Microscopic calculation and LDA 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 using a Local Density Approximation (LDA) and a contact interaction, with parameters which are quite different from those commonly used in more phenomenological approaches. 
A. Pastore, F. Barranco, R. A. Broglia and E. Vigezzi