A general perturbation method for solving the Smoluchowski equation with an arbitary but weak potential is presented. The perturbation scheme has a predictable applicability and accuracy and yields both the scavenging free rate of recombinationR(t), its Laplace transform quest;(s), and the full probability distribution. The uniform convergence of the perturbation series depends on the rsquo;rsquo;strengthrsquo;rsquo; of the potential, a quantity which is uniquely defined by a convergence criterion. However, the method is applicable to most potentials, for sufficiently small times. Also derived are expressions which give upper bounds to the perturbation error. A derived rsquo;rsquo;pseudoinfinitenth orderrsquo;rsquo; perturbation expression improves the accuracy of the perturbation calculation in cases where the convergence is slow; for those cases it gives an accuracy corresponding to an (n+1)th order perturbation calculation but requires calculation ofnth order quantities only. The method is applied to a Coulomb and a shielded Coulomb potential and closed form expressions are obtained for the first order quantities.
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