s-d Exchange lnteractjlon in a Superconductor

The scattering of a quasiparticle in a superconductor due to a magnetic impurity is calculated by a perturbation method. It is shown that the ratio of the dominant contribution of the successive order of terms in the perturbation series is given at T=O by the ratio 2J p log (2D/t:1) where p is the density of state at the Fermi surface divided by the number of atoms in the superconductor, J is the magnitude of the s-d exchange interaction, 2D is the band width, and t:1 is the energy gap. If this ratio is greater than one, the perturbation series does not converge. This is connected with the existence of a bound state attached to the impurity atom. Following Yosida's theory on the bound state due to the s-d interaction in a normal metal, we examine the possibility of a bound state in a superconductor. It is shown that, if the s-d interaction is antiferromagnetic and stronger than the pairing interaction, a bound state is formed around the impurity spin, and that, if it is weaker, an excited level appears in the energy gap irrespective of the sign of the interaction. The condition for the existence of the bound state is found to be the same as the 'condition for the divergence of the perturbation series mentioned above. The effect on the density of states of quasiparticles at finite concentration of magnetic impurities is briefly discussed