Theory of electron-electron interaction and superconductivity in dilute magnetic alloys above the Kondo temperature

The effective electron-electron interaction resulting from the virtual polarization of the impurity spin is investigated. Abrikosov's pseudofermion representation of spin operators has been applied. It is pointed out that the effective electron-electron interaction consists of two parts: 1) elastic scattering; 2) inelastic scattering. The second part shows a singularity of new type as (ω-ω′)^?1, whereω-ω′ is the energy transfer between the two electrons. Both parts have been calculated in logarithmic approximation. Inspite of the fact that the second one is found to be lower by one order of the typical logarithmic Kondo terms than the first one, both terms can be of the same order of magnitude. Studying the superconducting transition temperature Abrikosov and Gor'kov's calculation is extended to include these interactions in any order of perturbation theory keeping the leading logarithmic terms. Our results are restricted to the temperature region well above the Kondo temperature. Considering the decrease of the superconducting transition temperature due to the magnetic impurities in the antiferromagnetic case the effect of the elastic scattering can be essentially reduced by the inelastic one.