FBCS for odd nuclei and the inverse gap equations: Application to N = 50 isotones

Abstract

The single-quasiparticle descriptions of odd superfluid nuclei by BCS theory and by particle number projection methods are compared with the exact lowest-seniority shell model. The purpose is to trace systematic inadequacies of the inverse-gap-equations (IGE) method to extract single-particle energies from spectroscopic data on odd nuclei and to improve that method by using number projection techniques. The IGE method yields too large a spacing of single-particle energies especially near closed subshells and also the force strengths are not correctly given in general. A similar method based on particle number projection leads to correct results. A conventional two-quasiparticle BCS calculation of the spectra of even nuclei with parameters obtained by the IGE method leads to other results than when for both the odd and the even nuclei a number-conserving description is used. In the former approximation particle-hole like states are relatively too high and particle-particle or hole-hole like states too low in energy, which may strongly influence the configuration mixing. As a practical application the spectra and a few other spectroscopic properties of the even single-closed-shell nuclei with 50 neutrons are calculated.