  Two aspects of the problem of evaluating double odd-even mass differences D_2
in semi-magic nuclei are studied related to existence of two components with
different properties, a superfluid nuclear subsystem and a non-superfluid one.
For the superfluid subsystem, the difference D_2 is approximately equal to
2\Delta, the gap \Delta being the solution of the gap equation. For the
non-superfluid subsystem, D_2 is found by solving the equation for two-particle
Green function for normal systems. Both equations under consideration contain
the same effective pairing interaction. For the latter, the semi-microscopic
model is used in which the main term calculated from the first principles is
supplemented with a small phenomenological addendum containing one
phenomenological parameter supposed to be universal for all medium and heavy
atomic nuclei.
