Further study of a new dispersion relation for electron-atom scattering

A new recently proposed dispersion relation (DR) [Temkin, Bhatia, and Kim, J. Phys. B 19, L707 (1986)] is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore we start to investigate the analytic structure of the difference amplitude, previously assumed to be nonsingular, on the negative scattering energy axis. Even under severe approximations we find that the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering. We conclude with some brief general remarks on this problem.