The skyrme-plus-pairing effective interaction and the global neutron-excess dependence of the pairing gap

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The neutron and proton pairing gaps were recently found to have a global dependence on neutron excess. We investigate whether the couplings necessary to obtain this behaviour can be provided by a mean field associated with a Skyrme-type plus usual pairing effective interaction. The parameters of this effective interaction are constrained by nuclear-matter properties, such as binding energy, saturation density, effective mass and values of the second derivatives of the energy with respect to the four densities (neutron and proton with spin-up and spin-down), together with the surface energy. The pairing gaps are then calculated as a function of neutron excess for various parameter sets for very large systems and for finite nuclei in the local-density approximation. We find that the empirical results cannot be reproduced by this procedure. We put forward therefore the hypothesis that, to account for this failure, the usual phenomenology of effective interactions in nuclei ought to be modified; we propose a simple residual neutron-proton interaction that can do that, yet maintains all the previous successes.