Pseudo-Coulomb potential in singlet superconductivity

Reduction of the screened Coulomb potential parameter to *=/[1+ ln(EF/Latin small letter h with strokeD)] is related to the pair correlation function at r=0. This correlation function is calculated for both the simple Cooper-pair problem and standard Bardeen-Cooper-Schrieffer (BCS) theory by use of a two-square-well model (with and describing the attraction and repulsion). Results are compared with values obtained for a one-square-well model (having the suitable net attraction, e.g., -* in the BCS case). For the BCS case, the true pair correlation at r=0 is reduced by a factor (*/)2 relative to the fictitious (one-square-well) value (even though is the same for both models). The reduction factor is typically (1/25. It follows that any short-range attractive contribution to superconducting pairing will suffer a reduction similar to that for the Coulomb repulsion.