A general and powerful formalism has been developed for computation of energy-loss spectra of penetrating charged particles in the presence of charge exchange. Options on the input side are the cross sections for electron capture and loss, transition rates for radiative and nonradiative spontaneous processes and their associated energy losses or gains, and finally, cross sections for all processes that contribute to particle stopping but are not associated with charge exchange. The formalism generates an n × n transfer matrix, where n is the number of states needed for an adequate description of the projectile under consideration. This matrix delivers the joint distribution of energy loss and exit charge state for a given incident charge state and energy.

The formalism can be used in principle as an alternative for Monte Carlo simulation, but until now we have concentrated on direct evaluation of key experimental parameters related to the energy-loss spectrum integrated over all exit charge states, in particular, mean energy loss, straggling, and skewness. Generally, valid analytic expressions have been found for these quantities, each of which can be separated into a stationary term representing chargestate equilibrium and a transient depending on the incident charge state. A brief survey is given of current analytic and numerical efforts addressing other experimental parameters.