Analytical formula for electron-impact ionization cross section in the one Coulomb wave model

In the framework of the one Coulomb wave model, an analytical formula is derived for the triple differential cross section for the ionization of atomic target by electron impact. Both the direct and exchange terms of the transition amplitude are considered. The exchange term is calculated in the present work. However, the direct term is deduced from our previous work (Sahlaoui and Bouamoud. Can. J. Phys. 88, 905 (2010)). The obtained results can be used to compute the transition amplitude defined in others models, as for example, the distorted wave Born approximation and the Coulomb two-wave model. The mathematical techniques developed here can be also used to compute other complicated integrals that can be encountered in atomic physics and quantum chemistry. (author)