Microscopic-Macroscopic Approach for Ground-State Energies Based on the Gogny Force with the Wigner-Kirkwood Averaging Scheme

TL;DR

This paper develops a microscopic-macroscopic method to calculate ground-state energies of nuclei using the Gogny force and Wigner-Kirkwood averaging, achieving accurate mass and energy surface predictions across the periodic table.

Contribution

It introduces a combined approach using ETF potentials and densities with shell corrections from the Wigner-Kirkwood scheme for comprehensive nuclear ground-state calculations.

Findings

Accurately reproduces nuclear ground-state masses.

Provides detailed potential energy surfaces for various nuclei.

Demonstrates the effectiveness of the microscopic-macroscopic approach.

Abstract

In the previous paper I \cite{bhagwat20} we have shown that self-consistent Extended Thomas-Fermi (ETF) potentials and densities associated with a given finite-range interaction can be parametrized by generalized Fermi distributions. As a next step, a comprehensive calculation of ground-state properties of a large number of spherical and deformed even-even nuclei is carried out in the present work using the Gogny D1S force within the ETF scheme. The parametrized ETF potentials and densities of paper I are used to calculate the smooth part of the energy and the shell corrections within the Wigner-Kirkwood semiclassical averaging scheme. It is shown that the shell corrections thus obtained, along with a simple liquid drop prescription, yield a good description of ground-state masses and potential energy surfaces for nuclei spanning the entire periodic table.