A self-consistent Skyrme RPA approach

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Presentation transcript:

A self-consistent Skyrme RPA approach 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 pygmy IVGDR Experiments Collective? 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.

78Ni Relativistic RPA calc. 68Ni 78Ni Pygmy Resonance Giant Resonance 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

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

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

Mixed Representation RPA 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

Advantages Shortcomings 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.

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

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

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

Excitation to Continuum : 0.039

68Ni single-particle transitions 6.5 MeV 7.4 MeV

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

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

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

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

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.