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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_at_cea.fr
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Previous work,
HFRPA calculations in spherical symmetry for
exotic nuclei 78Ni 100Sn 132Sn 208Pb is taken
as a reference
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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
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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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HFBQRPA in axial Symmetry
Spherical nuclei 21 in O isotopes GMR in
90Zr Deformed nuclei 24Mg 22Mg 28
Si Inertia parameters Quadrupole mass
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Formalism
1HFRPA
2HFBQRPA
b 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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16O
Axial QRPA
Spherical RPA
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Skyrme results from E.Kahn and Nguyen Van Giai,
Phys. Lett.B 472 (2000)253.
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10
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M1 / M0 17.89 0.20 MeV
D.H.Younblood,H.L.Clark, and Y.-W.Lui, Phys. Rev.
Lett.82 ,4 (1999)
M1 / M0 17.65 MeV
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Restoration of rotational symmetry for deformed
states
We want to calculate
for all QRPA states (K J)
For example Jp 2
In intrinsic frame
Using rotational approximation and relation for
3j symbol
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24Mg ß.51
Jp2
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Quadrupole
9-41MeV HFBQRPA EWSR76.6 M1 /
M0 17.64 MeV Exp. EWSR 72
10 M1 / M016.9 0.6 MeV
Exp. D.H. Youngblood, Y.-W. Lui, and H.L.
Clark, Phys.Rev.C 60 (1999)014304
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24Mg ISGMR
EWSR72 10 M1 / M021.0 0.6 MeV
9-41 Mev
EWSR 94 M1 / M0 20.47 MeV
D.H. Youngblood, Y.-W. Lui, and H.L. Clark,
Phys.Rev.C 60 (1999) 014304
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Quadrupole
13-30meV 82EWSR, M1 / M0 18.72 MeV
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Monopole
13-40 MeV 92EWSR, M1 / M020.86 MeV
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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
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28Si Quadrupole
M1 /M0 18.54 0.25 MeV 68 9 EWSR
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
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Inertia parameters
ATDHF "Mass"
(a) QRPA
(b) Inglis-Belayev
Consistent calculations CHFB and QRPA (a)(c).
(c) Constraint HFB
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Summary Coulomb and spin-orbit terms have to be
taken into account, Effect of the pairing
treatment in 21 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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Gogny force
P? is isospin exchange operator P? is spin
exchange operator

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