On the Poles of the S Matrix for Long-Range Potentials

The analytic properties in the complex k plane of the S matrix for scattering by a screened Coulomb potential are studied. Particular attention is given to the limit as the screening radius tends to infinity, so as to show, in an explicit example, the effect of the tail of the potential on the properties of the analytically extended S matrix. It is shown that the pole configuration obtained in this way is different from that obtained in the usual description of the analytic properties of the Coulomb S matrix.