Kondo Effect in Superconductors

A self-consistent treatment of the Kondo scattering of conduction electrons from magnetic impurities is presented in order to treat finite concentrations of such impurities in superconductors. The present theory leads to a concentration dependence for the transition temperature which differs markedly from the Abrikosov-Gor'kov result. The theory appears to account nicely for various experimental results. We also find that superconductivity, under certain circumstances, does not exist at all temperatures below $T_c$.