Radial Dependence of the Nucleon Effective Mass and Ground-State Properties of Magic Nuclei

Within the framework of the self-consistent Hartree–Fock method based on a Skyrme-type energy density functional, the contributions of various terms to the nucleon effective mass have been studied. Additional terms of the EDF affecting the nucleon effective mass at the nuclear surface have been introduced, and their influence on the ground-state properties (nuclear charge radius, binding energy, and single-particle spectrum) of the doubly closed shell nuclei \({}^{16}\)O, \({}^{40,48}\)Ca, \({}^{56,78}\)Ni, \({}^{100,132}\)Sn, and \({}^{208}\)Pb has been analyzed. It has been found that the radial dependence of the effective mass of nucleons affects both the density diffuseness and the single-particle level scheme near the Fermi surface. Two new parameter sets of the energy density functional are proposed.