Pseudo-Coulomb potential in singlet superconductivity

L. L. Daemen; A. W. Overhauser

doi:10.1103/PhysRevB.38.81

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Pseudo-Coulomb potential in singlet superconductivity

L. L. Daemen, A. W. Overhauser

DOI 10.1103/PhysRevB.38.81 · Physical Review B

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Abstract

Reduction of the screened Coulomb potential parameter μ to μ*=μ/[1+μ ln(EF/ħωD)] 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 λ and μ describing the attraction and repulsion). Results are compared with values obtained for a one-square-well model (having the suitable net attraction, e.g., λ-μ* in the BCS case). For the BCS case, the ‘‘true’’ pair correlation at r=0 is reduced by a factor (μ*/μ)2 relative to the fictitious (one-square-well) value (even though Δ 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.