An analytic description of the influence of rf-magnetic fields on radical pair reactions in a strong static field

Accurate expressions are derived for the effect of a radiofrequency (rf) field on the reaction yield of a radical pair (RP). We consider the recombination yield of a geminate RP under the influence of a static magnetic field in combination with a radio frequency field perpendicular to the static field. The results are obtained by solving the steady state stochastic Liouville equation by an approximation scheme introduced in our previous work [M.J. Hansen, J.B. Pedersen, Chem. Phys. Lett. 361 (2002) 219]. The general formula is expressed in terms of a characteristic function for the relative motion of the radical pair. It can thus be applied to a wide range of systems, e.g. confined and low dimensional systems of biochemical interest, such as micelles and membranes. Explicit analytical expressions are given for free diffusion. The expressions are directly applicable to RYDMR spectra since the static magnetic field is assumed to be larger than the hyperfine interaction. The high accuracy of the expressions is illustrated by comparison with numerically exact results.