Threshold ionization of atoms by electron and positron impact

In two recent letters results for threshold ionization of hydrogen by electron impact (Rost, J.M. 1994 Phys. Rev. Lett. 72 1998) and positron impact (Rost, J.M. and Heller, E.J. 1994 Phys. Rev. A 49 R4289) were communicated. The results were obtained by calculating the S-matrix semiclassically in Feynman's path integral formalism. This paper gives a more complete account of the theoretical method. Moreover, it is shown how the ionization cross section of atomic targets other than hydrogen can be expressed with the hydrogen cross section through a scaling relation. This demonstrates the universality of the threshold behaviour.