Low energy excitations in Neon isotopes, N=16 isotones and 68 Ni within QRPA and Gogny force

1. 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

2. 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

3. 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 interactionD1Sis used both in the HFB mean field and in the QRPA matrix.

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

5. Spurious states « treatment »

6. 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) Dipole Monopole Approach limited to Spherical nuclei with no pairing  Such study have shown the role of the consistence between mean field and RPA matrix.

7. QRPA in axial symmetry : Potential Energy Surfaces

8. 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.

9. IV Dipole

10. 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

11. 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

12. B(E1) distributions

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

15. 26Ne ρ δρ Pygmy w.f.(10.7 MeV) Proton: 2qp contrib. 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]

16. 28Mg ρ Pygmy w.f. (11.6 MeV) Proton: 2qp contrib. 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]

17. 30Si ρ Pygmy w.f. (12.2 MeV) 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]

18. 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]

20. Correlations between PDR and symmetry energy Carbone et al. Phys. Rev. C (2010) Effective Lagrangians Skyrme Forces Similar study with Gogny: (absent in literature) M. Martini

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

22. Dipole response for Zr isotopes : 80Zr 84Zr 82Zr B(E1) B(M1) 86Zr 88Zr 90Zr 92Zr 94Zr 96Zr M1 γ strength for 92Zr, H. Utsunomiya et al, PRL 100, 162502 (2008) S.Goriely, H. Goutte, S. Hilaire, M. Martini, S. Péru, …

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

24. 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

25. QRPA/5DCH Sn isotopes

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

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

28. Spectroscopy in neutron rich Ni isotopes within QRPA

29. 0+ states in 68Ni within QRPA M. Martini & S. Péru

30. 0+ states in 68Ni within QRPA Protons Neutrons Transition densities Protons Neutrons Protons Neutrons M. Martini, S. Péru …

31. Test of QRPA and 5DCH (GCM) wave functions in proton inelastic scattering… … beyond the nuclear structure : 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

32. 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).