Electronic stopping power of liquid water for protons down to the Bragg peak

An improved dielectric response model that accurately represents the recent experimental data for liquid water over the whole Bethe surface is used to calculate the electronic stopping power of protons (of fixed-charge) in liquid water from several MeV down to the Bragg peak region. The results are by approximately 20% lower than the ICRU values and earlier studies. A shell-correction term with a contribution of 15-20% to Bethe's high-energy stopping number is obtained. The present work offers a first-principle approach for stopping power calculations that overcomes the well-known limitations of Bethe's stopping theory, namely, the need for separate determination of the mean excitation energy (the I-value) and the shell-corrections. In particular, all type of inner-shell effects are built into the model through the kinematically restricted integrals over the Bethe surface. The net contribution of higher-order corrections is found to be minimal over most of the present range. Thus, within the uncertainty of the dielectric model (few %) the present calculations are 'exact' down to approximately 100 keV.