  We study odd-even mass staggering of nuclei, also called pairing gaps, using
a Skyrme self-consistent mean-field theory and a numerically exact treatment of
the pairing Hamiltonian. We find that the configuration-space Monte Carlo
method proposed by Cerf and Martin offers a practical computational procedure
to carry out the numerical solutions in large-dimensional model spaces.
Refitting the global strength of the pairing interaction for 443 neutron
pairing gaps in our number-conserving treatment, we find the correction to the
pairing correlation energies and pairing gaps to have rms values of 0.6 MeV and
0.12 MeV, respectively. The exact treatment provides a significant improvement
in the fit to experimental gaps, although it is partially masked by a larger
rms error due to deficiencies in other aspects of the theory such as the
mean-field energy functional.
