Effects of intrinsic inelastic scattering on the critical current of a Josephson junction

It is shown that inelastic scattering suffered by tunneling electrons in the barrier of an S-I-S Josephson junction can lead to a remarkable nonmonotonic temperature dependence of the critical current of the structure. The understanding of this effect rests on the fact that under suitable conditions the inevitable loss of coherence can be more than compensated by a temperature-dependent exponential enhancement of the pair tunneling probability.