  We survey odd-even nuclear binding energy staggering using density functional
theory with several treatments of the pairing interaction including the BCS,
Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami
approximation. We calculate the second difference of binding energies and
compare with 443 measured neutron energy differences in isotope chains and 418
measured proton energy differences in isotone chains. The particle-hole part of
the energy functional is taken as the SLy4 Skyrme parametrization and the
pairing part of the functional is based on a contact interaction with possible
density dependence. An important feature of the data, reproduced by the theory,
is the sharp gap quenching at magic numbers. With the strength of the
interaction as a free parameter, the theory can reproduce the data to an rms
accuracy of about 0.25 MeV. This is slightly better than a single-parameter
phenomenological description but slightly poorer than the usual two-parameter
phenomenological form C/A^alpha . The following conclusions can be made about
the performance of common parametrization of the pairing interaction: (i) there
is a weak preference for a surface-peaked neutron-neutron pairing, which might
be attributable to many-body effects; (ii) a larger strength is required in the
proton pairing channel than in the neutron pairing channel; (iii) pairing
strengths adjusted to the well-known spherical isotope chains are too weak to
give a good overall fit to the mass differences.
