Quantitative spin-dependent electron-electron interaction to calculate the superconducting parameters ? and ?

The spin-dependent Kukkonen-Overhauser (KO) effective electron-electron interaction in electron gas with a deformable background is used to calculate the BCS superconducting parameters mu, mu*, and lambda. The density and spin local field factors are utilized to incorporate the quantitative effects of exchange and correlation. The repulsive parameter mu is compared to results using the historical Thomas-Fermi or nearly equivalent random phase approximation (RPA) interactions. The resulting mu using the KO interaction is 45% larger at rs = 1.65; rising to 153% larger at rs = 5.62. Retardation reduces the effective repulsion, but mu* is still 20 - 25% larger. The predicted superconducting transition temperature would be reduced by 5 - 20% using the McMillan formula. The attractive superconducting parameter lambda, which depends on the electron-test charge interaction and the phonon spectrum, is also calculated using simple Debye-based models for phonon dispersion. This leads to a larger value of lambda than the same calculation using Thomas-Fermi or RPA interactions. Modern calculations of the phonon dispersion relations are often done using density functional theory. With the proper exchange and correlation kernel, the self-consistency of the method should yield the correct phonon dispersion relation and electron-phonon matrix elements. If the Thomas-Fermi or RPA interactions are used at any stage, the results for lambda are probably quantitatively inaccurate.