Semi-microscopic model of pairing in nuclei

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab initio BCS gap equation with the Argonne v(18) force and the self-consistent energy density functional method basis characterized by the bare nucleon mass. The BCS theory is formulated in terms of the model space S-0 with the effective pairing interaction calculated from the first principles in the subsidiary space S'. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter, universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account approximately both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei are compared with empirical gap values derived from odd-even mass differences. The average disagreement is of the order of 0.1-0.2 MeV. The role of the self-consistent basis is analyzed.