Nuclear effective charge factor originating from covariant density functional theory

TL;DR

This paper develops a phenomenological formula for the Coulomb exchange term in relativistic density functional theory, accurately reproducing exchange energies and aiding in effective interaction modeling in finite nuclei.

Contribution

It introduces a new phenomenological formula for Coulomb exchange energy that matches exact calculations within 1% deviation in various isotopes.

Findings

Phenomenological formula reproduces Coulomb exchange energies with <1% deviation.

Validates the formula's applicability for effective interactions in relativistic Hartree models.

Demonstrates the formula's effectiveness across multiple semi-magic isotopes.

Abstract

Guiding by the relativistic local density approximation, we explore a phenomenological formula for the coupling strength of Coulomb field to take into account the Coulomb exchange term effectively in the relativistic Hartree approximation. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange energies in the relativistic Hartree-Fock-Bogoliubov approach. It is found that the exact Coulomb exchange energies can be reproduced by employing the phenomenological formula with the relative deviations less than 1% for semi-magic Ca, Ni, Sn, and Pb isotopes. Furthermore, we check the applicability of the phenomenological formula for the effective interactions in the relativistic Hartree approach by investigating the binding energy differences of mirror nuclei.