Low energy nuclear collective modes and excitations Low energy excitations in Neon isotopes, N=16 isotones and 68Ni within QRPA and Gogny force Sophie Péru Marco Martini

Beyond “mean field” … with RPA or QRPA RPA approaches describe all multipolarties and all parities, collective states and individual ones, low energy and high energy states with the same accuracy. A l’approximation de faible amplitude , i.e. pour des noyaux « harmoniques » E δ2E/δq2>0 δ2E/δq2 δE/δq=0 qμν 2

Formalism HFB+QRPA {b+ b} quasi-particle (qp) creation and annihilation operators. In axial symmetry , QRPA states {q+} are obtained for each block K . (Kp≤Jp) They are solution of In our approach, The effective interaction D1S is used both in the HFB mean field and in the QRPA matrix.

High energy collective states: giant resonances Giant resonances are related to nuclear matter properties Monopole Dipole Quadripole Octupole IS GMR spurious state GQR IV GMR IV GDR

Spurious states « treatment »

Approach limited to Spherical nuclei with no pairing RPA in spherical symmetry Giant resonances in exotic nuclei: 100Sn, 132Sn, 78Ni; S. Péru, J.F. Berger, and P.F. Bortignon, Eur. Phys. Jour. A 26, 25-32 (2005) Monopole Dipole Approach limited to Spherical nuclei with no pairing  Such study have shown the role of the consistence between mean field and RPA matrix.

Potential Energy Surfaces QRPA in axial symmetry : Potential Energy Surfaces

Formalism Restoration of rotational symmetry for deformed states For example: Jπ = 2+ In intrinsic frame Using time reversal symmetry, three independent calculations (Kπ = 0+, 1+, 2+) are needed.

IV Dipole

Quadrupole 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, 65, (2002) 034302

dipole response for Neon isotopes Increasing neutron number PDR and shift to low energies Increasing of fragmentation 20Ne 22Ne 18Ne PDR proton 24Ne 26Ne 28Ne PDR PDR PDR

B(E1) distributions

Evolution with A Néon isotopes N=16 Isotones Ne Ne Ne Ne Mg Si

ρ δρ 26Ne Pygmy w.f.(10.7 MeV) Proton: 2qp contrib. [e fm^-3] 15.97 MeV 2s1/2 1p1/2 X2=0.04 17.60 MeV 1d5/2 1p3/2 X2=0.02 17.48 MeV 1f7/2 1d5/2 X2=0.01 Neutron: 2qp contrib. 10.52 MeV 2p3/2 2s1/2 X2=0.67 13.68 MeV 1f7/2 1d5/2 X2=0.10 12.43 MeV 2p1/2 2s1/2 X2=0.09 10.82 MeV 2p3/2 1d3/2 X2=0.03 18.50 MeV 1d3/2 1p1/2 X2=0.01 [e fm^-3] [fm^-3]

ρ δρ 28Mg Pygmy w.f. (11.6 MeV) [e fm^-3] Proton: 2qp contrib. [fm^-3] 16.22 MeV 2s1/2 1p1/2 X2=0.06 16.02 MeV 1f7/2 1d5/2 X2=0.02 Neutron: 2qp contrib. 11.68 MeV 2p3/2 2s1/2 X2=0.40 11.93 MeV 2p3/2 1d3/2 X2=0.33 14.18 MeV 1f7/2 1d5/2 X2=0.06 13.98 MeV 2p1/2 2s1/2 X2=0.06 14.21 MeV 2p1/2 1d5/2 X2=0.03 [e fm^-3] δρ [fm^-3]

ρ δρ 30Si Pygmy w.f. (12.2 MeV) [e fm^-3] Proton: 2qp contrib 15.92 MeV 2s1/2 1p1/2 X2=0.19 14.33 MeV 1f7/2 1d5/2 X2=0.07 17.15 MeV 2p3/2 1d5/2 X2=0.01 Neutron: 2qp contrib. 12.61 MeV 2p3/2 2s1/2 X2=0.44 14.55 MeV 1f7/2 1d5/2 X2=0.11 12.79 MeV 2p3/2 1d3/2 X2=0.07 15.23 MeV 2p1/2 2s1/2 X2=0.07 [e fm^-3] δρ [fm^-3]

ρ δρ 18Ne Pygmy w.f.(14.2 MeV) Proton: 2qp contrib. 15.99 MeV 1f7/2 1d5/2 X2=0.26 15.98 MeV 2p3/2 1d5/2 X2=0.23 13.75 MeV 2s1/2 1p1/2 X2=0.12 18.19 MeV 2p3/2 2s1/2 X2=0.09 16.95 MeV 1d5/2 1p3/2 X2=0.09 19.14 MeV 2p1/2 2s1/2 X2=0.04 Neutron: 2qp contrib. 15.78 MeV 1d3/2 1p3/2 X2=0.04 14.18 MeV 2s1/2 1p1/2 X2=0.04 ρ δρ [e fm^-3] [fm^-3]

Correlations between PDR and symmetry energy Carbone et al. Phys. Rev. C (2010) Effective Lagrangians Skyrme Forces EWSR [%] L [MeV] D1S 1,2 22,5 D1N 1,5 33,6 D1M 1,3 25,3 Similar study with Gogny: (absent in literature) M. Martini

Dipole Resonances in 68Ni Gogny Effective Lagrangian Comparison among models and forces Skyrme M. Martini

Dipole response for Zr isotopes : B(E1) B(M1) 86Zr 88Zr 90Zr M1 γ strength for 92Zr, H. Utsunomiya et al, PRL 100, 162502 (2008) 92Zr 94Zr 96Zr S.Goriely, H. Goutte, S. Hilaire, M. Martini, S. Péru, …

= 5 Dimension Collective Hamiltonian Beyond mean field … with GCM (GCM+GOA 2 vibr. + 3 rot.) = 5 Dimension Collective Hamiltonian 5DCH

HFB+QRPA / HFB+5DCH with the same interaction: A. Obertelli, et al, Phys. Rev. C 71, 024304 (2005) N=16 isotones S. Péru,AIPS Conference proceedings No. 1165,NSD09, (Melville, New York, 2009), p165

QRPA/5DCH Sn isotopes

Ni isotopes S. Péru,AIPS Conference proceedings No. 1165,NSD09, (Melville, New York, 2009), p165

Spectroscopy in neutron rich Ni isotopes within QRPA L. Gaudefroy, S. Péru …

Spectroscopy in neutron rich Ni isotopes within QRPA

0+ states in 68Ni within QRPA M. Martini & S. Péru

0+ states in 68Ni within QRPA Transition densities Protons Neutrons Transition densities Protons Neutrons Protons Neutrons M. Martini, S. Péru …

… beyond the nuclear structure : Test of QRPA and 5DCH (GCM) wave functions in proton inelastic scattering… 36S HFB+5DCH E (2+1) = 2.34 MeV B(E2) = 375 e2fm4 HFB+QRPA E (2+1) = 3.29 MeV B(E2) = 139.7 e2fm4 Exp E (2+1) = 3.29 MeV B(E2) = 100 e2fm4 E. Bauge and S. Péru

differential cross sections for 14.1 MeV neutron on 238 U (a,c). Comparison between experimental data (circles) and one-step contributions (full curves) to the double- differential cross sections for 14.1 MeV neutron on 238 U (a,c). M. Dupuis ,E. Bauge,L. Bonneau,J.-P. Delaroche ,T. Kawano ,S. Karataglidis and S. Péru, Proceedings of the Second International Workshop on Nuclear Compound Reactions and Related Topics, (2010).