Empirical formula for cross section of direct electron-impact ionization of ions

Plasma ionization composition and level population calculations require, in particular, the cross sections of direct ionization from each quantum state into each state which may be generated by means of removal of any electron. We analysed published data and propose here an empirical formula for cross sections of direct electron-impact ionization of positive atomic ions. The cross sections given by this formula are in satisfactory agreement with those calculated in the distorted-wave (DW) approximation; therefore, we believe that for any direct state-to-state ionization channel this formula provides a reasonably accurate prediction of the DW result. Comparisons with published data and with the Lotz formula are reported as well.