On theory of pairing of fermions in superconductivity and superfluidity problem

In the paper we investigate the pairing of fermions due to direct interaction between particles in the superconductivity and superfluidity problem. The self consistent equation for transition temperature in the system of fermions of different kinds is derived. It is shown that in this case the results are qualitatively different from those in the BCS theory. The pairing between electrons and positrons due to the screened Coulomb interaction is investigated. It is found that the transition temperature is of asymptotic behavior both for high and low densities of electron-positron plasma