1. 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.

2. 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,
138Ba, 140Ce, 144Sm: A. Zilges et al., PLB542, 43.
208Pb: N. Ryezayeva et al., PRL 89,
204, Pb: J. Enders et al., NPA724, 243.
130, 132Sn: P. Adrich et al., PRL 95,

3. 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

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,

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

6. 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,
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 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.

8. 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

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

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

11. Excitation to Continuum : 0.039

13. 68Ni
single-particle transitions
6.5 MeV
7.4 MeV

14. 72Fe
SkM*
G= 1.0 MeV
Rbox= 12 fm

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

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

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

18. 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.