Asymptotic analysis of diffusion-influenced kinetics with a potential

A transformation is introduced and used to formulate a series of approximations for the time-dependent diffusion-controlled geminate reaction probability. Each approximation has the properties of a probability distribution function. The implications of the approximations are analyzed by use of established relationships to give corresponding approximations for the geminate reaction probability with a radiation boundary condition and for the time-dependent rate coefficient with a Boltzmann initial concentration profile. The first-order approximation, which holds when the interparticle forces are weak, is applied to the recombination of ions in an aqueous solution of a strong electrolyte; its accuracy is assessed by comparison with numerical results.