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Collectivity of pygmy resonance in spherical and deformed Ni and Fe isotopes:

Collectivity of pygmy resonance in spherical and deformed Ni and Fe isotopes: A self-consistent Skyrme RPA approach. RIKEN Symposium 2006 Methods of many-body systems: mean field theories and beyond March 20-22, 2006. T. Inakura and M. Matsuo Niigata Univ. Pygmy Resonance. Collective?

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Collectivity of pygmy resonance in spherical and deformed Ni and Fe isotopes:

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  1. Collectivity of pygmy resonance inspherical and deformed Ni and Fe isotopes: A self-consistent Skyrme RPA approach RIKEN Symposium 2006 Methods of many-body systems: mean field theories and beyond March 20-22, 2006 T. Inakura and M. Matsuo Niigata Univ.

  2. Pygmy Resonance Collective? pygmy IVGDR Experiments 116,124Sn: K. Govaert et al., PRC57, 5. 140Ce: R.-D. Herzberg et al., PLB390, 49. 138Ba: R.-D. Herzberg et al., PRC60, 051307. 138Ba,140Ce,144Sm: A. Zilges et al., PLB542, 43. 208Pb: N. Ryezayeva et al., PRL 89, 272502. 204,206-208Pb: J. Enders et al., NPA724, 243. 130,132Sn: P. Adrich et al., PRL 95, 132501.

  3. 78Ni Relativistic RPA calc. Vretenar, Paar, Ring et al. Fully self-consistent calc. Harmonic Oscillator basis Pygmy Resonance Giant Resonance NPA692, 496 9.0 MeV, 4.3% EWSR 68Ni IVE1 78Ni IVE1

  4. Skyrme-RPA+phonon coupl. Bortignon, Colo, et al. Skyrme HF-BCS Fully self-consistent calc. Harmonic Oscillator basis Relativistic QRPA Vretenar, Paar, Ring et al. Fully self-consistent calc. Harmonic Oscillator basis 132Sn 132Sn PLB 601, 27 At low energy, no single “collective” states. PRC 67, 034312

  5. Motivation • The different models have the different results. • What is the nature of the pygmy resonance? • How about in deformed nuclei?

  6. R. H. Lemmer and M. Veneroni, PR 170, 883. A. Muta et al., PTP 108, 1065. H. Imagawa and Y. Hashimoto, PRC 67, 037302. H. Imagawa, Ph.D. thesis, 2003. T. Inakura et al., NPA 768, 61. Mixed Representation RPA The coordinate representation is used for particles, while the HF basis for holes Including of continuum states

  7. Advantages • Suitable for 3D mesh calculation. We can treat deformed nuclei on same footing as spherical nuclei. • Easy to take into account all residual interaction.Fully self-consistent calculation with Skyrme interaction. • Free from upper energy cut-off. Numerical cut-off coming from mesh size is enough large. Shortcomings • Continuum states are descritized by the box boundary condition. • No pairing.

  8. protons neutrons positive dr negative dr Strengths for 16O. IS E1 strengths are less than O(10-6fm2). SkM* G= 2.0 MeV Rbox= 10 fm

  9. 68Ni EWSR up to 10MeV:1.7% of the TRK sum rule. SkM* interaction • = 1.0 MeV Rbox= 12 fm

  10. 68Ni 8.3MeV 1.0% of TRK positive dr negative dr protons neutrons

  11. Excitation to Continuum : 0.039

  12. 68Ni single-particle transitions 7.4 MeV 6.5 MeV

  13. 72Fe SkM* G= 1.0 MeV Rbox= 12 fm

  14. K=0 state at 8.1 MeV in 72Fe 0.4 % of TRK Excitation to Continuum : 0.152

  15. K=1 state at 7.2 MeV in 72Fe 0.6 % of TRK

  16. K=1 state at 7.2 MeV in 72Fe 0.6 % of TRK

  17. Summary • The fully self-consistent Skyrme RPA calculations. • Low-lying E1 states are obtained. • Superposition of some neutron excitations to loosely bound and resonant states. • Moderate collective states. • Small contributions of continuum states. • Coherence of transition densities. • The deformation hinders the collectivity.

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