Pairing correlations. II.: Microscopic analysis of odd-even mass staggering in nuclei

The odd-even mass staggering in nuclei is analyzed in the context of self-consistent mean-field calculations, for spherical as well as for deformed nuclei. For these nuclei, the respective merits of the energy differences ${\ensuremath{\Delta}}^{(3)}$ and ${\ensuremath{\Delta}}^{(5)}$ to extract both the pairing gap and the time-reversal symmetry breaking effect at the same time are extensively discussed. The usual mass formula ${\ensuremath{\Delta}}^{(3)}$ is shown to contain additional mean-field contributions when realistic pairing is used in the calculation. A simple tool is proposed in order to remove the time-reversal symmetry breaking effects from ${\ensuremath{\Delta}}^{(5)}.$ Extended comparisons with the odd-even mass staggering obtained in the zero-pairing limit (schematic model and self-consistent calculations) show the nonperturbative contribution of pairing correlations on this observable.