A superconductor in the external pair potential. Accounting of the Coulomb pseudopotential

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.