Diffusion coefficients and collision probabilities for annular regions of low optical thickness II: the general case

Collision probability theory has been used to calculate neutronics parameters in nuclear reactors for many years, although it has long been suspected that this technique breaks down in the presence of material voids. In this work, the circumstances under which the breakdown of the probability theory occurs is first carefully determined, to be followed by an excruciatingly detailed explanation showing how to cure the problem mathematically, and how to verify that the remedy is operating properly. Once cured, it becomes possible to more accurately calculate parameters, such as directed di€usion coecients, that are important to reactor analysis, par- ticularly in the estimation of reactivity coecients. Such calculations are performed here as a demonstration of the significance of the old and new mathematical methods to problems of practical interest. The most significant parameter investigated is a comparison of void reactivity in the presence of leakage by an experimental version of the lattice cell code WIMS-AECL using the old and new methods