Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

Meng-Hock Koh,Mohamad Nor Nurhafiza,M.H Koh,G Krishnan,F Mohd Noor

doi:10.1051/epjconf/201715600004

Meng-Hock Koh, Mohamad Nor Nurhafiza + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/201715600004

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Abstract

Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237 Np and 241 Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

Highlights

Self-consistent blocking calculations of band-head energies of odd-mass nuclei have been recently performed in Ref. [1] within the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF+BCS) framework
The general consensus was that the Slater approximation constitute a e-mail: kmhock@utm.my good approximation for heavy nucleus while it is less good for light nucleus
The latter is given in terms of energy parameter and was obtained after multiplying the moment of inertia by a factor of 1.32 as proposed by Ref. [13]. It appears that spectra obtained from exact Coulomb-exchange calculations and Slater approximation are almost similar

Summary

Introduction

Self-consistent blocking calculations of band-head energies of odd-mass nuclei have been recently performed in Ref. [1] within the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF+BCS) framework. Self-consistent blocking calculations of band-head energies of odd-mass nuclei have been recently performed in Ref. A possible reason for the poorer agreement with data for odd-proton nuclei is attributed to the usage of the Slater approximation [2] for the Coulomb-exchange term. As a follow-up to the previous work, we would like to investigate as to what extend the Slater approximation affects the agreement of bandhead energies with data. We want to check if exact calculations of the Coulomb-exchange term would improve the agreement of the quantity of interest with available data. [6,7,8]) This preliminary work is to the best of our knowlege, the first in which exact calculations of the Coulomb-exchange term is performed on top of breaking the time-reversal symmetry at the mean-field level

Details of the approach

Results

Conclusion

1: Excitation energies of band-head states