  We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate
space on the one-quasi-particle energies and binding energy odd-even staggering
(OES) in semi-magic nuclei with the zero-range volume, mixed and surface
pairing forces in order to explore the influence of their density dependence.
The odd-$N$ isotopes are calculated within the blocking scheme. The strengths
for the pairing forces are determined in two schemes by fitting locally to
reproduce pairing gap in $^{120}$Sn and globally to all available data on the
OES of semi-magic nuclei with $Z\geq8$. In the former calculations, there is a
noticeable difference between the neutron mean gaps in neutron-rich O, Ca, Ni
and Sn isotopes calculated with the surface pairing and those with the mixed
and volume pairing.
  The difference gets much smaller if the globally optimized pairing strengths
are employed. The heavier Pb isotopes show the opposite trend. Moreover, large
differences between the mean gap and the OES may be expected in both
calculations when one goes towards the neutron drip line.
