Anomalous Scattering by Magnetic Impurities in Superconductors

The effect of magnetic impurities in superconductors is studied by using the dispersion equations, which are simple extensions of those introduced by Suhl. In the case of a single impurity, we find that, if $T_{c0\mathrm{}}>T_r$ (where $T_{c0\mathrm{}}$ is the superconducting transition temperature and $T_r$ is the Suhl-Abrikosov resonance temperature), a pair of bound states appear in the energy gap, while if $T_{c0\mathrm{}}<T_r$, resonances appear at low temperatures. Also, self-consistent equations are constructed to treat the case of dilute concentration of impurity atoms. In the gapless region it is established that the Abrikosov-Gor'kov expressions are valid, except that ${\tau }_s$ in their theory must be replaced by the exact frequency-dependent spin-flip lifetime ${\tau }_s\left(\omega \right)$ in the normal state.