Inelastic cross-sections of energetic protons in liquid water calculated by model dielectric functions and optical data

Abstract

Total and differential inelastic inverse-mean-free-paths for the energy loss of protons in liquid water are calculated on the basis of the dielectric approach. Energetic protons, much above the Bragg peak, are considered where the first-Born-approximation is justified (∼0.3–10 MeV). A model dielectric-response-function for the valence electrons of liquid water is constructed in accordance with the general properties of the Bethe-surface. A modified Drude-expansion model developed earlier provided the long-wavelength response, whereas several dispersion schemes were examined for introducing the momentum-transfer dependence. In particular, we have examined the δ-oscillator dispersion models of Ashley and Liljequist, and Ritchie’s extended-Drude models. A comparison with optical dielectric models will also be presented for assessing the influence of the dispersion. In view of the limited experimental information for the inelastic properties of liquid water, the present work provides a comparative study of various – computationally tractable – schemes that may be used in analog Monte Carlo transport codes for protons and heavier ions in liquid water.