Practical calculation of amplitudes for electron-impact ionization

An integral expression that is formally valid only for short-range potentials is applied to the problem of calculating the amplitude for electron-impact ionization. It is found that this expression provides a practical and accurate path to the calculation of singly differential cross sections for electron-impact ionization. Calculations are presented for the Temkin-Poet and collinear models for ionization of hydrogen by electron impact. An extension of the finite-element approach using the discrete-variable representation, appropriate for potentials with discontinuous derivatives like the Temkin-Poet interaction, is also presented.