The Slater approximation for Coulomb exchange effects in nuclear covariant density functional theory

TL;DR

This paper introduces a relativistic local density approximation for Coulomb exchange in nuclear systems, combining the Slater approximation with relativistic corrections, and validates its accuracy across various isotopes.

Contribution

The paper develops and validates a relativistic LDA for Coulomb exchange, improving accuracy over non-relativistic methods in nuclear density functional theory.

Findings

Relativistic effects significantly impact Coulomb exchange energies.

The relativistic LDA reproduces exact energies within 5%.

Validation across multiple isotopes confirms the method's robustness.

Abstract

The relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems is presented. This approximation is composed of the well-known Slater approximation in the non-relativistic scheme and the corrections due to the relativistic effects. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange term in the relativistic Hartree-Fock-Bogoliubov theory. The relativistic effects are found to be important and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5% demonstrated by the semi-magic Ca, Ni, Zr, Sn, and Pb isotopes from proton drip line to neutron drip line.