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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 Perdew-Burke-Ernzerhof (PBE) functionalas an example of the GGA\@. For the correlation Coulomb energies, it is shownthat those functionals of electron systems are not suitable for atomic nuclei.

physical review. c

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