Extended Hartree-Fock study of the single-particle potential: the nuclear symmetry energy, nucleon effective mass, and folding model of the nucleon optical potential

TL;DR

This paper uses an extended Hartree-Fock approach with density-dependent interactions to analyze the nucleon potential, revealing effects on symmetry energy, effective mass, and improving the folding model for nucleon optical potentials.

Contribution

It introduces a consistent method to incorporate the rearrangement term and momentum dependence in Hartree-Fock calculations, enhancing the understanding of nuclear symmetry energy and nucleon optical potentials.

Findings

High-momentum tail significantly affects symmetry energy slope.

Rearrangement term impacts neutron-proton effective mass splitting.

Extended folding model successfully describes neutron scattering data.

Abstract

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (s/p) energies of nucleons in NM are determined according to the Hugenholtz-van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the s/p potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the s/p potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the s/p potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the s/p potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in details. The high-momentum tail of the s/p potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.