Threshold behavior and isotope effect in low-energy electronic stopping of light ions

Electronic excitation of an atom by an ion in the energy regime below $∼20$ keV/u can be strongly coupled with elastic scattering. This feature may cause noticeable deviations in the energy loss of light ions such as protons and deuterons from velocity-proportionality and is found to be an essential ingredient in the understanding of the stopping behavior near the threshold. We have incorporated this effect into the PASS stopping code and, in this way, expanded the range of validity of the code down to around 1 keV/u. Comparison of calculated with measured stopping cross sections for protons in Ag, Au, Cu, and Ni shows good agreement with recent data that deviate dramatically from the commonly assumed velocity proportionality. Most of these data were determined by the analysis of reflected-ion spectra. Computation of reflected-ion spectra with energy-loss functions from PASS leads to good agreement with measured spectra. A direct consequence of the coupling with elastic collisions is isotope dependence of the electronic-stopping cross section. Conventional stopping theory denies the existence of a significant isotope effect. Present calculations suggest an effect in the 1–10% range for hydrogen in Si at energies around and below 10 keV/u. This is found to be compatible with experimental data.