Recoil numbers, particle densities and reaction yields in linear atomic collision cascades

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Abstract
A comprehensive scheme is outlined for the calculation of statistical distribution functions relevant in the theory of random linear collision cascades. It is shown that the relevant one-particle densities as well as the conservation laws for energy and momentum can be expressed in terms of the time-integrated particle density or slo wing-down density. An essential feature of the theory is the trapping probability for scattered and recoiling collision partners, respectively. Explicit expressions have been derived mainly for step-like trapping probabilities q with 0 ≤ q ≤ 1, and explicit applications include the yields of focused collision sequences, displacement and replacement. Substantial errors in previous estimates of focuson yields are pointed out.