Green’s function calculation of electron spin polarization. I. Gyroscopic model formalism

Abstract

A gyroscopic model representation of chemically induced electron spin polarization (CIDEP) is advantageous in high magnetic fields where the ST0 approximation is valid. It reduces the dimension of the set of basic equations and separates different physical behaviors into separate quantities. We generalize the gyroscopic model to cover arbitrary recombination and dephasing rates of the radicals. By application of the Green’s function technique we derive general fundamental expressions for the stationary polarization without introducing any of the usual simplifying assumptions of the radical pair system, such as spherical symmetry or short range interactions. These expressions show which Green’s functions and what values are needed for an actual calculation of CIDEP. The expressions can be applied to a wide class of radical pair systems and they form an exact foundation for the development of systematic and consistent approximation schemes. The general results are applied to an assumed delta function exchange interaction and an exact expression for polarization generated in free diffusion is derived. The applicability of this expression to short range exchange interactions is investigated.