Equation of state of stellar nuclear matter and the effective nucleon mass

Using the generalized Skyrme force SkSP1, we calculate the equation of state (EOS) of nuclear matter appropriate to stellar collapse; we consider the full density range corresponding to the passage from the droplet phase (isolated nuclei) through the bubble phase up to homogeneous nuclear matter. This force, having a term with simultaneous momentum and density dependence, is able to give a good fit to nuclear masses in Hartree-Fock-BCS calculations while having the nuclear-matter value of the effective nucleon mass. We find that in the two inhomogeneous phases the new EOS resembles closely that given by a conventional Skyrme force fitted to nuclear masses, while in the homogeneous phase it rapidly crosses over with increasing density to approach the EOS given by a conventional Skyrme force with the correct nuclear-matter value of the effective mass. Thus it is possible with a Skyrme-type force to obtain an EOS with the correct effective-mass properties at both extremities of the density range.