The calculation of single-nucleon energies of nuclei by considering two-body effective interaction, n(k,rho), and a Hartree-Fock inspired scheme

TL;DR

This paper calculates single-nucleon energies in nuclei using a Hartree-Fock inspired scheme with two-body effective interactions, emphasizing the role of the momentum distribution function n(k,rho) over simplified models.

Contribution

It introduces a method incorporating the nucleon effective mass and density-dependent momentum distribution n(k,rho) to improve SPE calculations in closed shell nuclei.

Findings

Including n(k,rho) significantly improves SPE accuracy.

Correlation effects are effectively modeled via the effective mass factor.

The approach enhances understanding of valence level energies.

Abstract

The nucleon single-particle energies (SPEs) of the selected nuclei, that is, 16O, 40Ca, and 56Ni, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest order constrained variational (LOCV) calculations for the symmetric nuclear matter with the AV18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,rho), with the Heaviside functions, the role of n(k,rho) on the nucleon SPEs at the major levels of the selected closed shell nuclei, is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the AV18 density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including n(k,rho), instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.