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

sophie.peru-desenfants@cea.fr

2CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

HF+RPA calculations in spherical symmetry

for exotic nuclei :78Ni

100Sn132Sn

208Pb is taken as a reference

Previous work,

3CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

4CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

5CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

6CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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.

7CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

HFB+QRPA in axial Symmetry

Spherical nuclei:2+

1 in O isotopes

GMR in 90Zr

Deformed nuclei :24Mg 22Mg28 Si

Inertia parameters :Quadrupole “mass”

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

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

9CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

Axial QRPA

Spherical RPA

16O

10CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

11CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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)

12CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

13CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

24Mg β=.51

Jπ=2+

14CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

[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

15CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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]

16CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

Quadrupole

17CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

Monopole

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

18CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

19CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

20CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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":

21CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

22CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

23CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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.

24CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005

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

25CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005