Polarization corrections

Dimitar Tarpanov, Jacek Dobaczewski, Jussi Toivanen, Gillis Carlson

Energy from odd-even mass differences (OEMD)

for λ particle state for λ hole state

Polarization correction for a particle state

In DFT energy is functional of densities

Density matrix in neighboring system

Polarization corrections from odd-even mass differences

1

1

0

0

AEAEe

AEAEeoemd

oemd

MFAApol eEEe

01

AAAAA PTE ,,0

AA 1

eEEe AAAA 11

Polarization correction from particle-vibration coupling

In the case of interaction, that does not depend on density, one can show that: Here X and Y and

ω, are the RPA amplitudes and energies and h are given by the relation:

0

2

*

ph

phphphph YhXhe

hpph vh

MFAApol eEEe

01

100SnSV force

Self Interaction term

Density dependent functional

No pairing

Importance of high J phonons

Introducing pairing Results across the Sn chain with Sly5 parameterization of the Skyrme force,and volume type pairing

Paticle Vibration Coupling

Neutron Spectrum in 40Ca, theory (SLy5) and experiment

Singular Value Decomposition (SVD) analysis

Experimental data obtained from N.Schwierz et al.,arXiv:0709.3525v1

Fit on 16O, 40,48Ca, 132Sn, 208Pb

Experimental data obtained from M.G. Porquet

Fit on 16O, 40,48Ca,56Ni, 208Pb

Don’t forget self-interaction, in mean field calculations

Doing perturbation theory - the high J phonons cannot be neglected easily.

Deviations between the uncorrected mean-field single particle energies and experiment are, in general, not cured by PVC

Spectroscopic factors and single particle energies Many body perturbation theory for deformed nuclei.

Conclusions

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