Superconducting pairing from repulsion: Contact potential approximation

Pairing of repulsive particles with large total momentum results in essential relative-motion momentum dependence of the superconducting order parameter with a nodal line crossing the Fermi contour inside kinematically accessible domains of the momentum space. Repulsive interaction potential resulting in the superconducting pairing is reduced to a stepwise one with a degenerate kernel having two eigenvalues of opposite sign. Using such a kind of contact potential approach the self-consistency equation is transformed into a system of two integral equations determining average values of the order parameter inside the subdomains of its constant sign. The solution of this equation system is obtained in the weak coupling limit.