Excitation spectrum of « α-particle nuclear matter » and collective resonances

L a t e l y a g r e a t n u m b e r of e x p e r i m e n t s h a v e been ca r r ied ou t w i t h t he a im of s t u d y i n g t h e a -pa r t i c l e cor re la t ions . F o r l i gh t nuclei , t h e a -par t i c le mode l ha s been s h o w n to b e a successful m e t h o d for desc r ib ing t he b i n d i n g energies of e v e n e v e n nucle i a n d t he r o t a t i o n a l b a n d s exc i t ed in nuc lea r r eac t ions (1). Espec ia l ly g rea t i n t e r e s t in t h e mo lecu l a r aspec t s of t h e sys t em composed of a -par t i c les has been s t i m u l a t e d b y exper i m e n t a l i n f o r m a t i o n a f forded in h e a v y i o n reac t ions , a -nuc leus s c a t t e r i n g a n d so fo r th . Accord ing to t h i s mode l these are m a d e up of a -par t ic les w h i c h arc a r r a n g e d in space so as to g ive t h e closest poss ible pack ing . Most of t h e b i n d i n g ene rgy of each nuc l ide is due to t he b i n d i n g of i t s c o n s t i t u e n t a -par t ic les , t h e r e m a i n d e r be ing t h e ene rgy of t he b o n d s b e t w e e n t he a -par t ic les . I n t h e p r e s e n t no t e we exp lore t h e p rope r t i e s of a nuc leus as (( a -par t i c le nuc l ea r m a t t e r ,) r a t h e r t h a n t h e molecu la r aspects , in order to ge t some i n s igh t i n to t h e charact e r i s t i c b e h a v i o u r of t he nuc leus a t h i g h e x c i t a t i o n energy. I t is shown t h a t t he exci tat ion s p e c t r u m of t h e s y s t e m exh ib i t s a b e h a v i o u r s imi la r to t h a t of l i qu id h e l i u m (~-9) w h i c h swi tches g r a d u a l l y f rom p h o n o n s to s ing le -par t i c le t y p e pass ing t h r o u g h ro tons a n d also t h a t t h e cross-sec t ions in nuc lea r r eac t ions h a v e a r e sonance p e a k a r o u n d twice t he ene rgy of t h e e x t r e m u m p o i n t of t h e p h o n o n r o t o n d i spers ion curve . W e s t a r t w i t h a r ea sonab le a s s u m p t i o n t h a t t h e s y s t e m cons is t s of u-part ic les , wh ich is a va l i d one for l igh t nuc le i w i t h A = 4n. T he H a m i l t o n i a n of t h e s y s t e m of in te r -