Collision probabilities in spatially stochastic media

Formulae are obtained for the mean value of the collision probability in a spatially stochastic medium using two types of statistical averaging; the dichotomic Markov process and the binomial model. Numerical results are obtained for a slab and a sphere and compared with those obtained by using an averaged cross-section in the standard deterministic model. Significant deviations are noted between the results arising from the statistical models and with those from the deterministic case. Thus it is clear that, in particular circumstances, the use of the appropriate statistical model is essential.