A semiclassical S‐Matrix theory is described for electron–atom or electron–ion scattering. The development of semiclassical approximations is briefly reviewed and the justification for semiclassical perspectives in electronic problems is discussed and contrasted with the situation of nucleus–nucleus scattering. Special properties of classicalN–electron atoms are derived. On their basis quantitative results are presented for electron and positron impact ionization of hydrogen close to threshold. ©1995 American Institute of Physics.