As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov
(HFB) theory, we have developed a new calculational tool to find the HFB minima
of odd-A nuclei based on the gradient method and using interactions of Gogny's
form. The HFB minimization includes both time-even and time-odd fields in the
energy functional, avoiding the commonly used "filling approximation". Here we
apply the method to calculate neutron pairing gaps in some representative
isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82
spherical chains and the Z=62 and 92 deformed chains. We find that the gradient
method is quite robust, permitting us to carry out systematic surveys involving
many nuclei. We find that the time-odd field does not have large effect on the
pairing gaps calculated with the Gogny D1S interaction. Typically, adding the
T-odd field as a perturbation increases the pairing gap by ~100 keV, but the
re-minimization brings the gap back down. This outcome is very similar to
results reported for the Skyrme family of nuclear energy density functionals.
Comparing the calculated gaps with the experimental ones, we find that the
theoretical errors have both signs implying that the D1S interaction has a
reasonable overall strength. However, we find some systematic deficiencies
comparing spherical and deformed chains and comparing the lighter chains with
the heavier ones. The gaps for heavy spherical nuclei are too high, while those
for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei
show hardly any A-dependence, contrary to the data. Inclusion of the T-odd
component of the interaction does not change these qualitative findings