Analysis of charge-dependent stopping of swift ions

Rigorous expressions have been derived for the mean energy loss of ions penetrating through foils, specified into entrance and exit charge states. These expressions allow extraction of partial stopping cross sections and charge-exchange cross sections in solids from measured energy losses versus foil thickness. Particular attention is given to thin penetrated layers and the opposite limit of charge-state equilibrium which may be easier to deal with experimentally. Sum rules to be obeyed by measured parameters have been derived. Explicit results have been listed for the two-state case.