  This work aims at a global assessment of the effect of the density dependence
of the zero-range pairing interaction. Systematic
Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface and mixed
pairing forces are carried out to study the pairing gaps in even-even nuclei
over the whole nuclear chart. Calculations are also done in coordinate
representation for unstable semi-magic even-even nuclei. The calculated pairing
gaps are compared with empirical values from four different odd-even staggering
formulae. Calculations with the three pairing interactions are comparable for
most nuclei close to $\beta$-stability line. However, the surface interaction
calculations predict neutron pairing gaps in neutron-rich nuclei that are
significantly stronger than those given by the mixed and volume pairing. On the
other hand, calculations with volume and mixed pairing forces show noticeable
reduction of neutron pairing gaps in nuclei far from the stability.
