Energy relaxation in a superconductor with magnetic impurities

In a superconductor with magnetic impurities, Kondo scattering results in the formation of localized states inside the superconducting gap. We show that inelastic electronic transitions involving quasiparticle scattering into and out of the localized states may result in significant changes in the non-equilibrium properties of the superconductor. Using the model of Muller-Hartmann and Zittartz for the extreme dilute limit, and including both deformation potential and spin-lattice coupling, we have calculated the rates of such inelastic transitions between continuum and discrete states, and shown that they may greatly modify quasiparticle interactions. The individual processes are: quasiparticle trapping into discrete states, enhanced recombination with localized quasiparticles, and pair breaking and de-trapping of localized quasiparticles by sub-gap phonons. We find that all these processes give rise to clearly distinguishable temperature dependences of the kinetic parameters.