Theory of thin proximity-effect sandwiches. II. Effects ofs-wave elastic scattering

We show that Anderson's theorem concerning $s$-wave elastic scattering is inapplicable to certain types of inhomogeneous superconductors. The example of a proximity-effect sandwich consisting of a thin normal ($N$) metal in perfect contact with a thick superconducting ($S$) metal is considered in detail. The proper treatment of $s$-wave elastic scattering in the $N$ metal is developed. Previously inexplicable experimental results on tunneling into $\mathrm{NS}$ sandwiches are found to be understandable in terms of the theory presented.