  A semi-microscopic model for nucleon pairing in nuclei is presented starting
from the ab intio BCS gap equation with Argonne v18 force and the
self-consistent Energy Density Functional Method basis characterized with the
bare nucleon mass. The BCS theory is formulated in terms of the model space S0
with the effective pairing interaction calculated from the first principles in
the subsidiary space S0. This effective interaction is supplemented with a
small phenomenological addendum containing one phenomenological parameter
universal for all medium and heavy atomic nuclei. We consider the latter as a
phenomenological way to take into account both the many-body corrections to the
BCS theory and the effective mass effects. For protons, the Coulomb interaction
is introduced directly. Calculations made for several isotopic and isotonic
chains of semi-magic nuclei confirm the validity of the model. The role of the
self-consistent basis is stressed.
