  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 formulated in
terms of local density functionals for the effective interaction. We calculate
the Lipkin-Nogami corrections of both the mean-field energy and the pairing
energy. Various definitions of the pairing gap are discussed as three-point,
four-point and five-point mass-difference formulae, averaged matrix elements of
the pairing potential, and single-quasiparticle energies. Experimental values
for the pairing gap are compared with calculations employing both a delta
pairing force and a density-dependent delta interaction in the BCS and
Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking
approximation which neglects part of the the core polarization 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 nuclei.

Nuclear Theory