Green's function calculation of radical pair recombination: I. Gyroscopic model formalism

A general gyroscopic model description of radical pair recombination in high magnetic fields is formulated. Recombination is allowed to occur simultaneously from the singlet and triplet states. The description is valid for any diffusion model, symmetry of the system, and exchange interaction, as well as for any rate of recombination, dephasing, intra-radical relaxation, and singlet-triplet mixing. By use of Green's function technique we derive general fundamental expressions for the stationary recombination probability for spherical symmetric systems with contact recombination. These general expressions can be applied to a wide class of radical pair systems and they form an exact foundation for development of systematic and consistent approximation schemes. It is shown that the recombination and escape yields for any combination of reactive channels and precursor spin states can be calculated from the singlet recombination yield for a triplet precursor. The general results are applied to a locally weak exchange interaction and explicit expressions are derived for the recombination probability in terms of contact values of the Green's function for the relative motion of the radical partners. The resulting expressions can be adopted to experimental situations by inserting the required values for the adopted diffusion model.