Coulomb exchange functional with generalized gradient approximation for self-consistent Skyrme Hartree-Fock calculations

We perform self-consistent Skyrme Hartree-Fock calculations with the Coulomb exchange functional using the generalized gradient approximation (GGA). It is found that the Perdew-Burke-Ernzerhof GGA (PBE-GGA) Coulomb exchange functional is able to reproduce the exact-Fock energy for nuclei in a wide region of the nuclear chart with one adjustable parameter. The remaining error of the GGA Coulomb exchange energy with respect to the exact-Fock energy dominantly comes from the functional-driven error.