The intrinsic discontinuity and the possible microscopic foundation of the high-spin anomaly in rotational nuclear states

Abstract

I t is well k n o w n t h a t t he va r i ab l e -momen t -o f ine r t i a mode l (z) p red ic t s s mo o t h curves for t he ro t a t i ona l spec t ra in t he (~ -o2) -p lane and has p r o v e d r emarkab ly successful be fo re b a c k b e n d i n g occurs. The theore t i ca l f o u n d a t i o n of th is mode l has been shown to follow f rom ve ry general va r i a t iona l pr inc ip les w i t h reasonable a s sumpt ions (2.3). T h a t is, t h e in t r ins ic wave func t ion depends on some a p p r o p r i a t e set of p a r a m e t e r s {•i} such as t he de fo rma t ion fl, t he pa i r ing gap A, ... wh ich va ry cont inuous ly w i t h angular m o m e n t u m such t h a t a p e r t u r b a t i o n a l power series expans ion is possible. I f we are given a microscopic in t r ins ic wave func t ion , the set {X~} can be ca lcula ted as the exp e c t a t i o n values of some co r respond ing opera tors , t h a t is Zi = ( T I ~ I T ) . T h a t is to say, in order t h a t VMI is val id , t he in t r ins ic wave fu n c t i o n has to va ry con t inuous ly wi th angula r m o m e n t u m . Therefore , t he microscopic cond i t ion for VMI to break down or for b a c k b e n d i n g to occur is t h a t t he in t r ins ic wave fu n c t i o n has a d i s con t inu i t y for some values of angular m o m e n t u m such t h a t some of t h e p a r a m e t e r s Z~ m a y be d i scont inuous . There are ca lcula t ions in t he l i t e ra tu re showing the d i scon t inu i ty of some of t h e 9/~'s a t backbend ing (4.s). Also, by using a s imple model , STEPH~.NS and SIMON have shown t h a t t he Coriolis effects a t h igh spin m a y lower t he energy of t he s y s t em by the b reak ing-up of a pa i r (9). The purpose of th is no te is to suggest t h a t t he exis t ence of a microscopic d i scon t inu i ty in t he in t r ins ic s t a t e of a r o t a t i n g sys tem which follows na tu ra l l y f rom t h e c rank ing mode l m a y serve as a poss ib i l i ty for t he microscopic f o u n d a t i o n of t he h igh-sp in anomaly in ro t a t i ona l nuclei. In a r ecen t p a p e r (10) i t was sugges ted t h a t t he quas i -par t ic le v acu u m of t he int r ins ic s t a t e of a r o t a t i ng sys t em m a y become uns tab le w h e n the angular f r equency ~o