Some time ago, Wilemski and Fixman suggested an approximate method for calculating reaction rates for diffusionhyphen;controlled reactions. Their derivation contains a factorization assumption that makes it difficult to see how to derive higher order corrections systematically. In this paper, we assume that the reaction term can be regarded as small in a suitable sense, and develop a systematic perturbation analysis that yields the Wilemskindash;Fixman approximation in lowest order. This identification will be shown to imply that the Wilemskindash;Fixman approximation corresponds to a factorization of the resulting multiple integrals in a specific way. It will be shown that for a single localized reaction term (i.e., a delta function sink), the Wilemskindash;Fixman approximation leads to an exact expression for survival probability as a function of time, but the original factorizationansatzused by these authors is violated. We also develop a theory not making use of the restrictive assumption that the initial condition corresponds to an equilibrium density in the absence of reaction. Finally, we develop an exactly solvable model with a nonlocal reaction term against which the approximation can be tested.
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