Statistics of energy loss and charge exchange of penetrating particles: Higher moments and transients

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Abstract
Recent work on mean energy loss and straggling of ions in the presence of charge exchange has been extended to higher moments. The transient behavior of charge-exchange straggling has been determined as well as the skewness of the energy-loss profile. Formulas have been found for the two- and three-state cases where terms that have been well known in principle could also be written in a way that illustrates their respective origin. In addition to the frequently analyzed case of negligible energy loss in charge-changing events, we also mention explicitly the opposite situation where all energy loss is associated with charge exchange. The role of transients and skewness is very different in the two extremes. As in a previous paper by one of us, the notation has been kept general such as to allow for both collisional and spontaneous events, and no distinction needs to be made between charge exchange and change of excitation state. Finally we compare our calculations to recently obtained experimental results.