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 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. PACS. 21.60.Jz – 21.30.Fe – 21.60.-n