Application of Coulomb energy density functional for atomic nuclei: Case studies of local density approximation and generalized gradient approximation

TL;DR

This study evaluates Coulomb energy density functionals, specifically LDA and GGA, for atomic nuclei, revealing their varying accuracy and limitations in modeling exchange and correlation energies.

Contribution

It applies and tests electron system energy functionals to atomic nuclei, highlighting their accuracy and limitations in nuclear physics.

Findings

LDA and GGA exchange energies differ by 11% in helium and 2.2% in lead.

GGA functionals like PBE improve exchange energy estimates.

Correlation functionals for electrons are unsuitable for nuclei.

Abstract

We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it is found that the deviation between the LDA and GGA ranges from around $ 11 \, \% $ in $ {}^{4} \mathrm{He} $ to around $ 2.2 \, \% $ in $ {}^{208} \mathrm{Pb} $, by taking the Perdew-Burke-Ernzerhof (PBE) functional as an example of the GGA\@. For the correlation Coulomb energies, it is shown that those functionals of electron systems are not suitable for atomic nuclei.