The solution to a multichannel Bethe potential and its application to pion-nucleus reactions

We solve a radial Schr\"odinger equation for the case of a multichannel square well plus an exponential potential in one of the channels. The solution is obtained by summing exactly the infinite terms of the perturbative series for the evolution operator of the system. Analytical expressions for the scattering matrix and the scattering length are given, a Deser-like formula which connects approximate ground energies and scattering length is obtained for a particular case. Possible physical applications of these results are discussed briefly.