A numerical method is presented for the solution of the Smoluchowski equation describing the diffusion and reaction of an isolated ion pair in a dielectric medium in the presence of a scavenger. The method provides upper and lower bounds to the exact solution and a practical means for improving these bounds. A quantitative understanding of the neutralization and scavenging processes associated with isolated charge pairs is now demonstrated to be possible. This holds for all times and for all scavenger concentrations. Calculations are performed for various initial separations of the ion pair, and the results are compared with the scavenging experiments of Schuler et al. A comparison is also made with the results obtained by the method of ``prescribed diffusion.''
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Abell et al. (1972) studied this question.