Frozen-charge stopping of ions in the Bethe regime

Abstract

Analysis of energy losses resolved in ion charge state requires atomistic input that separates frozen-charge stopping from that due to charge-changing events. Adequate theoretical formalism is based upon a stopping matrix whose diagonal elements determine the frozen-charge stopping forces, while off-diagonal ones are associated with projectile ionization or electron capture. Following a brief outline of the stopping-matrix formalism, the paper aims to establish simple but rigorous formulae for frozen-charge stopping of partially stripped ions. Based upon first-order quantal perturbation, an attempt is made to account for all relevant contributions including those associated with excitation of a penetrating ion; meanwhile, the terms due to projectile ionization are consistently excluded from frozen-charge stopping. General high-velocity formulae for the frozen-charge stopping force are found that reduce nontrivial features to a single parameter characteristic for a projectile–target combination; this leads to a simple rule for extrapolation of experimental data in velocity. Simple and explicit analytical formulae for all contributions are found for projectiles carrying one or two electrons. Comparative magnitudes of various contributions are discussed, examplified by estimates pertaining to recent experiments by Ogawa and coworkers.