QUASI-PARTICLE RELAXATION RATES IN A SPATIALLY INHOMOGENEOUS SUPERCONDUCTOR

Effective quasi-particle relaxation rates in reduced pp regions of a dirty superconductor (S) at low temperatures are calculated from microscopic theory. Gap reduction in S caused by a proximity layer (S') with lower critical temperature is modeled by an effective trapping layer with zero gap and an effective thickness L(eff)/xi(S), which is a function of the proximity parameter gamma(M) = (sigma(S),xi(S)/sigma(S)xi(S),)(d(S),/xi(S)). The total rate is the sum of the rate of the reduced gap region and of the proximity layer. The effective trapping volume of the core of an Abrikosov vortex, which is trapped in the superconductor, is a cylinder with radius R(eff) almost-equal-to 2.7xi(S) and zero gap.