  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.
