Inelastic scattering of low-energy electrons in liquid water computed from optical-data models of the Bethe surface

We provide a short overview of optical-data models for the description of inelastic scattering of low-energy electrons (10-10,000 eV) in liquid water. The effect on the inelastic scattering cross section due to different optical data and extension algorithms is examined with emphasis on some recent developments.

The optical-data method whereby experimental optical data and theoretical extension algorithms are used to describe the dependence of the dielectric response function on energy- and momentum-transfer and obtain the Bethe surface of the material, currently represents the most used method for computing the inelastic scattering of low-energy electrons in condensed media. Two sets of experimental optical data for liquid water obtained from reflectance and inelastic X-ray scattering spectroscopy, respectively, and the extension algorithms of Ritchie, Penn, and Ashley are examined. Recent developments are discussed along with the role of corrections to the random phase approximation (RPA) of electron gas theory.

The inelastic scattering cross section in the energy range 200-10,000 eV was found to be rather insensitive (to within 10%) to the choice of optical data or the extension algorithm. In contrast, differences between model calculations increase rapidly below 200 eV with the influence of the extension algorithm being dominant.

The choice of the extension algorithm used to extrapolate optical data to finite momentum transfer and obtain the Bethe surface is crucial in modelling the inelastic scattering of electrons with energies below 200 eV. A new set of measurements on the dielectric response function of liquid water beyond the optical limit and the development of extension algorithms that will go beyond RPA by considering the effect of (short-range) electron exchange and correlation should be of some priority.