  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
$\Delta^{(3)}$ and $\Delta^{(5)}$ to extract both the pairing gap and the
time-reversal symmetry breaking effect at the same time are extensively
discussed. The usual mass formula $\Delta^{(3)}$, 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 time-reversal
symmetry breaking effects from $\Delta^{(5)}$. Extended comparisons with the
odd-even mass staggering obtained in the zero pairing limit (schematic model
and self-consistent calculations) show the non-perturbative contribution of
pairing correlations on this observable.
  PACS: 21.10Dr; 21.10.Hw; 21.30.-x.
  Keywords: Mean-field theories; Pairing correlations; Odd-even mass
staggering;
