Giant resonances and inertia parameters Within the QRPA with the Gogny force in axial symmetry

1CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

Giant resonances and inertia parametersWithin the QRPA with the Gogny force

in axial symmetry.

Giant resonances and inertia parametersWithin the QRPA with the Gogny force

in axial symmetry.

S.PÉRU, J.F. Berger, M. Girod,H. Goutte,N. Pillet.

CEA Bruyères-le-Châtel, France

[email protected]


HF+RPA calculations in spherical symmetry

for exotic nuclei :78Ni

100Sn132Sn

208Pb is taken as a reference

Previous work,


ISGMR

Central

+densité

Central

+densité

+SO

Central

+densité

+Coulomb

Central

+densité

+Coulomb

+SO

78Ni 18.55 17.10 18.59 17.17

100Sn 18.19 16.81 18.54 17.22

132Sn 16.07 15.06 16.26 15.29

208Pb 13.73 13.05 14.10 13.46




The Coulomb term is important for the dipole response.But it is time computer consuming.

The Spin-Orbit term can not be neglected.The calculation is relatively fast.


HFB+QRPA in axial Symmetry

Spherical nuclei:2+

1 in O isotopes

GMR in 90Zr

Deformed nuclei :24Mg 22Mg28 Si

Inertia parameters :Quadrupole “mass”


FormalismFormalism

1°HF+RPA

2°HFB+QRPA

,**

YX

Y

X

AB

BA

are quasi-particules states (qp).

In our approach The effective interaction D1S is used both in the mean field and in the QRPA matrix.As the axial symmetry is imposed, QRPA state are obtained by K blocs.

.0~

aaYaaX ph

ph

hph

p

ph

ij

ij

jij

i

ij

YX


Axial QRPA

Spherical RPA

16O


Skyrme results from E.Kahn and Nguyen Van Giai, Phys. Lett.B 472 (2000)253.


10 15 20 25

M1 / M0 = 17.65 MeV

M1 / M0 = 17.89 ± 0.20 MeV

D.H.Younblood,H.L.Clark, and Y.-W.Lui,Phys. Rev. Lett.82 ,4 (1999)


2,221,120,2020

ˆ05

1ˆ05

1ˆ05

1ˆ0~

KKKKKK QQQKJMQ

Restoration of rotational symmetry for deformed states

KJ

KM

KJ

KJMK DDd

JKJM

RR

4

12

We want to calculate : KJMQˆ0

~for all QRPA states (K ≤ J)

202

20ˆ YrQ

For example : Jπ = 2+

In intrinsic frame

YrDYr 22

Using rotational approximation and relation for 3j symbol


24Mg β=.51

Jπ=2+


[9-41MeV] HFB+QRPA %EWSR=76.6 ; M1 / M0 = 17.64 MeV

Exp. %EWSR= 72 ± 10; M1 / M0=16.9 ± 0.6 MeV

Exp. : D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999)014304

Quadrupole


D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999) 014304

24Mg ISGMR

%EWSR=72 ± 10M1 / M0=21.0 ± 0.6 MeV

%EWSR = 94M1 / M0= 20.47 MeV

[9-41 Mev]


[13-30meV] : 82%EWSR, M1 / M0 = 18.72 MeV

Quadrupole


Monopole

[13-40 MeV] : 92%EWSR, M1 / M0=20.86 MeV


28Si Monopole

D.H. Younboold, Y.-W. Lui, and H.L.Clark,Phys. Rev. C, 65,(2002) 034302

[10-35 MeV] 92% EWSR, M1 / M0 = 21.11 MeV

81 ± 10 % EWSR, M1 / M0 = 21.25 ± 0.38 MeV


28Si Quadrupole

D.H. Younboold, Y.-W. Lui, and H.L.Clark,Phys. Rev. C, 65, (2002) 034302

[13-35 MeV] 70% EWSR, M1 / M0 = 21.27 MeV [7-35 MeV] 71.5% EWSR, M1 / M0 = 20.49 MeV

M1 /M0 =18.54 ± 0.25 MeV68 ± 9 % EWSR


n

iE

QM i

n

nQ

0,0 202

20

Q

QM 21201

Consistent calculations CHFB and QRPA (a)=(c).

Inertia parameters

(c) Constraint HFB

(a) QRPA

i

HFBHFB

i

QQM

220 00

20(b) Inglis-Belayev

21

320

M

MQMATDHF "Mass":




Summary

Coulomb and spin-orbit terms have to be taken into account,

Effect of the pairing treatment in 2+1 states in QRPA?

Relatively good agreement with experimental data for giant resonnances.

Fragmented strength for monopole and quadrupole response in deformed nuclei.

Inertia parameters are very different from the Inglis-Belayev ones.


Gogny forceGogny force

21

2

21

211221.12

212103

jjjj

2

1

2

2112

2121

.

1

PPM- PH-PBW r-r

-exp

rr

ett

rriW

rrrrPxt

pv

zz

ls

s

j j

=

P is isospin exchange operatorP is spin exchange operator


Documents

Giant resonances and inertia parameters Within the QRPA with the Gogny force in axial symmetry