STATISTICAL-THEORY OF CHARGED-PARTICLE STOPPING AND STRAGGLING IN THE PRESENCE OF CHARGE-EXCHANGE

General expressions have been derived for the mean energy loss and straggling of a heavy charged particle penetrating through a thin slice of matter. The main input parameter is a differential energy loss rate that allows for transitions within an arbitrary number of projectile states. Both spontaneous and collision-induced events are potentially included, but different events are assumed statistically independent. Asymptotically, the mean energy loss is shown to approach a linear dependence on time or path length. The slope is given by the equilibrium energy loss rate, and the intercept at zero path length depends on the incident projectile state. Energy-loss straggling can be split into a collisional part and a contribution from variations in projectile state. The latter turns out to be related to the intercept in the mean energy loss for the pertinent projectile states. Previous results applying to a two-state system have been generalized to an arbitrary number of states. A full evaluation has been presented for a three-state system. A procedure is outlined that allows to empirically determine the magnitude of charge-exchange straggling.