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1CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 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 sophie.peru-desenfants@cea.fr

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2CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 HF+RPA calculations in spherical symmetry for exotic nuclei : 78 Ni 100 Sn 132 Sn 208 Pb is taken as a reference Previous work,

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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 78Ni18.5517.1018.5917.17 100Sn18.1916.8118.5417.22 132Sn16.0715.0616.2615.29 208Pb13.7313.0514.1013.46

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

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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.

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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 90 Zr Deformed nuclei : 24 Mg 22 Mg 28 Si Inertia parameters : Quadrupole mass

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

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9CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 Axial QRPA Spherical RPA 16 O

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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.

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11CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 10152025 M 1 / M 0 = 17.65 MeV M 1 / M 0 = 17.89 ± 0.20 MeV D.H.Younblood,H.L.Clark, and Y.-W.Lui, Phys. Rev. Lett.82,4 (1999)

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

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13CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 24 Mg β=.51 J π =2 +

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14CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 [9-41MeV] HFB+QRPA %EWSR=76.6 ; M 1 / M 0 = 17.64 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)014304 Quadrupole

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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 ± 10 M 1 / M 0 =21.0 ± 0.6 MeV %EWSR = 94 M 1 / M 0 = 20.47 MeV [9-41 Mev]

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16CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 [13-30meV] : 82%EWSR, M 1 / M 0 = 18.72 MeV Quadrupole

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17CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 Monopole [13-40 MeV] : 92%EWSR, M 1 / M 0 =20.86 MeV

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18CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 28 Si Monopole D.H. Younboold, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65,(2002) 034302 [10-35 MeV] 92% EWSR, M 1 / M 0 = 21.11 MeV 81 ± 10 % EWSR, M 1 / M 0 = 21.25 ± 0.38 MeV

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19CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 28 Si Quadrupole D.H. Younboold, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65, (2002) 034302 [13-35 MeV] 70% EWSR, M 1 / M 0 = 21.27 MeV [7-35 MeV] 71.5% EWSR, M 1 / M 0 = 20.49 MeV M1 /M0 =18.54 ± 0.25 MeV 68 ± 9 % EWSR

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20CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 Consistent calculations CHFB and QRPA (a)=(c). Inertia parameters (c) Constraint HFB (a) QRPA (b) Inglis-Belayev ATDHF "Mass":

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

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

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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.

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24CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005 Gogny force P is isospin exchange operator P is spin exchange operator

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

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