Recombination yield of geminate radical pairs in low magnetic fields - A Green's function method

An analytic expression for the recombination yield of a geminate radical pair with a single spin one half nuclei is derived. The expression is valid for any field strength of the static magnetic field. It is assumed that the spin mixing is caused solely by the hyperfine interaction of the nuclear spin and the difference in Zeeman energies of the two radical partners, that the recombination occurs at the distance of closest approach, and that there is a locally strong dephasing at contact. This is a special result of a new general approach where a Green's function technique is used to recast the stochastic Liouville equation into a low dimensional matrix equation that is particularly convenient for locally strong dephasing systems. The equation is expressed in terms of special values (determined by the magnetic parameters) of the Green's function for the relative motion of the radicals and it is therefore valid for any motional model, e.g. diffusion, one and two site models. The applicability of the strong dephasing approximation is illustrated by comparison with numerical exact results.