Contribution to the Theory of Weak Coupling Superconductors

Abstract

We have managed to simplify the Eliashberg equations for the case of weak coupling superconductors. Further, an explicit approximate analytic solution of the simplified equations has been obtained for the zero temperature gap edge. An expression for the critical temperature is also given. It is found to be of the BCS form and allows the BCS parameter N(0)V to be identified with a simple function of the normal state properties. The validity of our simplified integral equations and of our analytic solution is established by comparison with numerical solutions of the complete Eliashberg equations. The equations are used to discuss the effect of pressure on the gap, the isotope effect, as well as other properties.