VERTEX CORRECTIONS TO THE THEORY OF SUPERCONDUCTIVITY

With the eventual goal of understanding vertex corrections in the dope d fullerenes and the bismuthates, assuming that they may be electron-p honon superconductors, we have constructed a weak coupling perturbatio n theory that includes the lowest-order vertex corrections (and reduce s to Migdal-Eliashberg theory in the absence of the vertex corrections ). Vertex corrections are studied in the local approximation which neg lects the momentum dependence of the self energy. This approximation i s exact in the limit of infinite dimensions and appears to be accurate in three dimensions. We present results for the superconducting trans ition temperature as a function of omega D/E(f) and lambda and make co mparison with similar results calculated in the infinite-dimensional H olstein model in the weak coupling limit. We find that vertex correcti ons reduce T-c and the energy gap Delta(o); however, the ratio 2 Delta (o)/kappa(B)T(c) remains unaffected. We also find that the isotope eff ect is reduced in the presence of vertex corrections.