Absolute and scaled electron-impact ionization cross-sections for hydrogen-, helium-, and lithium-like ions

Scaling laws and semiempirical methods can be powerful tools to predict electron-impact ionization cross-section data for modelling purposes and many other practical applications where a quick estimate of a large number of reasonably accurate cross-sections in analytical form is needed. Scaling laws can also be useful for the prediction of cross-section values for targets for which no experimental data or rigorous theoretical calculations are available. This paper describes the development of a new scaling law for electron-impact ionization cross-sections of hydrogen-, helium-, and lithium-like atomic targets based on the semiclassical Deutsch-Märk (DM) formalism. We show that the DM approach provides quantitative justification for a scaling law similar to the widely used Z⁴ scaling law for hydrogen-like targets (where Z is the nuclear charge) and that a new scaling law for the calculation of absolute ionization cross-sections for other isoelectronic sequences can be derived in the framework of the DM formalism. A detailed comparison of scaled and absolute cross-section estimates based on this scaling law with available experimental data is made.