Application of Coulomb Energy Density Functional for Atomic Nuclei: Case Studies of Local Density Approximation and Generalized Gradient Approximation

摘要

We test the Coulomb exchange and correlation energy density functionals ofelectron systems for atomic nuclei in the local density approximation (LDA) andthe generalized gradient approximation (GGA). For the exchange Coulombenergies, it is found that the deviation between the LDA and GGA ranges fromaround $ 11 \, \% $ in $ {}^4 \mathrm{He} $ to around $ 2.2 \, \% $ in ${}^{208} \mathrm{Pb} $, by taking the PBE functional as an example of the GGA.For the correlation Coulomb energies, in the LDA the ratios of the correlationenergy to the exchange energy is around $ 2 \, \% $ in nuclei in the whole massregion, correspondingly $ E^{\mathrm{LDA}}_{\mathrm{c}} \simeq -550 \,\mathrm{keV} $ in $ {}^{208} \mathrm{Pb} $.