Effect of long-range interactions on the Kohn-Luttinger mechanism of the cooper instability in the Shubin-Vonsowsky model

The problem of Cooper instability is studied by implementing the Kohn-Luttinger mechanism in the framework of the Shubin-Vonsowsky model taking into account the intersite Coulomb interactions within the first and second coordination spheres. It is shown that the Kohn-Luttinger renormalization for the effective interaction in the second-order terms of perturbation theory, as well as the inclusion of intersite hoppings in the second and third coordination spheres, significantly affects the interplay between the superconducting phases with $d_{xy}$-, $p$-, $s$-, and $d_{x^2-y^2}$-wave symmetries of the order parameter.