Accurate electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range based on an improved dielectric description of the Bethe surface

Electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range are presented based on a recently developed dielectric response model for liquid water (D. Emfietzoglou, F. Cucinotta and H. Nikjoo, Radiat. Res. 164, 202-211, 2005) that is consistent with the experimental data over the whole energy-momentum plane. Both exchange and second-order Born corrections are included in a material-specific way using the dielectric functions of liquid water. The numerical results are fitted by simple analytic functions to facilitate their further use. Compared to previous studies, differential cross sections are shifted toward smaller energy losses resulting in smaller inelastic and stopping cross sections with differences reaching, on average, the approximately 20% and approximately 50% level, respectively. Contrary to higher energies, it is shown that the dispersion model for the momentum dependence of the dielectric functions (Bethe ridge) is as important as the optical model used. Within the accuracy of the experimental data (a few percent) upon which our dielectric model is based, the calculations are "exact" to first order, while the uncertainty of the results beyond first order is estimated at the 5-10% level. The present work overcomes the limitations of Bethe's theory at low energies by a self-consistent account of inner-shell effects and may serve to extend the ICRU electron stopping power database for liquid water down to 100 eV with a level of uncertainty similar to that for the higher-energy values.