Collectivity%20of%20pygmy%20resonance%20in%20spherical%20and%20deformed%20Ni%20and%20Fe%20isotopes:

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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.
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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.
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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
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Skyrme-RPAphonon 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
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Motivation

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

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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
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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.

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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
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68Ni
EWSR up to 10MeV1.7 of the TRK sum rule.

• SkM interaction
• 1.0 MeV
• Rbox 12 fm

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68Ni
8.3 MeV 1.0 of TRK
positive dr negative dr
protons neutrons
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Excitation to Continuum 0.039
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(No Transcript)
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68Ni single-particle transitions
6.5 MeV
7.4 MeV
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72Fe
SkM G 1.0 MeV Rbox 12 fm
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K0 state at 8.1 MeV in 72Fe
0.4 of TRK
Excitation to Continuum 0.152
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K1 state at 7.2 MeV in 72Fe
0.6 of TRK
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K1 state at 7.2 MeV in 72Fe
0.6 of TRK
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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.