T_c degradation by the Coulomb interaction in anisotropic disordered superconductors

The authors calculate the depression of T_c caused by the effect of a short mean free path on the Coulomb repulsion, for the special case of a very anisotropic superconductor. Specifically, they consider the linear chain model for A15 superconductors with a large difference between the in-chain and inter-chain scattering rates. Previous work based on the McMillan equation for T_c gave a large reduction in T_c. In this work they find T_c numerically from the Eliashberg equations. They find that the reduction of T_c due to this effect is about 25% to 30%, which is considerably less than observed experimentally. The effective Coulomb term is retarded, and as a result is frequency dependent. It is affected by the disorder mainly at small frequencies ( approximately 10 meV).