Analytic solution of the stochastic-Liouville model of spin exchange

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Abstract
An analytic solution is obtained for the stochastic‐Liouville model of spin exchange between a pair of radicals undergoing isotropic diffusion in solution and interacting via an exchange interaction that decays exponentialy with radical separation. The resulting spin exchange cross section is the sum of a ‘‘strong encounter’’ term that is approximately equal to the biomolecular reaction cross section and a ‘‘grazing encounter’’ term that is due to encounters in the tail of the exchange interaction. The latter term may range from negligible to twice the former term for plausible values of the diffusion rate and the range of the exchange interaction. It is shown that the theory combined with experimental data on the spin‐exchange contribution to spin–lattice relaxation can provide an estimate of the range of the exchange interaction between two radicals.