Properties of nuclear matter from macroscopic–microscopic mass formulas

Based on the standard Skyrme energy density functionals together with the extended Thomas–Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic–microscopic mass formulas: Lublin–Strasbourg nuclear drop energy (LSD) formula and Weizsäcker–Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are K∞=230±11MeV and 235±11MeV, respectively. The slope parameter of symmetry energy at saturation density is L=41.6±7.6MeV for LSD and 51.5±9.6MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [4]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron–proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrme Hartree–Fock–Bogoliubov calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of the mean-field potential.