a r e small. For exam- p l e t h e 2' resonance a t 5.6 MeV h a s a width of 130 keV w h i l e t h e 4' resonance a t 6.0 MeV width i s 100 keV. A t t h e top of t h e f i g u r e a r e t h e p o s i t i o n s of

t h e r e s o n a n c e s on t h e b a s i s of t h e extended Imanishi model a s c a l c u l a t e d by Kondo e t a l . [2]

.

The p r e d i c - t e d resonances i n t h e r e g i o n of 7 t o 8 MeV have s t i - mulated experimental measurements i n t h i s r e g i o n by b o t h t h e S a c l a y and Yale groups.Erb e t a l . [l11 a t Yale have looked a t t h e a n g u l a r d i s t r i b u t i o n of t h e t r a n s i t i o n s t o low l y i n g s t a t e s of 2 0 ~ e w h i l e Basrak e t a l . [12,13] have used b o t h t h i s r e a c t i o n and t h e

23 r e a c t i o n 1 2 ~ ( 1 2 ~ , p ) Na. L e t u s review t h e d a t a of Erb e t a l . I t w i l l p r o v i d e a n example of t h e s o r t of a n a l y s i s employed by most e x p e r i m e n t a l i s t s . I n f i g . 2, t h e a n g l e i n t e g r a t e d c r o s s - s e c t i o n s f o r t r a n s i t i o n s t o t h e i n d i c a t e d low l y i n g 2 0 ~ e s t a t e s a r e p l o t t e d . P a r t i c u l a r a t t e n t i o n should be p a i d t o t h e sum of t h e c r o s s - s e c t i o n s a t t h e top of t h e f i g u r e . The sum i s u s e f u l s i n c e i t t e n d s t o average o u t ' q s t a t i s t i c a l " f l u c t u a t i o n s a 1 though t h i s method w i l l p o i n t up t h e resonances o n l y i f t h e r e i s a s u b s t a n t i a l branching r a t i o t o most of t h e l e v e l s involved. There i s c o n s i d e r a b l e s t r u c t u r e . The a u t h o r s s e l e c t e d t h r e e of t h e anomalies a t 7.71, 9.84, 10.59 MeV t o examine a s p o s s i b l e resonances because t h e i r a n g u l a r d i s t r i b u t i o n t o t h e ground s t a t e of 2 0 ~ e e x h i b i t e d p u r e [pL ( c o s o)] d i s t r i b u - t i o n s ( f i g . 3 ) . I n F i g . 4 two of t h e s e a r e p l o t t e d ; c u r v e ( a ) f o r t h e 7.71 resonance i s j u s t 2 [p4 (COB o)] g i v e n by t h e s o l i d l i n e w h i l e t h e 9. 84 MeV resonance a n g u l a r d i s t r i b u t i o n f i t s t h e [p8 (COS 0 ) 1 2 . The resonance a t 7.71 MeV w i t h a width of 145 keV seems s e c u r e because of t h e s t r o n g c o r r e l a t i o n s i n t h e energy dependence, s e e f i g . 2, £0; t h e f o u r e x i t channels. The evidence i s q u i t e s t r o n g ' f o r t h e 9.84 MeV c a s e where t h r e e of t h e f o u r c h a n n e l s e x h i b i t anomalies. The a u t h o r d i d n o t l i s t t h e 10.59 MeV c a s e a s a resonance. It showed anoma- l i e s i n two of t h e f o u r c r o s s - s e c t i o n s .

The summed c u r v e shows o t h e r anomalies. The S a c l a y group i n a n independent i n v e s t i g a t i o n h a s r e p o r t e d resonances a t 7.50, 8.45 and 8.85 MeV. The anomalies which c o u l d b e a s s o c i a t e d w i t h t h e l a s t two a r e

Fig. 2 - A n g l e i n t e r a t e d c r o s s - s e c t i o n s a s f u n c t i o n of energy t h e 1 2C(13C ,a) r e a c t i o n p o p u l a t i n g low- l y i n g l e v e l s of 20Ne.

p r e s e n t i n t h e Yale d a t a b u t t h e 7.5 resonance does n o t seem t o b e p r e s e n t . The S a a l a y group r e p o r t s a minimum on t h e summed i n t e g r a t e d c r o s s - s e c t i o n s i n c l u d i n g t h e g . s . , t h e 1.63, 4.25, 4.97 and 6.72 MeV e x c i t a t i o n i n 2 0 ~ e . ~ h e y a l s o r e p o r t a peak i n

23

t h e 1 2 ~ ( 1 2 ~ , p ) Na r e a c t i o n . They a s s i g n a s p i n of 6' t o t h e 7.50 MeV anomaly, 6+ f o r t h e resonance a t 8.45 MeV, and 6+ o r 8+ f o r t h e 8.85 MeV c a s e . Clear- l y f u r t h e r work needs t o b e d k e b e f o r e one c a n be s u r e of t h e r e l i a b i l i t y of t h e r e s u l t s r e p o r t e d . But i t i s a p p a r e n t t h a t t h e r e i s c o n s i d e r a b l e s t r u c t u r e and t h a t t h e w i d t h s a r e narrow.

INTERHEDIATE STRUCTURE C5- 179 F i g . 4

-

The I 2 c ( l 2 c , a ) 2 0 ~ e a n g u l a r d i s t r i b u t i o n s a r e compared w i t h a r b i t r a r i l y n o r m a l i z e d L e g e n d r e f u n c t i o n s [P ( c o s 0 ) ] 2 ( a ) a t E = 7.71 MeV (L = 4 ) and ( b ) E c S m ' = 9.84 MeV (L = 8 ) . F i g . 3

- Legendre $ o l y n o m i a l f i t s t o t h e measured

g r o u n d s t a t e 1 2 ~ ( l c,a)20Ne a n g u l a r d i s t r i b u t i o n . The c r o s s - s e c t i o n s c a l e i s l i n e a r w i t h a maximum of 25 m b l s r . P e a k s r i s i n g a b o v e t h i s v a l u e a r e shown a s p l a t e a u s . The a n g u l a r d i s t r i b u t i o n s of Ec*m.= 7.7 9.84 and 10.59 a r e drawn w i t h w i d e r l i n e s . l a t i n g t h e f i r s t e x c i t e d s t a t e of 2 0 ~ e , 2 3 ~ a , a n d 2 3 ~ g . T h i s sum r e f l e c t s , a c c o r d i n g t o t h e a u t h o r s , most o f t h e c r o s s - s e c t i o n . The r e s u l t s a r e shown i n F i g . 5 . Note t h a t t h e Coulomb b a r r i e r f a c t o r u s e d i s f o r a f i n i t e n u c l e u s w h e r e a s t h a t f o r F i g . 1 i s f o r a p o i n t n u c l e u s . The p r e s e n c e of t h e r e s o n a n c e a , t 7.71 keV i s c l e a r . But t h e r e i s c o n s i d e r a b l e a d d i - t i o n a l s t r u c t u r e between i t and t h e C h a l k R i v e r r e s o n a n c e a t r o u g h l y 6.5 MeV which n e e d s f u r t h e r i n - v e s t i g a t i o n . New i n f o r m a t i o n i s a l s o a v a i l a b l e i n t h e r e g i o n below t h e C h a l k R i v e r r e s o n a n c e s . The d a t a p r e s e n t e d i n F i g . 1 below E = 4 MeV shows a s t r o n g r i s e

c.m.

which was o f c o n c e r n t o t h e a s t r o p h y s i c i s t s . It was v e r y d i f f i c u l t t o u n d e r s t a n d . Michaud and Vogt [l41

E,,, ( M W )

H . FESHBACH ? ,., 3.0

-

I,-

S1634 exrracrea trc I

-

t d a t a (ref. 10) n v 1 4 p g / c m 2 8 2.5- _{o 55 p g / cm2}

L

0 #?

2

I \ . 'D

1

U v C ) 1.0

0.5

-

g Er = 4 4 0 keV

---*---

5440

extracted from Penn

-

d a t a (ref. 10)

11

'a

I 2.5 o

2.5 3.0 3.5 4.0 4.0 5.0 5.5 6.0 Center of Moss Energy (MeV)

F i g . 6

-

12c + 12c gamma r a y i e l d from f i r s t e x c i t e d s t a t e s

3:

of ~ O N ~ ( E = 1634 keV) and % a ( ~ = 440 keV

.

The connected p o i n t s a r l e x t r a c t e d from t h e pen%. d a t a [ I O j .

which l e a d s t o high f u s i o n c r o s s - s e c t i o n s a t low energy. A group from Munster [l51 has c a r e f u l l y exa- mined t h i s r e g i o n by o b s e r v i n g t h e gamma r a y t r a n s i - t i o n s from a l a r g e number of e x c i t e d s t a t e s i n 2 0 ~ e and 2 3 ~ a . They r e p o r t t h e r e s u l t s f o r t r a n s i t i o n s from t h e f i r s t e x c i t e d s t a t e s i n 2 0 ~ e ( ~ = 1634 keV) Y and 2 3 ~ a ( ~ Y = 440 keV). T h e i r r e s u l t s a r e p r e s e n t e d i n Fig. 6. The s u b s t a n t i a l d i f f e r e n c e from t h e o r i - g i n a l Pennsylvania d a t a [l61 below 3 MeV i s apparent. The r i s e i n t h e energy decreased turned o u t t o be a n a r t i f a c t of t h a t experiment which was of importance a t low energy. T h i s o b v i a t e s t h e need f o r "under t h e b a r r i e r absorption". I n a d d i t i o n c o n s i d e r a b l e s t r ' u c t u r e 'below t h a t v i s i b l e i n F i g . 1 i s a p p a r e n t i n t h a t peaks a r e common t o b o t h t h e 2 0 ~ e and 2 3 ~ a channels.

Resonances of h i g h s p i n a r e a l s o s e e n a t conside- r a b l y h i g h e r e n e r g i e s . I n t h i s energy domain t h e r e i s a n o n - t r i v i a l d i f f i c u l t y of proving t h a t t h e peaks a r e resonances. There a r e many c a s e s f o r which peaks

a r e f l u c t u a t i o n s . One c a n u s u a l l y e l i m i n a t e t h e s e i n view of t h e absence of c o r r e l a t e d peaks i n o t h e r c h a n n e l s

- t h a t i s by showing t h a t o t h e r c h a n n e l s

do n o t e x h i b i t anomalies a t a p p r o x i m a t e l y t h e same energy. One should b e a r i n mind a number of com- p l i c a t i o n s . Because of t h e n a t u r e of t h e s t a g e s i n v o l v e d , t h e branching r a t i o s t o some channels may be small s o t h a t n o t a l l c h a n n e l s need t o e x h i b i t c o r r e l a t e d resonances. Secondly t h e r e i s g e n e r a l l y a background non-resonant amplitude which c a n i n -

t e r f e r e w i t h t h e r e s o n a n t amplitude and s h i f t t h e peak ( o r v a l l e y ) and change i t s c h a r a c t e r . Of cour- s e a s h i f t l a r g e r t h a n t h e width would be v e r y s u r p r i s i n g . T h i s e f f e c t may cause some d i f f i c u l t i e s a s t h e coherence l e n g t h which s c a l e s t h e f l u c t u a - t i o n s i s of t h e same o r d e r a s t h e w i d t h , p e r m i t t i n g t h e presence of a c c i d e n t a l c o r r e l a t i o n s . However i t would be remarkable i f t h i s a c c i d e n t were t o occur i n s e v e r a l c h a n n e l s s i m u l t a n e o u s l y .

INTERMEDIATE STRUCTURE

s i g n a l from t h e n o i s e i d e n t i f i e s t h e quantum number _''C

₊

_I2c

_{RESONANCES IN 2 4 ~ g} of t h e resonance. Angular c o r r e l a t i o n experiments

a r e a n example and we have seen e a r l i e r t h e u s e of t h e unique [pL (cos

@)l2

a n g u l a r d i s t r i b u t i o n s . This

g+

-

c r i t e r i o n i s on t h e one hand too s e v e r e i f reso- S+

-

nances o v e r l a p and on t h e o t h e r hand n o t s u f f i c i e n t i n i t s e l f . It c a n be t h e c a s e ( t h i s o b j e c t i o n

4'

-

a p p l i e s t o a l l t h e t e s t s ) t h a t we may be d e a l i n g 3'-

w i t h a n e n t r a n c e channel phenomenon. The transmis-

s i o n c o e f f i c i e n t may e x h i b i t o s c i l l a t i o n s because - - - ' Z C + ~ ~ C p

Thresh

of shape resonances. However t h e s e o s c i l l a t i o n s a r e

of t h e o r d e r of a few MeV. Hence we c a n d i s p o s e of _{C( +"Ne} t h e c a s e i f t h e widths of t h e resonance a r e much

s m a l l e r , e.g., of t h e o r d e r of a few hundred keV. A second problem was p o i n t e d o u t by Rolf Siemssen

i n a d s i c u s s i o n e a r l i e r t h i s week. I f a new channel open up w i t h a n amplitude which h a s a r a p i d l y i n c r e a - s i n g energy dependence, a s w i l l be t h e c a s e when l a r g e angular momenta a r e involved, and then compe- t i t i o n s e t s i n r a p i d l y a s w i l l , a peak w i l l be gene- r a t e d . However we can d i s p o s e of t h i s problem i f t h e r e a r e s e v e r a l such peaks.

An a n a l y s i s of t h e type which emphasizes channel c o r r e l a t i o n has been performed f o r example by a group from M. I.T., BNL, Argonne and Copenhagen [l 71 i n which they measure t h e e x c i t a t i o n f u n c t i o n f o r

I 2 c ( l 2 c , p ) t o a number of s t a t e s i n c l u d i n g f o u r of h i g h s p i n i n 2 3 ~ a . They have a l s o c o l l e c t e d t h e d a t a o b t a i n e d by o t h e r a u t h o r s . The open channels invol- v i n g emission of l i g h t p a r t i c l e s up t o and i n c l u d i n g a l p h a p a r t i c l e s a r e shown i n Fig. 7. We s h a l l l a t e r be a l s o d i s c u s s i n g t h e product channel of ' ~ e + 160. I n Fig. 8 t h e r e s u l t s a r e p r e s e n t e d . One immediately s e e s s t r o u g c o r r e l a t i o n s f o r t h e l e v e l s a t 19.3 MeV, a t 14.3 and 11.4 MeV. By comparing t h e v a r i o u s bran- c h i n g r a t i o s t h e s e a u t h o r s concluded t h a t t h e s e

+

+

l e v e l s had a s p i n of 12

,

10 and 8+ r e s p e c t i v e l y . From t h e e x c i t a t i o n c u r v e s f o r Ex = 14.7, 15.9 +

16.0, and 17.3 one s u s p e c t s a l e v e l a t almost 25 MeV. From E = 12.30, 8.94, 13.82, 14.40, a l e v e l a t about

X

22.5 MeV. S i m i l a r l y t h e r e i s p o s s i b l y a l e v e l a t 18.5 MeV. The e x i s t e n c e of t h e l a t t e r h a s been v e r i - f i e d by Eberhard e t a l . [l81 using t h e 16 12c(12c, 8 ~ e _g. ) 0 g. S. r e a c t i o n . They o b t a i n a S. 2 [pL = 1 2 (COS

e)]

d i s t r i b u t i o n t h e s e i d e n t i f y t h e

+

s p i n of t h e resonance a t 12

.

The F l o r i d a group [l91 h a s done a v e r y e x t e n s i v e s t u d y u s i n g t h e same reac-

-Fig. 7

- Open channels p e r m i t t i n g emission of l i g h t

p a r t i c l e s from e x c i t e d s t a t e s of 2 4 ~ ~ . TABLE I E x i t channel Ec.m. Tc.m. J~ (MeV) (keV) 'Be + 160 11.43 200 8+ F l e t c h e r e t a l . [l91 (11.78)

...

(8') 12.0 200 8+ 12.35 300 8' 12.86 350 8' 13.35 350 10+ 13.85 260 10' 1 4 . 3 280 10' 15.3 600' 10+ 1 6 . 2 800* 10' 17.15 350 10' 17.75 500 12' (18.4)

...

12' 18.8 400 12' 18.8 < 400 10' 19.45 250 12' a + " ~ e * 17.9 340260 Fortune e t a l . [20] 18.4 400230 18.6 3752100 19.0 310260 19.4 320+_30 'Be + 1 6 0 18.5 12+ Eberhardt e t a l .

Cl4

p + 2 3 ~ a * 11.4 8+ Cosman e t a l . [l71 14.3 1 O+ 19.3 12+ da S i l v e i r a [ZI] 26 (12+) a + " ~ e * 7.71 145 4' Erb e t a l . [l l] 9 . 8 4 small 8' Basrak e t a l . b 2 , 1 4 8 . 8 5 ( 6 + , 8 + )

H. FESHBACH

F i g . 8

-

E x c i t a t i o n f u n c t i o n s of s e l e c t e d "C

+

12C r e a c t i o n c h a n n e l s . The 12c

+

"C and 2 0 ~ e + a r e a c t i o n s c a l e s a r e a l i g n e d t o correspond t o t h e same E ( 2 4 ~ g ) v a l u e s i n

X

t h e f i g u r e .

C l e a r l y t h e i s s u e of why some resonances a r e s e e n i n one r e a c t i o n and n o t i n a n o t h e r and which ones a r e i d e n t i c a l a l t h o u g h s h i f t e d i n energy needs t o be r e s o l v e d . But t h e r e a p p e a r s t o be much s t r u c t u r e w i t h a c o n s i d e r a b l e grouping of l e v e l s of a p a r t i c u -

l a r s p i n and p a r i t y . The l e v e l spacing o m i t t i n g t h e p o s s i b l y unresolved resonances a t 15.3 and 16.2 MeV i s about 0.5 MeV w h i l e t h e w i d t h s a r e somewhat l e s s , of t h e o r d e r of a few hundred keV. The 10+ resonan- c e s a r e spread over a b o u t 3.8 MeV w h i l e t h e 12+ reso- nances extend over about 1.7 MeV b u t t h e r e may be o t h e r s above t h e energy range i n v e s t i g a t e d by t h e F l o r i d a group. These d a t a a r e c o l l e c t e d i n F i g . 9. The s t r a i g h t l i n e a p p r o p r i a t e t o a r o t a t i o n a l band p r o v i d e s a good average f i t b u t i t i s apparent t h a t t h e r e a r e s e v e r a l resonances a t each v a l u e s of J

r a t h e r t h a n j u s t one. We s h a l l come back t o t h i s p o i n t l a t e r .

I n cdmparison t o t h e "C + "C c a s e , t h e d e t e r - m i n a t i o n and n a t u r e of t h e resonances of t h e system

"C + 160 have formed more d i f f i c u l t problems. A

resonance a t 19.71 MeV, width 300 keV, h a s been found by s e v e r a l groups [22]

.

The d a t a of t h e Yale group shown i n F i g . 10 i n c l u d e s b o t h elastic and i n e l a s t i c s c a t t e r i n g t o e x c i t e d s t a t e s of 60. The resonance i s n o t s e e n i n t h e e x i t channel

24

*

12 16 27 8 ,

1 2 ~ ( 1 6 0 , a ) Mg b u t i t i s s e e n i n C( 0,p) A 1 The l a t t e r r e a c t i o n was s t u d i e d by t h e M.I.T.

-

B.N.L. groups. H a l b e r t e t a l . [23] have s e e n a n

24

INTEHNEDIA'I'E STRUCTURE

12c

+

I2c

Thresh.

F i g . 9

- A summary of t h e r e p o r t e d

I 2 t + I2C r e s o n a n c e s

r e s o n a n c e a t 22.7 MeV. They h a v e r e p o r t e d new r e m a i n s t o b e done. l e v e l s a t 17.3 and 20.8 MeV a t t h i s c o n f e r e n c e C251

from a n a n a l y s i s of t h e e l a s t i c s c a t t e r i n g . These need t o be o b s e r v e d i n o t h e r c h a n n e l s . Two l e v e l s a t 20 and 22.5 MeV, F i g . I 1 , a r e r e p o r t e d by ~ a l m i n and P a u l [26]. B r a n f o r d e t a l . [27] have s e e n one l e v e l a t 16.0 MeV and r e p o r t ' o t h e r l e s s c e r t a i n examples. R e c e n t l y t h e F l o r i d a g r o u p 1181 s t u d y i n g t h e

2 7

H. FESHBACH

F i g . 10

-

I2c

+ 160 r e a c t i o n s i n t h e v i c i n i t y of t h e 19.7 MeV resonance.

The f i t s o b t a i n e d w i t h t h e s e p o t e n t i a l s have t h e c o r r e c t c h a r a c t e r a s can be s e e n from F i g . 20, 1361 , b u t a r e by no means p e r f e c t . A s c a n be seen from F i g . 21, [36], a t p a r t i c u l a r e n e r g i e s t h e a n g u l a r d i s t r i b u t i o n f o r 160 + 160 a r e pure [pL ( c o s

O)lZ,

t h e v a l u e s of L a r e given on t h e r i g h t hand s i d e of t h e f i g u r e . A t t h e s e e n e r g i e s t h e phase s h i f t s a r e c l o s e of ~ / 2 . The width i s of t h e o r d e r of 3-4 MeV. The small v a l u e s of t h e imaginary p o t e n t i a l a r e e s s e n t i a l i n o r d e r t o o b t a i n t h e observed o s c i l l a - t i o n s i n t h e c r o s s - s e c t i o n and t h e s e v a l u e s of t h e width of t h e g r o s s - s t r u c t u r e anomaly. One needs o n l y

t o r e c a l l t h a t t h i s width i s approximately equal t o

0

0

14

16

18

20

22

24

C.M.

Energy

(

M e V

1

F i g . 11

- E x c i t a t i o n f u n c t i o n s f o r i n e l a s t i c s c a t -

t e r i n g i n t h e 1 2 ~ + 160 system i n v o l v i n g t h e 3-, 0+ d o u b l e t a t 6 MeV i n 160.

twice t h e magnitude of t h e imaginary p o t e n t i a l .

The v a l u e of energy, Ec,m., a t which, a c c o r d i n g t o t h e p o t e n t i a l of T a b l e 11, t h e

I2c

+

12c

s c a t - t e r i n g e x h i b i t s a g r o s s s t r u c t u r e resonance a t a g i v e n v a l u e of L h a s been determined by Arima e t a l . 1371 u s i n g Regge a n a l y s i s . The s t r a i g h t l i n e of F i g . 22 g i v e s t h e i r r e s u l t . I t i s remarkable t h a t t h e measured resonance e n e r g i e s and a s s o c i a t e d v a l u e s of L a v a i l a b l e a t t h a t time f a l l c l o s e t o t h e v a l u e s p r e d i c t e d from t h e Yale

12c

+

I2c

p o t e n t i a l . However t h e i r s u g g e s t i o n t h a t t h e observed reso- nances a r e simply shape resonances i s u n t e n a b l e s i n c e t h e width of a shape resonance i s of t h e o r d e r of a few MeV whereas t h e observed resonances have w i d t h s of t h e o r d e r of a few hundred keV. Moreover we now have many r e s o n a n c e s f o r each v a l u e of J.

INTERMEDIATE STRUCTURE C5-184

-

30 p g cm-'

1mpq cm"

reoctor qrophale

F i g . 12

- The q u a n t i t y S

= E

a

exp ( 2 7 ~ ~ ) a s a func- t i o n o f E where a i s t h e t o t a l r e a c t i o n c r o s s - s e c t i o n f o r 1% + 160.

F i g . 13

-

T o t a l f u s i o n c r o s s - s e c t i o n f o r 160 +

I2c.

a t a s h a p e r e s o n a n c e we have j u s t b e e n d i s c u s s i n g , i s weakly c o u p l e d , and I emphasize t h e weakness of t h e c o u p l i n g , t o e x c i t e d s t a t e s of t h e system. The r e s u l t i s a f r a g m e n t a t i o n t of t h e s h a p e r e s o n a n c e i n t o a number of components, s e e F i g . 23. A r o u g h c h e c k on t h i s i d e a i s g i v e n by t h e f a c t t h a t t h e sum of a l l t h e w i d t h s of t h e 10' s t a t e s which f a l l c l o s e t o t h e Arima l i n e i s 2.65 MeV o f t h e o r d e r of magnitude of t h e g r o s s s t r u c t u r e w i d t h . We s h a l l come back t o t h i s d e s c r i p t i o n l a t e r i n t h i s p a p e r . I n t h e l a n g u a g e of t h e p a p e r w i t h ~ e r h ; a n and Lemmer C381 t h e "C and

I2c

r e s o n a n c e a r e examples of i s o l a t e d doorway s t a t e s . L e t me remind you of t h e e q u a t i o n s d e s c r i b i n g i s o l a t e d doorway s t a t e s and of some p e r t i n e n t p r o p e r t i e s . The doorway s t a t e (J

d and t h e i n c i d e n t c h a n n e l

JI

s a t i s f y a p a i r o f c o u p l e d e q u a t i o n s ( E - H ) $ = H $ PP Pd d These wave f u n c t i o n s a r e e n e r g y a v e r a g e d s o t h a t t h e H a m i l t o n i a n o p e r a t o r s a r e complex. The complex p a r t of Hdd r e f l e c t s t h e s p r e a d i n g w i d t h . The com- p l e x p a r t of t h e c o u p l i n g H a m i l t o n i a n g i v e s r i s e t o t h e asymmetry i n t h e doorway r e a c t i o n c r o s s - s e c t i o n s . I f t h e s e i m a g i n a r y t e r m s a r e l a r g e t h e r e s o n a n c e w i l l n o t b e s e e n s o t h a t i n t h e I 2 c

+

I2C c a s e t h e y must b e s m a l l . The i m a g i n a r y p a r t of H PP must b e s m a l l e r t h a n t h a t which i s used i n t h e o p t i c a l p o t e n t i a l t o f i t t h e s c a t t e r i n g d a t a s i n c e t h e r e i s a c o n t r i b u t i o n t o t h e r e a c t i o n c r o s s - s e c t i o n f r o m t h e c o u p l i n g t o t h e second e q u a t i o n . Thus t h e i m a g i n a r y p a r t o f H must b e s m a l l e r t h a n P P 0.4 + 0. IE. I n o r d e r t o u n d e r s t a n d t h e p r o p e r t i e s of t h e doorway s t a t e s i t i s n e c e s s a r y t o c o n s i d e r t h e i r w i d t h . F o r t h i s p u r p o s e we c a n make u s e of t h e

H. FESHBACH

1.4-

I I I I _I

_I

"

Total Fusion Cross

INTERMEDIATE STRUCTURE C5- 187 C.M. ENERGY (MqV) F i g . 17

-

The 90' e l a s t i c s c a t t e r i n g e x c i t a t i o n f u n c t i o n s f o r s e v e r a l heavy i o n systems. 4 5 6 7

C M

ENERGY F i g . 18

-

I2c + "C' e l a s t i c s c a t t e r i n g a t 90° i n t h e r e g i o n of t h e Coufdmb.ba.rrier

HEAVY ION ELASTIC SCATTERING

90" EXCITATION FUNCTIONS

CENTER

OF

MASS ENERGY-MeV

Fig. 1 9

-

The 90° e x c i t a t i o n f u n c t i ns f o r e l a s t i c s c a t t e r i n g of

IZc

+

I2c

and 160 + 180 systems o b t a i - ned a s i n d i c a t e d a t Yale and t h e Oak Ridge Labora- t o r y .

d i s c u s s i o n t o a few q u a l i t a t i v e p o i n t s . The forma- l i s m assumes a s e q u e n t i a l p r o c e s s i n which t h e system proceeds from t h e doorway s t a t e t o s t a t e s of h i g h e r complexity ( s e e F i g . 24). More p r e c i s e l y i t assumes t h a t t h e r e s i d u a l ~ a m i l t o n i a * c a n couple t h e n' t h s t a t e w i t h only t h e ( n + 1) s t o r ( n - 1) s t s t a g e . The e s c a p e width of t h e doorway i s g i v e n by e m i s s i o n from i t w h i l e t h e s p r e g d i n g w i d t h i n v o l - v e s t h e sum of t h e p r o b a b i l i t y of t h e e m i s s i o n from a l l t h e l a t e r s t a g e s . T h i s r e s u l t p o i n t s up one p o s s i b l e s o u r c e of c o n f u s i o n . The e s c a p e width i s n o t t h e sum of a l l t h e p r o b a b i l i t i e s of r e a c t i o n s of v a r i o u s k i n d s connected w i t h t h e doorway s t a t e resonance. Some of t h e s e c o n t r i b u t e t o t h e s p r e a - ding width,. I n t h e e v e n t of s t r o n g c o u p l i n g b e t - ween t h e more complex s t a g e s , t h e s t a t i s t i c a l com- pound n u c l e u s r e s u l t i s o b t a i n e d . However more g e n e r a l l y i t may be n e c e s s a r y t o i n c l u d e t h e c o n t r i - b u t i o n of t h e pre-compound terms.

H. FESHBACH

E L A S T I C S C A T T E R I N G

' 6 0

+

' 6 0

30"

60"

90°

30"

60°

90°

CENTER OF MASS ANGLE

OPTICAL MODEL

Q

2

22.25

LL 0

a

W l-

z

W

19.00

U

F i g . 20

-

Comparison of t h e e x p e r i m e n t a l angle-energy c r o s s - s e c t i o n s u r f a c e s w i t h t h e corresponding o p t i c A I model f o r t h e 160 + 160 and

12c

+ 12c systems.

1

OPTICAL MODEL

s e c t i o n e x h i b i t s shape resonances t h e r e i s no evi-

- -.

EXPERIMENT

-

. ,

I I

I

I I

I

dence f o r r e s o n a n c e s i n t h e r e a c t i o n c h a n n e l s (Fig. 25, [40] ) . Even though

12c

+

I2c

ddek r e s o n a t e ,

12c

+ 13c does n o t a s i s c l e a r from'Fig. 26, [41]. The f u s i o n c r o s s - s e c t i o n of 12c

+

180' system shows no f l u c t u a t i o n s w h i l e t h a t of

I2c

+

160 does (Fig.

14). The o s c i l l a t i o n s i n e l a s t i c s c a t t e r i n g c r o s s - s e c t i o n s a r e much pronounced i n 160 + '60 s c a t t e r i n g t h a n i n 160 + 180. We n o t e a l s o t h a t t h e o b l y sys- t e m s which do e x h i b i t doorway s t a t e r e s o n a n c e s a r e 12c + 12c and p o s s i b l y 12c + 160. ~ a n d e * b o s c h e t a l . 12 C421 showed t h a t t h e e l a s t i c s c a t t e r i n g of C by 2 0 ~ e d i f f e r s s h a r p l y from t h a t of 160 +-160 i n t h a t b o t h t h e a n g u l a r d i s t r i b u t i o n a t E = 23.3'MeV c.m.

and t h e energy dependence of t h e c r o s s s e c t i o n a r e smooth and f e a t u r e l e s s . T h i s i s a n i n t e r e s t i n g c a s e because t h e b i n d i n g energy of b o t h systems d i f f e r s by o n l y 2.4 MeV, t h e y have t h e same compound n u c l e u s , and t h e g r a z i n g a n g u l a r momenta d i f f e r by no more t h a n one u n i t of

-k

f o r t h e same e x c i t a t i o n of t h e

EXPERIMENT

compound n u c l e u s .

The s u b s t a n t i a l d i f f e r e n c e s amongst t h e s e r a t h e r s i m i l a r n u c l e a r systems need t o b e understood. We have a l r e a d y noted a number of c o n d i t i o n s which need t o b e s t a t i s f i e d i f resonances a r e t o b e obser- ved. The e l a s t i c s c a t t e r i n g f o r t h e p a r t i a l L wave i n q u e s t i o n should have a r e l a t i v e l y l a r g e ampli- tude. I f t h i s i s n o t t h e c a s e i t w i l l b e d i f f i c u l t t o p i c k o u t e f f e c t s i n t h e L channel from a l l t h e o t h e r e f f e c t s which a r e s i m u l t a n e o u s l y p r e s e n t . A g r o s s - s t r u c t u r e resonance i s t h e b e s t t h a t c a n o c c u r i n t h i s r e g a r d . This r e q u i r e s a s u r f a c e transpa- rency of t h e n u c l e u s ; t h a t i s a b s o r p t i o n i n t h e n u c l e a r s u r f a c e i s low. We have noted empirical evi- dence t h a t i n d i c a t e s t h a t s u r f a c e a b s o r p t i o n i s low. The f i t t o t h e e l a s t i c s c a t t e r i n g c r o s s - s e c t i o n f o r

INTERMEDIATE STRUCTURE C5-189

Fig. 21

-

An o p t i c a l model a n a l y s i s of t h e 160

+

160 e l a s t i c s c a t t e r i n g . The panel on t h e l e f t shows t h e o p t i c a l model p o t e n t i a l s f o r d i f f e r e n t p a r t i a l waves. The c e n t r a l panels show t h e phase s h i f t s , t h e a t t e - nuation c o e f f i c i e n t f o r each p a r t i a l wave and t h e 90° c a l c u l a t e d s c a t t e r i n g cross-sections. The panel on the r i g h t i s a n energy a n g l e s u r f a c e f o r t h e s c a t t e r i n g f o r the Yale d a t a . The h o r i z o n t a l l i n e s i n d i c a t e where the d i f f e r e n t p a r t i a l waves become dominant. I n the panel on the r i g h t , the heavy l i n e s , which have been f i t t e d t o the experimental d a t a , a r e squares of t h e Legendre polynomials of the i n d i c a t e d order.

Many authors have ~ o i n t e d o u t [43] t h a t a t t h e angu- l a r momenta and energies i n question t h e r e e x i s t very few ways f o r the system t o proceed to higher

s t a t e s of i n t e r n a l e x c i t a t i o n with the t o t a l angu- l a r momentum remaining c o n s t a n t , thus reducing the number of a b s o r p t i o n channels.

The d e n s i t y of l e v e l s of t h e compound system a s well a s the number of channels e n t e r importantly

i n t o the value f o r the doorway s t a t e width. The values of these parameters a t the Coulomb b a r r i e r energy a r e shown i n Table 111, a s c a l c u l a t e d by Hansen e t a l . [U]

.

The ''C +

12c

h a s t h e s m a l l e s t l e v e l d e n s i t y and number of open channels, t h e

12c

+ 160 systems next. However t h e r e a r e o t h e r p o s s i b i l i t i e s such a s ' ~ e

+

12c, and 12c +

13c y e t n e i t h e r of these sys-

tems e x h i b i t resonances. It i s c l e a r another mecha- nism must be operating.

The one I b e l i e v e t o be involved i s described a s follows. The reader w i l l r e c a l l t h a t one of t h e consequences of t h e i n t e r a c t i o n between the c o l l i - ding 12c nuclei was the fragmentation of the shape resonance f o r a given L i n t o ones of considerably narrower width. The i n t e r a c t i o n needed t o be weak s i n c e t h e resonances were grouped c l o s e t o be ener- gy of t h e shape resonance. A p o s s i b l e explanation of t h e absence of resonance i n o t h e r l i k e l y systems mentioned above i s t h a t i n those c a s e s the i n t e r a c -

t i o n i s strong. A s a consequence n o t only w i l l t h e L shape resonance be fragmented b u t the fragments w i l l be s u b s t a n t i a l l y displaced. The L s t r e n g t h w i l l be dispersed and f a r l e s s v i s i b l e . Vandenbosch

[45] has given an example. He has performed a cou- pled channel c a l c u l a t i o n f o r both 160 + 160 and

180 + 160. The 2+, 6.9 MeV l e v e l and the 3-, 6.1

MeV l e v e l i n 160, were taken i n t o account i n the f i r s t c a s e while f o r t h e second case the 2+, 1.98 MeV and the 3-, 5.09 MeV l e v e l s of 180 were inclu-

+

C5- 190 H. FESHBACH 100 2 0 0 3 0 0

I l l

I 1 J ( J + I ) I I I I I 2 4 6 8 10 12 14 16 J 0

SPINS OF STATES IN ROTATIONAL BANDS 3 4 5 6 7 8

CENTER OF M A S S ENERGY IN MeV F i g . 22

- Energy and a n g u l a r momenta of g r o s s s t r u c -

t u r e r e s o n a n c e s , compared w i t h v a l u e s from experi- F i g . 25 - Comparison of t h e g a m a r a d i a t i o n y i e l d ments of Cosman e t a l . [l71

.

f o r t h e systems 160

+

160 and I2c + ''C.

I l e v e l i n 180 t h a t n u c l e u s i s e a s i l y p o l a r i z a b l e ;

s t a t e s . A number of p o s s i b l e mechanisms have been suggested by Imanishi and Nogami [I], Michaud and Energy

-

Vogt [14], G r e i n e r and Schied w i t h v a r i o u s c o l l a b o -

r a t o r s [46]:, Leander and Larsson [47], and Eaye who C 0

.-

₊ U W V) U) V) 0 L U

F i g . 23 - Schematic i l l u s t r a t i o n of t h e f r a g m e n t a t i o n r e p o r t e d on h i s work e a r l i e r t h i s week. There a r e of a shape resonance. _{d i f f e r i n g examples of t h e g e n e r a l mechanism which} gross - s t r u c t u r e t h e coupling i s thereby e f f e c t i v e l y s t r o n g . Vanden-

J

_{b o s c h ' s c a l c u l a t i o n s show a marked r e d u c t i o n i n t h e} amplitude of t h e 160 + 180 o s c i l l a t i o n s a s a func- t i o n of a n g l e a s compared with t h a t of 160 + 160. / \ / \

'

/

'.

A

'

&

I n t h e s e concluding pages, we c o n s i d e r t h e dyna- intermedlote structure mics involved i n t h e g e n e r a t i o n of t h e doorway

l i e s behind any d e s c r i p t i o n of a resonance

-

namely

4 4 I

I /

f

t h e i n c i d e n t channel c o u p l e s t o a n o t h e r degree of

/ I

.

/- freedom of t h e r e s o n a t i n g system. I f t h i s second d e g r e e of freedom h a s s p e c i a l s t a t e s which have a

r e l a t i v e l y long l i f e t i m e , t h e n a resonance w i l l

doorway 2 nd 3 rd n ' t h

s t o a e of s t o q e of s t a g e of occur whenever t h e energy of t h e system e q u a l s t h e comp\exity complexity complexity _{energy of t h e s e s p e c i a l s t a t e s . I t i s i m p o r t a n t}

t h a t t h e system l e a v e s t h e i n c i d e n t channel and t h a t F i g . 24

-

S t a g e s i n t h e decay of a doorway s t a t e .

INTERMEDIATE STRUCTURE

I l I I I I

GAMMA R A Y S AT

90°

TABLE 111

I3c on

I2c

g n R e l a t i v e R e l a t i v e

ET> 1.7 MeV Compound l c v e l number of 0 s y s t e m R e a c t i o n (MeV) d e n s i t y o p e n c h a n n e l s Halbert and N o g a t o n i l 10 I I 12 13 14 15 16 E , BEAM E N E R G Y IN MeV F i g . 26

- T o t a l gamma r a d i a t i o n y i e l d measured a t

90" f o r

I2c +

I2c,

12c

+

13c, and

+

1 % systems. F o r 1%

+

2~ o n l y t h e 1.63 MeV gamma r a y from t h e f i r s t e x c i t e d s t a t e of 2 0 ~ e h a s been measured. For t h e r e a c t i o n s i n v o l v i n g a l l gamma r a d i a t i o n w i t h energy g r e a t e r t h a n 1.7 MeV h a s been measured. Note t h a t t h e beam energy i s g i v e n i n t h e l a b o r a t o r y system.

mode of motion. Only t h e n w i l l t h e r e be t h e long i n t e r a c t i o n time n e c e s s a r y f o r t h e e x i s t e n c e of a

resonance.

One c a n c l a s s i f y t h e v a r i o u s t h e o r i e s a c c o r d i n g t o t h e manner i n which they propose t o o b t a i n t h i s long d e l a y time. One method presumes e x c i t a t i o n of t h e 12c nucleus. Imanishi t a k e s i n t o a c c o u n t t h e e x c i t a t i o n of t h e I2c n u c l e u s t o i t s f i r s t e x c i t e d 2+ s t a t e a t 4.44 MeV. Kondo, Matsuse, and Abe [2], took i n t o account t h e simultaneous e x c i t a t i o n of b o t h 12c n u c l e i . The a l p h a p a r t i c l e model of Michaud and Vogt [l41 amounts t o c o n s i d e r i n g t h e e x c i t a t i o n of t h e 12c n u c l e u s t o t h e 0+, 7.653 MeV l e v e l which l i e s above t h e 8 ~ e

+

t h r e s h o l d ' a l t h o u g h t h e y d i d n o t d e s c r i b e i t i n t h e s e terms. The model of Schied, G r e i n e r and Lemmer 1451 and F i n k , Scheid, and Greiner

[43] i s e s s e n t i a l l y i d e n t i c a l t o t h a t of Imanishi. They p r o v i d e a n important i n s - i g h t which i s a l s o

H. FESHBACH

complaints. One was t h a t t h e r e were t o o few l e v e l s . However a s Kondo, Matsube, and Abe [2] showed t h a t t h e r e a r e many more l e v e l s , which appear t o have roughly t h e c o r r e c t approximate d e n s i t y ( s e e F i g . l )

,

i f t h e Imanishi-Nogami model i s extended t o i n c l u d e t h e p o s s i b l e simultaneous e x c i t a t i o n of b o t h carbon n u c l e i . Perhaps t h e most important o b j e c t i o n i s t h a t Imanishi d i d n o t c a l c u l a t e t h e e l a s t i c s c a t t e - r i n g and show t h a t t h e r e s u l t s a g r e e w i t h e x p e r i - ment. It was claimed by some t h a t t h e v a l u e of t h e imaginary p o t e n t i a l Imanishi used was much too low. However t h i s o b j e c t i o n i s premature. The v a l u e of t h e r e a c t i o n c r o s s - s e c t i o n must i n c l u d e n o t o n l y t h e c o n t r i b u t i o n from t h e i n c i d e n t channel b u t a l s o t h a t which a r i s e s from t h e o t h e r channels. It i s hoped t h a t t h e Japanese group w i l l o r have a l r e a d y c a l c u l a t e d b o t h t h e e l a s t i c and r e a c t i o n c r o s s - s e c t i o n . U n t i l t h i s i s done and compared w i t h expe- r i m e n t t h e remarkable agreement recorded i n Table I V i s n o t meaningful. Some experimental evidence on t h e mechanism w i l l a l s o become a v 2 i l a b l e i f t h e y i e l d of t h e gamma r a y s from t h e d e - e x c i t a t i o n of t h e "C n u c l e i i s measured. This o b j e c t i v e i s now being pursued by t h e Yale group.

The a l p h a p a r t i c l e model [l41 has n o t been as

f u l l y developed theoke t i c a l l y a s t h e one d i s c u s s e d

*

above. I t h a s however been pursued e x p e r i m e n t a l l y F i g . 27

-

Ei i s t h e i n c i d e n t energy, E t h e energy

f o r e x c i t a t ~ o n of t h e i n t e r a c t i n g n u c l e i l e a d i n g t o by both the Erlangen

C4']

and the Saclay groups a q u a s i bound l e v e l i n t h e i n d i c a t e d p o t e n t i a l . _{[49]. The method employed, i s i l l u s t r a t e d by t h e}

f o l l o w i n g example. I n t h e r e a c t i o n 12c(12c , a ) 2 0 ~ e Imanishi [l] h a s c a r r i e d o u t a d e t a i l e d c a l c u l a - those s t a t e s of 2 0 ~ e which have a l a r g e a l p h a par- t i o n assuming t h a t t h e i n c i d e n t channel i s coupled

t o a channel i n which one of t h e carbon n u c l e i i s e x c i t e d t o t h e 4.44 MeV l e v e l . The coupling poten- t i a l i s obtained by

deforming

t h e o p t i c a l p o t e n t i a l . Be f i n d s the doorway s t a t e s t o be i s o l a t e d . They a r e l i s t e d i n Table I V f o r one of h i s c h o i c e s f o r t h e o p t i c a l p o t e n t i a l .

TABLE I V

Spin Energy Width Escape width (MeV) (keV) (keV) 2 Theo. 5.66 115 11.5 Exp

.

5.6 130 19.5 4 Theo. 5.90 116 8 . 2

Exp

.

6.0 100 7 . 5

0 Theo. 6.37 150 52.1

At t h e time t h i s was p r e s e n t e d t h e r e were two

t i c l e width should be p r e f e r e n t i a l l y populated a c c o r d i n g t o t h e a l p h a p a r t i c l e model. I w i l l n o t review t h i s s u b j e c t a s i t has been c a r e f u l l y d i s - cussed by Siemssen i n h i s review paper [5]. S u f f i c e i t t o s a y t h e evidence i s mixed and no hard conclu- s i o n s c a n be reached. On t h e o t h e r hand i n the 12c + 160 c a s e t h e r e i s d i r e c t n e g a t i v e evidence. 'fn t h i s r e a c t i o n on t h e b a s i s of t h e a l p h a p a r t i c l e model one would expect p r e f e r e n t i a l e x c i t a t i o n of

t h e "4p bh" 0' s t a t e i n 160. A measurement has been performed by Malmin and Paul 1501. I n f a c t i t t u r n s o u t t h a t i t i s t h e 3-, 6.13 MeV l e v e l which i s t h e more s t r o n g l y e x c i t e d . The a l p h a p a r t i c l e model

seems t o f a i l i n t h i s c a s e .

INTERMEDIATE STRUCTURE C5- 193

and t h e o r e t i c a l l y remain t o b e done. Whatever t h e r e s o l u t i o n it i s c l e a r l y a n e x t r a o r d i n a r y unique system. The carbon n u c l e i a v o i d b o t h t h e S c y l l a of being too e a s i l y p o l a r i z e d and t h e Charybdis of n o t being p o l a r i z a b l e a t a l l . Once t h e mechanism invol- ved i s completely c l a r i f i e d we w i l l n o t only f i n d new p r o p e r t i e s of s t a t e s of carbon n u c l e i bu a l s o and more important we may l e a r n how two deformed n u c l e i , i n t e r a c t when t h e y a r e i n c l o s e c o n t a c t a s i s presumably t h e c a s e f o r a shape resonance. We may l e a r n under what circumstanc,es such systems may e x i s t . A s of t h e moment the only o t h e r candidate i s

t

t h e 12c + 60 systems

.

I am v e r y much indebted t o D. A l l e n Bromley and E r i c Cosman f o r t h e i r h e l p i n t h e p r e p a r a t i o n of t h i s a d d r e s s .

' ~ n t e r m e d i a t e s t r u c t u r e has been r e p o r t e d f o r t h e r e a c t i o n 1 0 ~ ( 1 4 ~ , a ) 2 0 ~ e [51] b u t t h e s e a r e s e e n p r i n c i p a l l y a t O0 where however they may r e f l e c t d i f f r a c t i o n e f f e c t s r a t h e r t h a n resonances.

BIBLIOGRAPHY

L11 B. l m a n i s h i , Nucl. Phys.

A125

(1969) 33.

[2] Y. Kondo, T. Matsuse, and Y. ABE, Proceedings of t h e Second I n t e r n a t i o n a l Conference on c l u s t e r i n g phenomena i n n u c l e i a t t h e U. of Maryland, eds. D.A. Goldberg, J . B . Marion, and S. J . Wallace (1975)

[3] D.A. Bromley, "Nuclear molecular s t a t e s "

Proceedings of t h e Second I n t e r n a t i o n a l Confe- r e n c e on c l u s t e r i n g phenomena i n n u c l e i a t t h e U. of Maryland, eds. D.A. Goldberg, J . B . Marion and S.J. Wallace (1975).

"Physics of l a r g e tandems" Conference h e l d a t t h e I n t e r n a t i o n a l Center f o r theo. p h y s i c s , T r i e s t e , I t a l y (March, 1976).

[4] N. Cindro " I n t e r m e d i a t e s t r u c t u r e i n t h e c o n t i - nuum by heavy i o n reaction1' I n t e r n a t i o n a l w i n t e r school of n u c l e a r spectroscopy, Zakopane

(Poland) Feb. (1 976).

[5] R.H. Siemssen "Resonance phenomena and s u r f a c e transparency i n heavy i o n i n t e r a c t i o n s " I n t e r - n a t i o n a l symposium on c l u s t e r s t r u c t u r e of n u c l e i and t r a n s f e r r e a c t i o n s induced by heavy i o n s , Tokyo (Japan) Mar. (1975).

[6] R.G. S t o k s t a d , Proceedings of t h e europhysics s t u d y Conference i n i n t e r m e d i a t e processes i n n u c l e a r r e a c t i o n s , P l i t v i c e ( J u g o s l a v i a ) (1972) eds. N. Cindro, P. K u l i s i c and T. Mayer-Kuckuk, Springer-Verlag, B e r l i n (1973), Proceedings r e a c t i o n s between complex n u c l e i (1974) eds. R.L. Robinson, F.K. McGowan, J . B . B a l l and J . H . Hamilton, North Holland, Amsterdam (1974). [7] H. Spinka and H. Winkler

,

Nucl. Phys.

A233

(1974) 456.

D.A. Bromley, J.A. Kuehner, and E. Almqvist, Phys. Rev. L e t t e r s

4

(1960) 365, Phys. Rev.

G

(1961) 878.

E. Almqvist, D.A. Bromley, J.A. Kuehner, Phys. Rev. L e t t e r s

A

(1960) 515.

E. Almqvist, D.A. Bhomley, J . A . Kuehner and B. Whalen, Phys. Rev.

130

(1962) 1140.

[g] J . R . P a t t e r s o n , B.N. Nogorka, G.D. Symons, and W. Zuk, Nucl. Phys. (1971) 545.

[IO] M. Nazarakis and W.E. Stephens, Ap. J. ]71

(1972); Phys. Rev. C7 (1973) 1280.

[l l] K.A. Erb, R.R.. B e t t s , D.L. Hanson, M.W. Sachs, R.L. White, P.P. Tung and D.A. Bromley, t o be p u b l i s h e d .

[l21 Z. Basrak, F. Auger, B. Fernandez, J. Gastebois and N. Cindro, J. Phys. L e t t .

2

(1976) L 131. [l31 Z . Basrak, F. Auger, B. Fernandez, J. Gastebois

and N. Cindro, t o b e published.

[l41 G. Michaud and E.W. Vogt, Phys. L e t t e r s (1969) 85; Phys. Rev. (1972) 350.

[l51 K.V. K e t t n e r , H. Lorenz-Wirzba, C. R o l f s and H. Winkler, t o be published.

1161 Reference 10.

1171 E.R. cosman; T.M. Cormier, K. van Bibber,

A. Sperduto, G. Young, 3. E r s k i n e , L.R. Grean-

wood, and 0. Hanson, Phys. Rev. L e t t e r s 3 5 (1975) 265.

C181 K.A. Eberhard, E. M a t l i a k , J. S t e t t m i e r , W. Trombik, A. Weidinger, L.N. Wuesterfeld and

K.G. Bernhardt, Phys. L e t t e r s (1975) 445. K.G. Bernhardt,'K.A. Eberhard, and A. Weidinger Proceedings of t h e Second I n t e r n a t i o n a l Confe- r e n c e on c l u s t e r i n g phenomena i n n u c l e i a t t h e U. of Maryland, eds. D.A. Goldberg,

J . B . Marion, and S.J. Wallace (1975). [l91 N.R. F l e t c h e r , J.D. Fox, G . J . K e k e l i s ,

G.R. Morgan, and G.A. Norton, Phys. Rev. (1976) 1173.

L201 H.T. Fortune, L.R. Greenwood, R.E. S e g e l , and J . R . E r s k i n e , unpublished.

[2

11

E.F. d a s i l v e i r a r e p o r t e d i n r e f e r e n c e [l31

.

C221 R. Pliddleton, 3.D. G a r r e t t and H.T. F o r t u n e ,

Phys. Rev. L e t t e r s

4

(1970) 1435.

E.R. Cosman, A. Sperduto, T.M. Moore, T.N. Chin and T.M. Cormier, Phys. Rev. L e t t e r s 2 (1971)

C5- 194 H. FESHBACH

E.R. Cosman, A. Sperduta-, T.M. Cormier, [35] F i r s t r e f . of [32]. T.N. Chin, H.E. Wegner, M . J . LeVine, and

D. Schwalm, Phys. Rev. L e t t e r s

2

(1972) 1341. [36] A. Gobbi, R. Wieland, L. Chua, D. S h a p i r a , R. S t o k s t a d , D. S h a p i r a , P. P a r k e r , L. Chua, and D.A. Bromley, Phys. Rev. C7 (1973) 30. M.W. S a c h s , and D.A. Bromley, Phys. Rev.

L e t t e r s 2 8 (1972) 1523. [37] A. Arima, G. Scharff-Goldhaber, and R.E. Malmin, R.H. Siemssen, D.A. S i n k , K.W. McVoy, Phys. L e t t .

9

(1972) 7. P.P. S i n g h , Phys. Rev. L e t t e r s

3

(1972) 1598.

R.E. Malmin, J . W . H a r r i s , P. P a u l , B u l l . Am. C381 H. Feshbach, A.K. ~erma2:nd R.H. Lemmer, Phys. Soc.

18

(1973) 134. Ann. Phys. (N.Y.)

3

(1967) 230,.

R. Wieland, R. S t o k s t a d , A. h b b i , D. S h a p i r a ,

L. Chua, M.W. S a c h s and D.A. Bromley, Phys. L391 H. Feshbach i n P r o c e e d i n g s of t h e I n t e r n a t i o n a l Rev. (1 974) 1474. C o n f e r e n c e o n n u c l e a r p h y s i c s , Munich, Vol: 2 , D. S h a y i r a , R.G. S t o k s t a d , M.W. S a c h s , A. Gobbi, e d s J . d e Boer and H.J. Mang, N o r t h H o l l a n d , and D.A. Bromley, Phys. Rev. (1975) 1907. Amsterdam (1973).

P. S p e r r , D . E v e r s , A. Harasium, W. Assmann,

P. Konrad, K. Rudolph, G. Denhoefer and C. Ley, C401 H. S p i n k a and H. W i n k l e r , Ap. J .

174

(1972) Phys. L e t t . (1975) 438. 455.

P. S p e e r , W. Hanning and J.R. E r s k i n e t o b e

p u b l i s h e d . L411 M.L. H a l b e r t and K. N a g a t a n i , B u l l . k6. Phys. D.R. James, G.R. Morgan, N.R. F l e t c h e r , Soc.

M

(1972) 530; q u o t e d by r e f . [3]. M.B. G r e e n f i e l d , t o b e p u b l i s h e d .

L421 R. Vandenbosch, M.P. Webband, M.S. Zism, Phys. [23] M.L. H a l b e r t , F.E. Durham, and A. v a n d e r Woude, Rev. L e t t s . 2_3 (1974) 842.

Phys. Rev.

162

(1967) 899.

C431 H. J. F i n k , W. S c h e i d , and W. G r e i n e r , Nucl. C241 P. C h a r l e s , I. Badawy, B. B e r t h i e r , M. D o s t , Phys. a 8 (1972) 259.

B. F e r n a n d e z , P r o c . I n t . Conf. on n u c l e a r

p h y s i c s , Munich, v o l . I, e d s . J. d e Boer and [44] D.L. Hanson, R.G. S t o k s t a d , K.A. E r b , H.J. Mang, N o r t h H o l l a n d , Amsterdam (1973). C. Olmer, M.W. S a c h s and D.A. Bromley, Phys.

Rev. -Q (1974) 1760. C251 P. C h a r l e s , F . Auger, I. Badawy, B. B e r t h i e r ,

M. D o s t , J. G a s t e b o i s , B. F e r n a n d e z , S.M. Lee L451 R. Vandenbosch, W.N. R e i s d o r f a n d P.H. Lau, and E. P l a g n o l . Nucl. Phys.

A230

(1974) 59.

1261 R.E. Malmin and P. P a u l , q u o t e d i n t h e second e n t r y r e f .

[?I

and i n [5].

[27] D. B r a n f o r d , J . O . Newton, J . M . Robinson, and B.N. Nagorcka, J . Phys.

4

(1974) 1193. [28] A.H. Lumpkin, G . J . K e k e l i s , K.W. Kemper,

A.F. Z e l l e r , Phys. Rev. C13 (1976) 2564. L 2 4 B. Cuje-, and C.A. B a r n e s , Nucl. Phys.

(1976) 461.

[3C$ P. S p e r r , S. Vigdor, Y. E i s e n , W. Henning, D.G. Kovar, T.R. O p h e l d a n d > B . Zeidman, Phys. Rev. L e t t .

36

(1976) 405.

B. Zeidman, e t a l . quoted by r e f . [6] i t e m 2. [3fl P. Debevec, H.J. K o r n e r , and J . P . S c h i f f e r ,

Phys. Rev. L e t t e r s

13

(1973) 171.

[32] W. R e i l l y , R. Wieland, A. Gobbi, M.W. S a c h s , J.V. Maher, R.H. Siemssen, D. Mingay and D.A. Bromley, Nuovo Cimento (1973) 897. R.E. Malmin, R.H. Siemssen, D.A. S i n k , and P.P. Singh, Phys. L e t t .

28

(1972) 1590. J.V. Maher, M.W. S a c h s , R.H. Siemssen,

A. Weidinger, and D.A. Bromley, Phys. Rev.

188

(1969) 1665.

R.H. Siemssen, H.T. F o r t u n e , A. R i c h t e r , and J . W . T i p p i e , Phys. Rev.= (1972) 1839. R.W. Shaw, J r . R. Vandenbosch, and M.K. Mehta, Phys. Rev. L e t t .

3

(1970) 457.

1331 H. Spinka and H. W i n k l e r , Ap. J.

174

(1 972) 455

[46] R e f . [43] W. G r e i n e r and W. S c h e i d , J . P h y s . X ( l 9 7 1 ) C6-91. J . Y . P a r k , W. S c h e i d , and W. G r e i n e r , Phys. Rev. (1974) 967. H.J, F i n k , W. S c h e i d , i n P r o c e e d i n g s of t h e C o n f e r e n c e o n r e a c t i o n s between complex n u c l e i e d s . by R.L. Robinson, F.K. McGowan, J . B . B a l l and J.H. Hamilton, N o r t h H o l l a n d , Amsterdam

(1974). G. Leander

(1975) 93.

a n d S.E. L a r s o n , Nucl. Phys.

8239

1481 H. V o i t , G. Hartmann, H.D. Helb, G. I s c h s n k o and F . S e l l e r , J . Phys.

255

(1972) 425. H. V o i t , G. I s c h e n k o , F. S e l l e r and H.D. Helb, Nucl. Phys. (1972) 23. H. V o i t , P. Duck, W. G a l s t e r , E. H a i n d l , G. Hartmann, H.D. H e l b , F. S i l l e r , and G . I s c h e n k o , Phys. Rev. (1974) 1331. H. V o i t , G. I s c h e n k o , a n d F. S i l l e r , Phys. Rev. L e t t e r s

30

(1973) 564. C491 R. B a l l i n i , N. C i n d r o , J . P . Fouan, C. Kalbach, M. Lepareux, and N. S a u n i e r , Nucl. Phys.

A234

[ 5 q Rr Malmin and P. P a u l , B u l l . Am. Phys. Soc.

18

(1973) 134; q u o t e d by b o t h r e f . [3] and

p].

[51] N. M a r q u a r d t , R. V o l d e r s , C. C a r d i n a l and

J. L'Ecuyer, Phys. Rev. L e t t e r s

3

(1974) 1389.