Skyrme force and the mass formula

Coefficients of the mass formula related to the property of the nuclear surface are calculated from the Skyrme forces SII, SIII and SV defined by the Orsay group. Comparing with Myers' mass formula parameters, it is found that the effective stiffness Q for separation of the neutron and proton surfaces is too large by a factor of about two for SIII. The discrepancy can also be stated by saying that the surface symmetry energy calculated from SIII is too small, and related to this is a too thin neutron skin for N > Z nuclei. The SV force gives a much too small value for Q. The SII force, with a repulsive term somewhere intermediate between SIII and SV gives a better value for Q. The strong density dependence of SIII is needed, however, to give good single-particle spectra (or the effective mass large enough). The SIII force has a density dependence between unlike nucleons only (between neutrons and protons). In this paper we modify the Skyrme force so as to allow for a density dependence also between like nucleons. A many-body theoretical justification for this modification is given in the paper. The mass formula parameter Q is reproduced with our new force maintaining a sufficiently strong density dependence. The neutron skin thickness is increased and the ⁴⁰Ca-⁴⁸Ca isotope shift of the charge radius is also well reproduced with this new force. A change of the density dependence from a linear to a one-third power dependence improves the agreement with the compressibility, and also affects the neutron-proton distributions in the surface.