Pairing gaps from nuclear mean-field models

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models, The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formu lated ill terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both thr mean-field energy a nd the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averag ed matrix elements of the pairing potential, and single-quasiparticle energ ies. Experimental values for the pairing gay. are compared with calculation s employing both a delta pairing force and a density-dependent delta intera ction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core p olarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nucle i.