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The time-dependent Smoluchowski equation with a Coulomb potential is solved analytically for a general boundary condition, and expressions for the distribution function, reaction rate, and survival probability are given. The expressions are evaluated numerically and the long-time behavior is derived. The theoretical results apply to experiments involving ion recombination without an electric field (or where there is a time delay in the application of the field), to scavenging experiments, and to fluorescence quenching.
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Hong et al. (1978) studied this question.
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