The Origin and Limitation of the Universal Nature of the Direct Ionization of Atoms

The dependence of the direct ionization cross section on a single scaled velocity variable makes ionization of a given subshell a universal phenomenon common to all particle-atom Coulomb ionization collisions. Constructing universal plots of a wide range of data has led to a refined description of the direct Coulomb ionization process. The sources of this universality lie in the PWBA, the lower limit of the momentum transfer and a description of the atomic states which has a scaling length. Universality is exact in the low velocity limit but the cross section develops a parametric dependence on the target binding energy as velocity increases. This dependence is usually ignored, but for some cases it is significant.