CONTINUUM FLUID DYNAMICS AND RPA FOR GIANT RESONANCES

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CONTINUUM FLUID DYNAMICS AND RPA FOR GIANT RESONANCES

G. Eckart, K. Andō

To cite this version:

G. Eckart, K. Andō. CONTINUUM FLUID DYNAMICS AND RPA FOR GIANT RESONANCES.

Journal de Physique Colloques, 1984, 45 (C6), pp.C6-285-C6-288. �10.1051/jphyscol:1984634�. �jpa- 00224236�

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G. Eckart and K. And5

Siegen University, Faehbereich 7-Physik, 59 Siegen 21, F. R. G.

RQsum6 - On inclut le continu 2 une dynamique de fluide nucl6aire irrota- tionnel. Des forces d e transition des rssonances geantes isovectorielles sont calcul6es dans ce modsle et compar6es aux r6sultats de la R.P.A.

Abstract - Irrotational nuclear fluid dynamics is extended to include the continuum. Isovector giant resonance strengths are calculated in this model and are compared with RPA results.

Under the restriction of irrotational flow the macroscopic fluid- dynamical (FD) theory of giant resonances based on the generalized scaling approach can be used to calculate excitations in the continuum'). It is essential to employ a selfconsistent description of the ground-state ensuring the correct asymptotic properties of the single particle wave functions for large radii r. The irrotational (IFD) fluid-dynamical equation of motion then shows an excitation spectrum with the correct onset of the continuum at the particle emission thre- shold ktd=IEJ(Ferrni energy), just as in the selfconsistent RPA. For the comparison of RPA and IFD results the same simple density-dependent force has been used, corresponding to the energy functional

containing six parameters to , t3 , xo , x3 - , d , a+ (a-=o). This is

simple enough for performing RPA calculations within reasonable com- puter time; although the Coulomb, spin-orbit and effective mass con- tributions to E [ r I 9 J have been neglected reasonable groundstate distributions can be obtained.

The HF-IFD formalism represents a certain "average1! description of the RPA. This is most clearly seen if the IFD equation of motion -

is formulated in terms of the Hartree-Fock single particle wave func-

+)A detailed andextensive presentation of the subject including more references will appear in Nucl. Phys. &( 1984) (ref. I)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984634

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C6-286 JOURNAL DE PHYSIQUE

tions y ; and energies &; ( H , yj = E j \Oj )

.

ⁱ^l^l^e^find

dU being the residual interaction, h D the generalized scaling 6 9

operator and &fpD the fluid-dynamical transition density. The RPA equations may be formulated in terms of the first order change dy.of the

2 ) ^b

real part of the TDHF single-particle wave functions

By comparing (2) with (5) and (4) with (6) it is seen that in IFD

6% is replaced by h Dy; , and the summation & y;)C (.. - ) yields one sixth order differential equation for the displacement potential out of the complicated set of coupled equations (5). A careful analy- sis of the asymptotic IFD equation of motion (2) shows that this model takes properly into account centrifugal barriers for the "escapingn particle, as well as energy conservation which allows only occupied states j with E; t 6 > o ~ to participate in the escaping mechanism.

Furthermore the energy- and cubic energy-weighted sum rules m, and m3 are identical in the RPA and HF-IFD models.

Streng4h functions, velocity fields and transition densities obtained from RPA and IFD are systematically compared. It is demonstra- ted that the simple irrotational fluid-dynamical model yields satis- factory results in cases where the single-particle structure plays no important role and the fragmentation of the strength is not signifi- cant. As an example we show in figs. 1 and 2 the isovector monopole and quadrupole strength distributions (excitation operators ~ r : Y , , ~ 3 t i )

and $ ^T: Y 2 , ( ~ t ) r , ( ; ) , respectively) in two systems with mass num-

bers A=212 and A=80.

The simple IFD is certainly very limited, because, by construc- tion, this model rules out excitations with transverse flow. In this connection we have studied the significance of transverse components of the scaling field within the framework of the "rotational" fluid- dynamical model (RFD) which has been used previously for the description of bound states3). For this purpose we have calculated static polarizabilities (inverse energy-weighted sum rule m-,) resulting

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F i g . ^{2 .} I s o v e c t o r q u a d r u p o l e s t r e n g t h i n a A=80 model s y s t e m

from t h e HF-IFD, HF-RFD and RPA d e s c r i p t i o n s . I t h a s b e e n shown from t h i s s t u d y t h a t t h e HF-RFD model f i n d s t h e same " c o r r e c t n i r r o t a t i o n a l i s o s c a l a r q u a d r u p o l e s t a t e as t h e IFD i n model s y s t e m s h a v i n g n o c o l -

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C6-288 JOURNAL DE PHYSIQUE

l e c t i v e low-lying quadrupole s t a t e s . I n systems where such s t a t e s a r e p r e s e n t , t h e RFD model t r i e s t o s i m u l a t e t h e s t r o n g l y enhanced qua- d r u p o l e p o l a r i z a b i l i t y by making t h e b e s t u s e of t h e t r a n s v e r s e component. T h i s i s , however, f a r from b e i n g s u f f i c i e n t , d e m o n s t r a t i n g t h e l i m i t a t i o n of t h e g e n e r a l i z e d s c a l i n g approach. I n c o n t r a s t t o t h i s t h e t r a n s v e r s e component h a s been found t o p l a y a r e a l l y s i g n i - f i c a n t r o l e i n t h e i s o v e c t o r d i p o l e p o l a r i z a b i l i t y : It now s e r v e s t o b r i n g m-l(RPD) i n e x c e l l e n t agreement w i t h m - l ( R P ~ ) f o r a l l examined model systems w i t h mass numbers r a n g i n g from 16 t o 0 0

.

R e f e r e n c e s

1 ) ECKART G . and HOLZWARTH G . , Phys. L e t t . (1982) 9

AND0 K. and ECKART G., S i e g e n u n i v e r s i t y p r e p r i n t Si-83-21, t o a p p e a r i n Nucl. Phys. A642 (1984)

2) BERTSCH G.F., Suppl. Prog. f h e o r . Phys. 74 & 75 (1983) 115 3) ECKART G . , HOLZWARTH G . and da PROVIDENCIA J.P., Nucl. Phys.

A364 (1981) 1 ; KOCH H., ECKART G., SCHWESINGER B. and HOLZWARTH G .

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Nucl. Phys. A373 (1982) 173