Electron ionization cross-section calculations for liquid water at high impact energies

Cross-sections for the ionization of liquid water is perhaps the most essential set of data needed for modeling electron transport in biological matter. The complexity of ab initio calculations for any multi-electron target has led to largely heuristic semi-empirical models which take advantage elements of the Bethe, dielectric and binary collision theories. In this work we present various theoretical models for calculating total ionization cross-sections (TICSs) for liquid water over the 10 keV–1 MeV electron energy range. In particular, we extend our recent dielectric model calculations for liquid water to relativistic energies using both the appropriate kinematic corrections and the transverse part. Comparisons are made with widely used atomic and molecular TICS models such as those of Khare and co-workers, Kim–Rudd, Deutsch–Märk, Vriens and Gryzinski. The required dipole oscillator strength was provided by our recent optical-data model which is based on the latest experimental data for liquid water. The TICSs computed by the above models differ by up to 40% from the dielectric results. The best agreement (to within ∼10%) was obtained by Khare’s original model and an approximate form of Gryzinski’s model. In contrast, the binary-encounter-dipole (BED) models of both Kim–Rudd and Khare and co-workers resulted in ∼10–20% higher TICS values, while discrepancies increased to ∼30–40% when their simpler binary-encounter-Bethe (BEB) versions were used. Finally, we discuss to what extent the accuracy of the TICS is indicative of the reliability of the underlying differential cross-sections.