An exact relation for the reactivity dependence of the recombination probability in the presence of a scavenger is derived. For a spherical symmetric system with a uniformly distributed scavenger this relation expresses the partially diffusion controlled recombination probability in terms of the totally diffusion controlled recombination probability. The relation is valid for a space-dependent diffusion coefficient and for an arbitrary potential energy between the particles. The relation is proved only for a three-dimensional system, but it appears to be valid also for one- and two-dimensional systems.
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J. Boiden Pedersen (1980) studied this question.
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