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Polarization corrections. Dimitar Tarpanov , Jacek Dobaczewski , Jussi Toivanen , Gillis Carlson. Polarization corrections from odd-even mass differences. Energy from odd-even mass differences (OEMD) for λ particle state for λ hole state Polarization correction for a particle state - PowerPoint PPT Presentation
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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
THANK YOUFOR YOUR ATTENTION
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