Eur. Phys. J. A (2000) 8: 59-75
https://doi.org/10.1007/s10050-000-4504-z

Pairing gaps from nuclear mean-fieldmo dels

¹ Institut für Theoretische Physik, Universität Frankfurt, Robert-Mayer-Str. 10, D-60325, Frankfurt am Main, Germany
² Department of Physics and Astronomy, The University of North Carolina, Chapel Hill, NC, 27516, USA
³ Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA
⁴ Institut für Theoretische Physik II, Universität Erlangen-Nürnberg, Staudtstr. 7, D-91058, Erlangen, Germany
⁵ Joint Institute for Heavy-Ion Research, Oak Ridge National Laboratory, P. O. Box 2008, Oak Ridge, TN, 37831, USA

Received: 15 September 1999
Revised: 10 March 2000
Published online: 11 September 2013

Abstract

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.