Scaling and formulary of cross-sections for ion-atom impact ionization

The values of ion-atom ionization and stripping cross-sections are frequently needed for many applications that utilize the propagation of fast ions through matter. When experimental data and theoretical calculations are not available, approximate formulae are frequently used. This paper briefly summarizes the most important theoretical results and approaches to cross-section calculations in order to place the discussion in historical perspective and offer a concise introduction to the topic. Based on experimental data and theoretical predictions, a new fit for ionization cross-sections is proposed. The range of validity and accuracy of several frequently used approximations (classical trajectory, the Born approximation, and so forth) are discussed using, as examples, the ionization cross-sections of hydrogen and helium atoms by various fully stripped ions. A formulary of analytical approximations for cross-sections is presented.