A stochastic theory of particle transport. II

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Abstract
For pt.I see Proc. R. Soc., A358, p.105 (1977). The authors are concerned with the development of radiation damage cascades initiated by fast incident particles. They derive a general probability balance equation for the number of vacancies and interstitials in given regions of space, subject to an initial atom of specified velocity. The scattering model is quite general but they do employ the radiation damage model due to Kinchin and Pease (1955). Introduction of a generating function enables the various moments of the vacancy and interstitial distributions to be obtained. Explicit equations for the vacancy and interstitial densities and their two particle correlation functions are derived. They introduce the straight-ahead approximation and solve the resulting density equations by Laplace transform. Explicit expressions are obtained for the two densities over the complete space and energy range. Calculations show the existence of a vacancy rich region near the point of origin of the cascade. The proportionality of the size of the vacancy rich zone to the logarithm of the incident energy is noted and a useful semi-empirical formula is obtained.

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