  The values of ion-atom ionization 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 formulas 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.
