1CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Giant resonances and inertia parameters Within the QRPA with the Gogny force in axial symmetry. Giant resonances and inertia parameters Within 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

2CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july HF+RPA calculations in spherical symmetry for exotic nuclei : 78 Ni 100 Sn 132 Sn 208 Pb is taken as a reference Previous work,

3CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july ISGMR Central +densité Central +densité +SO Central +densité +Coulomb Central +densité +Coulomb +SO 78Ni Sn Sn Pb

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

5

6 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 HFB+QRPA in axial Symmetry Spherical nuclei: in O isotopes GMR in 90 Zr Deformed nuclei : 24 Mg 22 Mg 28 Si Inertia parameters : Quadrupole mass

8CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Formalism 1°HF+RPA 2°HFB+QRPA 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.

9CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Axial QRPA Spherical RPA 16 O

10CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 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 M 1 / M 0 = MeV M 1 / M 0 = ± 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 Restoration of rotational symmetry for deformed states We want to calculate : for all QRPA states (K J) For example : J π = 2 + In intrinsic frame Using rotational approximation and relation for 3j symbol

13CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Mg β=.51 J π =2 +

14CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july [9-41MeV] HFB+QRPA %EWSR=76.6 ; M 1 / M 0 = MeV Exp. %EWSR= 72 ± 10; M 1 / M 0 =16.9 ± 0.6 MeV Exp. : D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999) Quadrupole

15CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999) Mg ISGMR %EWSR=72 ± 10 M 1 / M 0 =21.0 ± 0.6 MeV %EWSR = 94 M 1 / M 0 = MeV [9-41 Mev]

16CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july [13-30meV] : 82%EWSR, M 1 / M 0 = MeV Quadrupole

17CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Monopole [13-40 MeV] : 92%EWSR, M 1 / M 0 =20.86 MeV

18CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Si Monopole D.H. Younboold, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65,(2002) [10-35 MeV] 92% EWSR, M 1 / M 0 = MeV 81 ± 10 % EWSR, M 1 / M 0 = ± 0.38 MeV

19CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Si Quadrupole D.H. Younboold, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65, (2002) [13-35 MeV] 70% EWSR, M 1 / M 0 = MeV [7-35 MeV] 71.5% EWSR, M 1 / M 0 = MeV M1 /M0 =18.54 ± 0.25 MeV 68 ± 9 % EWSR

20CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Consistent calculations CHFB and QRPA (a)=(c). Inertia parameters (c) Constraint HFB (a) QRPA (b) Inglis-Belayev ATDHF "Mass":

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

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

23CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july Summary Coulomb and spin-orbit terms have to be taken into account, Effect of the pairing treatment in 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 Gogny force P is isospin exchange operator P is spin exchange operator

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