Using plane waves to describe the incident and scattered particles, and screened hydrogenic and Coulomb functions to describe the atomic electrons before and after ejections, we have calculated the differential and total ionization cross sections of 11 atoms and one ion by electron impact, and ionization of helium by proton impact. The effective charges of the screened hydrogenic functions are fixed by the Hartree-Fock calculations. Calculations have been carried out for the atomic $s$, $p$, and $d$ electrons. For low atomic numbers we find reasonable agreement with the experimental data. For intermediate atomic numbers we expect our results to overestimate the actual cross sections, since our choice of a unit charge for the Coulomb function of the ejected electrons will overestimate the atomic dipole potential strength, and in turn the high-energy cross sections. Our results agree closely with the calculational results of Peach, based on a model similar to ours except that the atomic electrons before ejections are described by the Hartree-Fock wave functions. For intermediate atomic numbers and inert gases, the calculated results of McGuire seems to agree better with the experimental data compared to other calculations. The advantage of the method presented here is that the ionization amplitude is given in analytic form. This may allow further analysis on this amplitude, and facilitates extension of the numerical integration for the cross section to high impact energies. We have also given some cross sections for the production of doubly charged ions due to the single ionization.

• Received 5 May 1971

DOI:https://doi.org/10.1103/PhysRevA.5.1174