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STRUCTURE OF THE GIANT ANGLE DIPOLE
R. Hilton, S. Iwasaki, H. Mang, P. Ring, M. Faber
To cite this version:
R. Hilton, S. Iwasaki, H. Mang, P. Ring, M. Faber. STRUCTURE OF THE GIANT ANGLE DIPOLE.
Journal de Physique Colloques, 1987, 48 (C2), pp.C2-59-C2-63. �10.1051/jphyscol:1987209�. �jpa-
00226474�
STRUCTURE OF THE GIANT ANGLE DIPOLE
R.R. HILTON, S. IWASAKI, H.J. MANG, P. RING and M. FABER',
Physics Department, Technical University Munich, D-8046 Garching.
F.R.G.
* ~ n s t i t u t e of Nuclear Physics, Technical University, A-1020 Wien.
Austria
ABSTRACT
An e x t e n s i v e i n v e s t i g a t i o n o f t h e angular analogue t o t h e Giant Dipole, t h e "Giant Angle D i p o l e " , undertaken w i t h i n t h e framework o f a s e l f - c o n s i s t e n t QRPA formalism employing Gkyrme f o r c e s , has r e v e a l e d a number o f f a c e t s about t h i s s t a t e . I n t h e case o f '="Gd, t h e QRPA s o l u t i o n s obtained showed f r a g m e n t a t i o n o f t h e B (MI) s t r e n g t h occurs w i t h o u t t h e need t o p o s t u l a t e t r i a x i a l l i t y o r o c t u p o l e deformations.
Overlaps unambiguously r e v e a l t h e dominant component o f t h e fragmented s t a t e found a t 3.41 Mev, h a v i n g BM(1)=1.49tSIa w i t h l i t t l e s p i n f l i p c o n t r i b u t i o n , t o be a c o n t r a angular r o t a t i o n a l o s c i l l a t i o n o f t h e p r o t o n and n e u t r o n d e n s i t i e s , together w i t h i s o v e c t o r p l u s i s o s c a l e r admixture o f two orthogonal shears, i n agreement w i t h t h e o s c i l l a t o r model. The i m p l i c a t i o n s o f t h i s s t a t e as a t o o l i n n u c l e a r s t r u c t u r e p h y s i c s a r e discussed.
INTRODUCTION
The i d e n t i f i c a t i o n o f t h e l o n g c o n j e c t u r e d "Giant Angle D i p o l e "
1 - 7 , i n r e c e n t e,e' s c a t t e r i n g experiments on lJ'Gd / 8 / , and i t s c o n f i r m a t i o n i n independent photo e x c i t a t i o n and f o r w a r d a n g l e p,pe measurements 1 0 - 1 2 have opened t h e way f o r a new t o o l i n n u c l e a r s t r u c t u r e physics, w i t h t h e promise o f g a i n i n g h i t h e r t o i n a c c e s s i b l e i n f o r m a t i o n . I n t h e l a s t t h r e e years w e l l over 100 t h e o r e t i c a l and experimental s t u d i e s o f t h i s s t a t e have been undertaken, d u r i n g t h e course o f w h i t h many names have been g i v e n t o t h i s mode v i z : p o s i t i v e p a r i t y quadrupole resonance; K=l' resonance; mixed symmetry mode;
s c i s s o r mode; g i a n t magnetic d i p o l e ; g i a n t M I mode and n u c l e a r wobble.
However h e r e we s h a l l r e f e r t o i t by i t s o r i g i n a l name, t h e "Giant Angle D i p o l e " , + o r f u r t h e r r e f e r e n c e s c.6. / 4 , 5 / . The p i c t u r e o f c o l l e c t i v e motion i n which p r o t o n and n e u t ~ o n d e n s i t i e s v i b r a t e a g a i n s t one another i n angular f a s h i o n about an a x i s p e r p e n d i c u l a r t o t h e symmetry a x i s o f t h e nucleus has, almost w i t h o u t exception, been t h e common b a s i s o f these many i n v e s t i g a t i o n s . However, such a p i c t u r e , b u i l t i n s t r i c t analogy w i t h t h e G i a n t Dipole, i s quantum mechanically i n c o n s i s t e n t w i t h t h e d e s c r i p t i o n o f a coherent low energy c o l l e c t i v e s t a t e /2-5/.
THE OSCILLATOR MODEL
For a l a r g e p a r t i c l e number fermion system c o n t a i n e d i n a deformed o s c i l l a t o r , c o l l e c t i v e c o o r d i n a t e s 5 and momenta
JT
corresponding t o t h e Giant Angle D i p o l e can be found. I n terms o f t h e s e v a r i a b l e s , t h e s h e l l model Hamiltonian may be shown t o d i s p l a y t h e form /2,3/Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987209
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i n which t h e v a r i a b l e s Cql,pr> d e s c r i b e remaining degrees o f freedom o f t h e system commuting w i t h 5 and
.
The ground s t a t e i s then Q o ( q ) X o ( J ) and wavefunctions o f t h e form o f cPo(q)&(S) may be i n t e r p r e t e d as G i a n t Angle D i p o l e c o l l e c t i v e e x c i t a t i o n s , i n much t h e same s p i r i t as f o r t h e G i a n t D i p o l e /14/.From t h e model we l e a r n t h a t t h i s e x c i t a t i o n i s a p o s i t i v e p a r i t y quadrupole e x c i t a t i o n c a r r y i n g i s o s p i n T = l ( w i t h s m a l l i s o s p i n T=O a d m i x t u r e ) , comprising a l i n e a r combination o f angular momentum z - p r o j e c t i o n M= 2 1. (For a s e l f -conjugate nucleus i t r e v e r t s t o p u r e T=1). The e x c i t a t i o n energy o f t h e G i a n t Angle D i p o l e t u r n s o u t t o be low, around 3-4 Mev f o r t h e w e l l deformed r a r e earths. T r a n s i t i o n s t r e n g t h s may a l s o be assessed, and i n t h e case of "&Gd we g a i n a B(M1) v a l u e around 7.5h2, w i t h no s p i n f l i p c o n t r i b u t i o n s s i n c e we have a s p i n s a t u r a t e d system. The e f f e c t s o f c o r r e l a t i o n s modify these values somewhat /3/. I n t h e case o f '"*Gd an energy a t 3 Mev and a B(M1) v a l u e o f around 4. 9 k 2 a r e expected. The u n d e r l y i n g p h y s i c a l n a t u r e o f t h i s s t a t e , d i s c l o s e d by examining t h e Giant Angle D i p o l e generators, show i t t o be a AN=O e x c i t a t i o n , comprising a sum o f motionsx a p u r e c o n t r a a n g u l a r r o t a t i o n a l o s q i l l a t i o n t o g e t h e r w i t h an i s o v e c t o r p l u s i e o s c a l e r admixture o f two orthogonal shears. The p i c t u r e o f p u r e c o n t r a r o t a t i o n a t t h e h e a r t o f many models, i t becomes apparent, i s i n c o m p a t i b l e w i t h t h e d e s c r i p t i o n of a low energy coherent s t a t e , a s t h e g e n e r a t o r s o f such motion l e a d t o c o l l e c t i v e e x c i t a t i o n s b u i l t o u t o f l i n e a r combinations o f s i n g l e p a r t i c l e s t a t e s coming from d i f f e r e n t o s c i l l a t o r s h e l l s , i.e. AN=O and AN=2. The o s c i l l a t o r model r e v e a l s how t o marry t h e p i c t u r e o f t h i s low energy c o l l e c t i v e e x c i t a t i o n w i t h an u n d e r l y i n g s i n g l e p a r t i c l e s t r u c t u r e c o n s i s t e n t w i t h quantum mechanics.
MICROSCOPIC DESCRIPTION
A h i g h r e s o l u t i o n search o f t h e ( e , e ' ) s c a t t e r i n g spectrum o f IabGd c a r r i e d o u t a t t h e Darmstadt L I N K r e v e a l e d a sharp 1' resonance a t 3.07 Mev, c a r r y i n g a B(M1) s t r e n g t h o f 1.31h2 /8,9/. The marked discrepancy between t h e observed B(M1) s t r e n g t h and our c o l l e c t i v e model v a l u e s t r o n g l y i m p l i e d a fragmented s t r u c t u r e t o t h e 1'. and a microscopic f o r m a l i s m was r e q u i r e d i n which t h e i n t e r p l a y between t h e s i n g l e p a r t i c l e and c o l l e c t i v e aspects o f t h e system c o u l d be t r e a t e d . To t h i s end, an e x t e n s i v e i n v e s t i g a t i o n w i t h i n t h e framework o f a s e l f - c o n s i s t e n t QRPA formalism employing Skyrme f o r c e s was undertaken.
A f u l l y s e l f - c o n s i s t e n t H. F. c a l c u l a t i o n g e n e r a t i n g t h e s i n g l e p a r t i c l e e n e r g i e s and s t a t e s served as t h e i n p u t f o r t h e QRPA formalism. F u r t h e r d e t a i l s o f n o t a t i o n and formalism a r e g i v e n i n /4,S, 15/.
For a r b i t r a r y v a r i a t i o n s 6 9 , we g a i n from t h e Schrodinger equation,
<01C6Q,CH,Q'.33:0> = (E, -Ec)<O: t(SQ,Q'.I :O>
( 2 ) R e s t r i c t i n g o u r s e l v e s t o c o l l e c t i v e o p e r a t o r s Q o f t h e form
we g a i n t h e QRPA equations
The eigenvaluee w.~. and e i g e n v e c t o r s corresponding t o (4) were t h e n c a l c u l a t e d u s i n g (3). Shown i n f i g . 1 a r e t h e B(M1) s t r e n g t h s found f o r each s t a t e up t o 5 Mev, c a l c u l a t e d from t h e expression
Fig. 1 B (Ill) strength
Here IHFB> i s t h e HFB ground state. In fig.1 the spin flip contributions are shown as dotted lines. T h e height of typical two quasi-particle grass i s indicated by the horizontal dashed line. We observe fragmentation of t h e B ( M 1 ) strength has occurred without the need t o introduce either triaxial or octupole deformations. The dominant component in t h e spectrum i s seen at 3.41 Mev, having a B ( M 1 ) strength of 1 . 4 9 k 2 with little spin flip admixture. The physical nature of t h i s state was obtained from calculating t h e overlap,
a s a function of t h e shear admixture parameter I.A s seen in fig.2 t h e overlap with a state describing pure contra rotation (?PO) i s already over 53%. However, the maximum overlap occurs at r non vanishing 1 value (l\nax=O. 2 5 )
,
unambiguous1 y demonstrating that t h e isovector component of this state comprises a pure contra rotation plus a shear, as had already been anticipated from the oscillator model. In fact t h e microscopic description indicates more shear admixture than t h e oscillator value ( T O ) .PURE CONTRA CONTRA ROTATION ROTATION SHEAR ADMIXTURE
Fig. 2 Overlap shown a s a function of q
ISOSPIN ADMIXTURE
Fig.3 Overlap shown a s a function of E The investigation was extended and the overlap,
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c a l c u l a t e d as a f u n c t i o n o f t h e i s o s c a l e r m i x i n g parameter E ( w i t h 9 f i x e d a t r\,,,). As seen from f ig.3, t h e o v e r l a p reaches i t s maximum value f o r ( C a r = -0.075), showing an i s o s c a l e r admixture which i s a l s o l a r g e r t h a n t h a t g i v e n by t h e o s c i l l a t o r (Eo= -0.033) a t t h e same deformation.
Fig.4 i l l u s t r a t e s t h e geometric p i c t u r e
T
of t h e motion which emerges f o r t h e
dominant component. The i soscal e r
.--.
admixture r e f l e c t s t h e f a c t t h a t t h e p r o t o n s and neutrons do n o t deform by t h e same amount d u r i n g t h e i r motion. The e x c i t e d s t a t e t h u s encapsulates t h e p r o p e r t i e s a n t i c i p a t e d a f t h e Giant Angle D i p o l e and we i d e n t i f y i t w i t h t h i s mode.
Fig. 4 P i c t o r i a l impression o f G i a n t Angle D i p o l e motion However, t h e correspondence t o t h e c o l l e c t i v e model p i c t u r e should r e a l l y be sought i n t h e subset o f fragmented s t a t e s h a v i n g s i m i l a r u n d e r l y i n g s t r u c t u r e . O f t h e s t a t e s c a r r y i n g any s i z a b l e B(M1) s t r e n g t h , o n l y those a t e n e r g i e s 2.67, 3.04, 3.65 and 4.89 Mev seem t o have p h y s i c a l s t r u c t u r e r e l a t e d t o t h e dominant component s i t u a t e d a t 3.41 Mev. Common t o a l l o f these s t a t e s i s t h e i r s m a l l s p i n f l i p t o o r b i t a l M I s t r e n g t h , and t h e f a c t t h a t t h e i r o v e r l a p s n o t i c e a b l y increase i f shear admixture i s allowed. The d i f f e r e n c e s appear i n t h e amount o f i s o v e c t o r and i s o s c a l e r admixture p r e s e n t i n each s t a t e . Although none o f these s t a t e s have o v e r l a p s (7) a s l a r g e a s t h a t f o r t h e dominant component, t y p i c a l l y t h e y l i e i n t h e range (3KL-48%). The s t r e n g t h s shown i n f i g . 1 should however be thought o f as a guide o n l y , s i n c e b a s i s t r u n c a t i o n e f f e c t s may s t i l l produce some changes /4,5/.
ACCESSIBLE INFORMATION
The experimental c o n f i r m a t i o n o f t h i s s t a t e a l l o w s u s access t o a wealth o f i n f o r m a t i o n about t h e nucleus. Knowledge o f new i n e r t i a l parameters and r e s t o r i n g f o r c e s r e l a t e d t o b o t h r o t a t i o n and deformation a r e r e q u i r e d f o r t h e d e s c r i p t i o n o f t h e G i a n t Angle D i p o l e and as a l r e a d y demonstrated / 3 / , t h e l a t t e r may d i f f e r c o n s i d e r a b l y from t h a t o b t a i n e d from a p u r e c o n t r a r o t a t i o n p i c t u r e . The c h a r a c t e r of t h e mode, as a sum o f c o n t r a r o t a t i o n and shear, accords n o t o n l y w i t h t h a t expected from an incompressible f l u i d /16/. The shear i s o s p i n admixture may a l s o be echoed i n t h e o b s e r v a t i o n s t h a t neutron and p r o t o n t r a n s f e r t i m e s a r e d i f f e r e n t /17/, i n d i c a t i n g response d i f f e r e n c e s between n e u t r o n s and p r o t o n s t o deformation changes, and hence c o l l e c t i v e f l o w p r o p e r t i e s . The form o f t t i e f r a g m e n t a t i o n spectrum a l s o promises t o shed l i g h t on t h e way t h e n u c l e u s responds t o shear. A p i c t u r e o f breakup, a t l e a s t a t lo^ energy, may be p o s s i b l e t o read o f f . Recent measurements 1 3 i m p l y v e r y small s p i n - f l i p c o n t r i b u t i o n s t o t h i s s t a t e . Since t h e s p i n - o r b i t f o r c e p l a y s a c r u c i a l r o l e here, i n these measurements we may have an instrument g i v i n g u s a p r e c i s e handle on i t s s t r e n g t h . I n f a c t more g e n e r a l l y t h e G i a n t h n g l e D i p o l e a l r e a d y appears t o act as a s o r t of t e s t bench w i t h which one w i l l be a b l e t o "weed o u t " some t y p e s of e f f e c t i v e i n t e r a c t i o n s .
A r i c h source f o r f u t u r e n u c l e a r s t r u c t u r e p h y s i c s i s c l e a r l y i n prospect.
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