Microscopic calculation and local approximation of the spatial dependence of the pairing field with bare and induced interactions

The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field by using either a local approximation, which fully takes into account finite size effects, or a contact interaction, with parameters that are quite different from those commonly used in more phenomenological approaches.