Approximate Solutions to the Diffusion-Kinetic Equations

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Abstract
The partial differential diffusion-kinetic equations describing the diffusion and reaction of chemically active species along the tracks of ionizing radiation are discussed. The few limiting cases of these equations that possess exact analytic solutions form the basis for a general expansion of the probability densities of reactive species in terms of time-dependent Gaussian distribution functions. In this expansion, the familiar prescribed diffusion hypothesis of Samuel and Magee appears as the first-order approximation. The convergence of the expansion technique and its applicability to multiradical reaction mechanisms are illustrated by means of example calculations. One of the chief advantages of the method introduced is that it allows the work of Ganguly and Magee on overlapping spherical spurs to be extended to multiradical models.