  Formulated in [Low Temperature Physics/Fizika Nizkikh Temperatur, 41, 482
(2015)] model of hypothetical superconductivity with the source term (external
pair potential) in BCS hamiltonian is generalized for a case if electrons
interacts via both BCS model attraction and screened Coulomb repulsion. Unlike
the previous work the superconductor has critical temperature which determined
with the Coulomb interaction within a Cooper pair. It has been shown the
external pair potential is effective for superconductors where Tolmachev
logarithm is small (nonadiabatic case). A free energy functional and equations
similar to Ginzburg-Landau equations have been found for such a model.
