Semiclassical approximation to the Hartree-Fock method in finite nuclei

TL;DR

This paper reviews the semiclassical extended Thomas-Fermi theory for finite nuclei, focusing on calculating ground-state properties and methods to incorporate shell effects missing in the semiclassical approximation.

Contribution

It introduces techniques like the expectation value method and Kohn-Sham scheme to include shell effects in semiclassical nuclear models.

Findings

Semiclassical energies lack shell effects, similar to mass formulas.

Techniques like expectation value and Kohn-Sham schemes can incorporate shell effects.

Numerical applications demonstrate the methods with Skyrme and Gogny forces.

Abstract

In this paper we review the semiclassical extended Thomas-Fermi theory for describing the ground-state properties of nuclei. The binding energies calculated in this approach do not contain shell effects and, in this sense, they are analogous to those obtained from the mass formula. We discuss some techniques for incorporating the shell effects which are missing in the semiclassical calculation, such as the so-called expectation value method and the Kohn-Sham scheme. We present numerical applications for effective zero-range Skyrme forces and finite-range Gogny forces.