Integral representation for the Glauber scattering amplitude for direct Coulomb ionization by charged particles

An integral representation is developed for the scattering amplitude for ionization by charged particles in the Glauber approximation. Unlike previous results based on a series expansion in the momentum of the ejected electron, ${\overrightarrow{\mathrm{k}}}_e$, the present results are rigorously convergent for all physical values of ${\overrightarrow{\mathrm{k}}}_e$. Results calculated by this method agree with earlier results for ionization of atomic hydrogen by electron impact using Padé approximants to approximately sum the series. Total cross sections for the ionization of atomic hydrogen by proton impact are presented and compared to experimental data. This technique is applicable to the ionization of neutral atoms whose participating electron is represented by a hydrogenic wave function, and the remaining electrons are ignored.