Anomalies of the Schwinger phase shifts in the static exchange approximation

The Schwinger variational method is applied to the static exchange approximation of the electron–hydrogen-atom scattering. Spurious singularities are encountered in singlet scattering processes. The position of the poles is investigated by a simple numerical procedure. Anomalous poles appear in narrow regions of the nonlinear scale parameter. Results are presented which illustrate the behavior of the phase shifts around the spurious poles. No Kohn-type anomalies are encountered in the triplet case. As a byproduct, it is discussed that the Schwinger formula may be approximated in a separable form which is relatively simple but not free of anomalies.