Green’s function calculation of electron spin polarization. II. Approximation schemes

Abstract

We present two approximation schemes to the previously derived Green’s function method that utilizes a gyroscopic representation of the spin state. First a consistent approximation scheme is developed in which the exact equations are expanded in terms of the small parameter lx/d, where lx is the decay length of the exchange interaction and d is the distance of closest approach. A general and explicit expression, correct to first order in the expansion parameter, is derived for spherical symmetric systems. Secondly, we introduce a modified kinematic approximation which for the first time accounts for recombination and dephasing processes. We show that for spherically symmetric systems the results of the modified kinematic approximation is equivalent to the first order results. This equivalence constitutes the first formal proof of the validity of a kinematic approximation. The derived expression depends only on the magnitude and decay length of the exchange interaction, the recombination and dephasing rate constants, and on the free Green’s function. The problem of calculating electron spin polarization (CIDEP) is thus reduced to a calculation of the free Green’s function, which describes the relative motion of the radicals in the absence of recombination.