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RECENT PROGRESS IN HIGH SPIN NUCLEAR PHYSICS
Z. Szymański
To cite this version:
Z. Szymański. RECENT PROGRESS IN HIGH SPIN NUCLEAR PHYSICS. Journal de Physique
Colloques, 1980, 41 (C3), pp.C3-125-C3-128. �10.1051/jphyscol:1980316�. �jpa-00219835�
RECENT P R O G R E S S I N H I G H . S P I N N U C L E A R P H Y S I C S
Z . ~ z ~ m a A s k i ,
*
Institut des Sciences NucZdaires, 38026 Grencble, France
I. The aim of t h i s c o l l o q u e i s t o d i s c u s s some p r o p e r t i e s o f a t o m i c n u c l e i i n t h e p r e s e n c e of l a r g e a n g u l a r momentum. The i n t e r e s t i n t h i s f i e l d h a s i n c r e a s e d recen- t l y owing t o t h e p r o g r e s s i n t h e p h y s i c s o f r e a c t i o n s w i t h heavy i o n s . When t h e two i o n s c o l l i d e , a c o n s i d e r a b l e amount o f a n g u l a r momentum ( o f t e n o f t h e o r d e r o f 100fi) may b e t r a n s f e r r e d t o t h e r e a c t i o n p r o d u c t s l e a d i n g t o n u c l e a r r o t a t i o n w i t h v e r y h i g h a n g u l a r v e l o c i t y .
The i n v e s t i g a t i o n of n u c l e a r s t r u c t u r e a t l a r g e a n g u l a r momenta may r e v e a l new f e a t u - r e s o f t h e n u c l e u s r e g a r d e d a s a q u a n t a l system o f many p a r t i c l e s i n t e r a c t i n g w i t h s t r o n g f o r c e s . T h i s new d i r e c t i o n i n n u c l e a r p h y s i c s h a s been i n i t i a t e d and emphasized w i t h i n r e c e n t few y e a r s by Cohen, P l a s i l and S w i a t e c k i /1/ and by Bohr and M o t t e l s o n /2/, a l t h o u g h f i r s t a t t e m p t s were s t a r t e d a s e a r l y a s i n 1967 by Grover and G i l a t /3/.
2. L e t u s f i r s t d i s c u s s t h e b e h a v i o u r o f an a t o m i c n u c l e u s a s a whole i n t h e s t a t e of a f a s t r o t a t i o n . The problem o f r o t a t i n g p i e c e o f n u c l e a r m a t t e r i s s t r i c t l y a n a l o g o u s t o t h a t o f r o t a t i o n s of s t a r s and p l a n e t s . I n l a t t e r c a s e t h e " o r d i n a r y " m a t t e r i s s u b j e c t t o g r a v i t a t i o n a l a t t r a c t i o n i n a d d i t i o n t o c e n t r i f u g a l and C o r i o l i s f o r c e s . I n v e s t i g a - t i o n s i n t h i s d i r e c t i o n s t a r t e d w i t h t h e famous p r e d i c t i o n of I s a a k Newton f o r t h e o b l a t e d e f g r m a t i o n of E a r t h i n d u c e d by r o t a t i o n . These i n v e s t i g a t i o n s w e r e t h e n c o n t i n u e d by M a c l a u r i n , J a c o b i , L , i o u v i l l e , D i r i c h l e t , Rieman and many o t h e r s . More r e - c e n t l y , an e x c e l l e n t book by Chandrasekhar /4/ was p u b l i s h e d w i t h a b r o a d p r e s e n t a t i o n o f t h e s u b j e c t , a s w e l l , a s t h e h i s t o r i c a l
- ' On l e a v e o f absence £son I n s t i t u t e o f T h e o r e t i c a l P h y s i c s , U n i v e r s i t y o f Warsaw and I n s t i t u t e f o r N u c l e a r Research, Warsaw, Poland.
i n t r o d u c t i o n . An a n a l o g o u s problem o f ro- t a t i o n o f a p o r t i o n o f n u c l e a r m a t t e r h a s been c o n s i d e r e d by Cohen, P l a s i l and*
S w i a t e c k i /1/ who have shown t h a t v e r y s i m i l a r , b e h a v i o u r i n n u c l e i i s g e n e r a l l y e x p e c t e d i n s p i t e of t h e e s s e n t i a l d i f f e - r e n c e s i n n a t u r e o f n u c l e a r and g r a v i t a - t i o n a l f o r c e s . A d r o p o f " n u c l e a r l i q u i d "
which i s s p h e r i c a l a t t h e s t a r t i n g p o i n t , w i l l become s l i g h t l y o b l a t e when r o t a t i n g s l o w l y . I n a s t a t e o f f a s t r o t a t i o n a s e r i e s o f t r i a x i a l e q u i l i b r i u m s h a p e s i s n o t e x c l u d e d ( i n f u l l a n a l o g y w i t h J a c o b i e l l i p s o i d s f o r r o t a t i n g s t a r s ) l e a d i n g f i n a l l y t o t h e phenomenon o f f i s s i o n f o r an even f a s t e r r o t a t i o n .
I t i s i n t e r e s t i n g t o i n v e s t i g a t e t h e i n - f l u e n c e o f t h e q u a n t a l s t r u c t u r e i n n u c l e a r dynamics f o r a r o t a t i n g n u c l e u s . These a s p e c t s seem t o have no a n a l o g y w i t h t h e r o t a t i o n o f p l a n e t s o r s t a r s . The f i n i t e number of d e g r e e s o f freedom i n t h e n u c l e u s m a n i f e s t s i t s e l f by t h e e x i s t e n c e o f a s h e l l s t r u c t u r e t h a t may modify si- g n i f i c a n t l y t h e b e h a v i o u r o f a r o t a t i n g n u c l e u s . S u r p r i s i n g l y new f e a t u r e s c a n emerge a s a d i r e c t consequence of a quan- t a l c h a r a c t e r and f i n i t n e s s o f t h e n u c l e a r s y s t e m i n a s t a t e o f a f a s t r o t a t i o n /5,6, 7/. F i g u r e 1 ( t a k e n from Ref. /5/) i l l u s - t r a t e s some o f t h e e f f e c t s o f t h i s t y p e . 3. R e c e n t l y , a c o n s i d e r a b l e p r o g r e s s h a s been a c h i e v e d i n t h e i n v e s t i g a t i o n o f n u c l e a r r o t a t i o n a l s p e c t r a i n t h e r a n g e o f a n g u l a r momentum t h a t d o e s n o t exceed ge- n e r a l l y 2 0 , o r 30 u n i t s o f E . ( s e e t h e r e v i e w /8/ f o r t h e p r e s e n t a t i o n o f a pro- blem and r e f e r e n c e s ) . F o l l o w i n g t h e sug- g e s t i o n s o f Bohr, filottelson and Eamamoto
/9,10/11/, Bengtsoon and Frauendorf /12,
13,14/ have developed a method f o r t r e a t m e n t
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980316
C3-126 JOURNAL DE PHYSIQUE
of t h e high s p i n r o t a t i o n i n a s u p e r f l u i d n u c l e a r system by means of t h e independent q u a s i p a r t i c l e e x c i t a t i o n s i n a r o t a t i n g n u c l e a r p o t e n t i a l .
Fia.1.-(taken from Ref. /5/). Trajectories in the
i s i l l u s t r a t e d i n f i g u r e 2 taken from r e f e r e n c e /15/. The a p p a r e n t slowing down i n n u c l e a r c o l l e c t i v e r o t a t i o n o c c u r r i n g i n 1 6 6 ~ b and 170yb f o r example, i s caused by t h e r a p i d a l i g m e n t of soae nucleonic o r b i t s w i t h t h e a x i s of r o t a t i o n . This e f f e c t of alignment t h a t has been p r e d i c t e d and analysed by Stephens /16/ seems t o occur i n many n u c l e i both on c a s e of s t r o n g defor- mations and i n n u c l e i t h a t a r e almost
s p h e r i c a l .
(E,Y) plane of the minimum equilibrium shape.
Radial coordinate E denotes an ellipsoidal defor- mation parameter which is defined as a deviation of the ellipsoidal shape from the sphere /5/.
Angular coordinate y determines /5/ the deviation from the axially symmetric shape with the two limiting values (Y=OO and Y=6Oo) corresponding to the two axially symmetric shapes (prolate and oblate ellipsoids, respectively). Angular momentum values I are indicated along the curves. Part (a) corresponds to the classical picture of a rotating liquid drop of nuclear matter for lS8yb. One can see that the drop is spherical at I=O, then becomes oblate for low angular momenta, At I=70 the oblate shape becomes unstable and further increase in I corresponds to a series of triaxial shapes leading finally to very large elongations ("superdeformed"
region).
,
Part (b) shows the predictions for the influence of the quanta1 'shell structure on nuclear shape at high angular momenta for 160yb. One can see that the 160Yb quanta1 system originates with a prolate shape at I=O. When I increases the nucleus becomes first triax9a1, then oblate and finally leads to the super- deformed region. This behaviour is in line with the predictions for the average behaviour characteristic for the classical picture illustrated in part (a).
The i n s t a b i l i t y of t h e s u p e r f l u i d n u c l e a r ground s t a t e ("vacuum s t a t e " ) w i t h r e s p e c t t o t h e two q u a s i p a r t i c l e e x c i t a t i o n s may cause a s u b s t a n t i a l rearrangement i n t h e nu- c l e a r i n t r i n s i c c o n f i g u r a t i o n a t some a n g u l a r momenta, l e a d i n g t o t h e s i n g u l a r behaviour i n t h e n u c l e a r c h a r a c t e r i s t i c s . T h i s e f f e c t which i s o f t e n r e f e r r e d t o a s "backbending"
Fig.2.- (taken from Ref. /15/)
.
Upper part illustra- tes the change in the gap parameter A which may be considered as a certain measure of the degree in nuclear superfluidity as function of the square of angular velocity w2 in the three isotopes of Yb, Lower part of the figure illustrates the change in nuclear moment of inertia as function of w2 for the three nucleides. The values of angular momen- tum I are indicated in all curves. Solid lines give the-experimental results, while dashed lines show the results of calculation. One can see that the two nucleides'
Yb and'
Yb exhibit rapid changes in angular velocity w. The increase in moment of inertia turns out to be so rapid that it induces the local decrease in w. The effect that is oftenreferred to as "backbending" is a result of a fast alignmentin nucleonic orbits that are especially sensitive to a Coriolis interaction. It may be described by a crossing of the two rotatio- nal bands. The effect is analogous to the pheno- menon of a gapless superconductivity known in the solid state physics, In the nucleus'
Yb, on the other hand, the interaction between the two bands is strong enouah to produce a mixing between the bands. As a result of the mixing the backbending phenomenon disappears.4. An i n t e r e s t i n g s i t u a t i o n o c c u r s when s e v e r a l n u c l e o n i c o r b i t s a l i g n t h e i r angu- l a r momenta w i t h t h e n u c l e a r symmetry a x i s . One may t h e n speak of a " r o t a t i o n " of a nucleus about i t s symmetry a x i s although t h e e f f e c t i s r a t h e r of a n o n c o l l e c t i v e c h a r a c t e r . A s a r e s u l t of an i n d i v i d u a l - p a r t i c l e c h a r a c t e r of t h e n u c l e o n i c motion
and relative stability of isomers of this type is intimately related to the large an- gular momentum. An example of such effect is illustrated in figure 3 where the relevant configurations of the isomers are shown (see Refs. /17-22/). High spin nuclear isomers have been recently detected in many experi- ments /23/.
Fig.3.-(reproduced from data of Refs. /17/ and /18/ ; see also Ref. /20/). Single particle eigen- values ev for the valence protons in the nucleus
Rn as functions of the projection of angular momentum m\, on nuclear symmetry axis. Five active shells (h9/2, f7/2, i13/2, f5/2, and p3/2) are shown, The slightly oblate deformation
(E=0.02, y=60Q) causes a bending of the curves down which corresponds to favouring the orbits with large
I
mv1 .
The two configurations shown in the upper and lower parts of the figure correspond to two known isomers with I" = 12+ and 17-, respecti- vely. Both the configurations are chakacterized by a "convenient" distribution of protons over the orbits ("optimal states"). As a result, the Ferni surface dividing the occupied orbits from the unoccupied ones can be drawn in both cases as til- ted straight lines. The intermediate states with I=13-16 do not have this property ("nonoptimal states") and consequently are characterized by a less convenient distribution of protons. This leadsat IT = 17-.
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