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

We present two approximation schemes to the previously derived Green's func tion method that utilizes a gyroscopic representation of the spin state. Fi rst a consistent approximation scheme is developed in which the exact equat ions are expanded in terms of the small parameter l(x)/d, where l(x) 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 ac counts for recombination and dephasing processes. We show that for spherica lly symmetric systems the results of the modified kinematic approximation i s equivalent to the first order results. This equivalence constitutes the f irst 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 fre e 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 recombinat ion. (C) 1999 American Institute of Physics. [S0021-9606(99)30818-7].