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 v18 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 S0 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.