Inelastic cross-sections for electron transport in liquid water: a comparison of dielectric models

Abstract

Various methodologies for constructing inelastic cross-sections for low-energy (<10 keV) electron transport in liquid water are presented and compared. They are all based on an optical-data model which provides the dependence on energy loss, and a dispersion algorithm which incorporates the momentum-transfer dependence. A Drude dielectric model was used to analytically represent the optical data. Various dispersion schemes were examined: the Bethe approximation, the δ-oscillator models of Ashley and Liljequist, and two forms of Ritchie's extended-Drude model. They all have been used in Monte-Carlo (MC) codes for analog electron transport in the condensed phase. Results in the form of differential and total inelastic cross-sections are presented. Where possible, comparisons with results of other studies are made. It was found that, despite the application of general constraints (e.g. sum rules), the optical model has a notable influence on the single-collision energy loss spectrum. In addition, both the shape and peak position of the total and differential cross-section distributions depend strongly on the dispersion model adopted. The work is particularly relevant to the development of event-by-event MC transport codes for liquid water, as well as, to the calculations of stopping-powers below the range of applicability of Bethe's formula.