About the Possibility of Increasing the Superconducting Transition Temperature by the Phonon Mechanism

The equations for the energy gap and for the critical temperature T-c are investigated in the case of superconductors with strong coupling, with regard for the dependence of the interaction constant on the phonon frequency. The effective interaction constant lambda, which determines T-c in the Einstein model and delta-function phonon peak model, is calculated, and its dependence on the ordinary interaction constant, phonon frequency and momentum, Fermi momentum, and other parameters is determined. It is shown that the maximum possible value of lambda is unity. A solution is found for the critical temperature equation in the case of a delta-function peak and the Einstein model. It is demonstrated that in the latter case T-c has a sharp maximum as a function of the electron density.