Relativistic correction of the Coulomb interaction in the local density approximation for energies and radii in doubly-magic nuclei

TL;DR

This paper investigates the impact of relativistic corrections to the Coulomb interaction within the local density approximation on energies and radii of doubly-magic nuclei, revealing significant energy shifts especially in heavy nuclei.

Contribution

It introduces a method to incorporate relativistic Coulomb corrections in Skyrme Hartree-Fock calculations and compares their effects to vacuum polarization contributions.

Findings

Relativistic correction adds about 2.4 MeV to the total energy of Pb-208.

Proton and neutron radii are minimally affected by the correction.

In heavy nuclei, the correction's energy contribution is comparable to vacuum polarization effects.

Abstract

Effects of the relativistic correction of the Coulomb interaction on doubly-magic nuclei are discussed with Skyrme Hartree--Fock calculations. The relativistic correction is treated by using the local density approximation. It is found that the correction to the total energy is about $ 2.4 \, \mathrm{MeV} $ for $ {}^{208} \mathrm{Pb} $, while proton and neutron radii do not change significantly. This difference is larger than the difference of the Coulomb exchange (Fock) energy calculated with the local density (Hartree--Fock--Slater) approximation and that with the exact treatment and the neutron finite-size effect. Effects of the correction are also compared to the correction due to the vacuum polarization. It is shown that the two contributions to the total energy are comparable in light nuclei, but the latter dominates in heavy nuclei, while the contribution of the relativistic correction to the total energy is non-negligible compared to the target accuracy of the DFT calculation.