Backward equation formalism for magnetic field effects and an efficient numerical method

Abstract

By using the backward stochastic Liouville equation we derive direct equations for the spin dependent recombination probability (CIDNP) and for the chemically induced electron spin polarization (CIDEP). These equations are inhomogeneous second order differential equations in theinitial separation and they differ only in the inhomogeneous term and can thus be solved simultaneously. Thet → ∞ limits of the quantities are obtained directly as solutions to the equations. We introduce a transformed spatial variable which gives a more satisfactory description of the problem and which leads to a simple and symmetric form of the diffusion operator. This variable can represent the solution with a very small number (25–50) of equidistantly discretized points and it is thus particularly well suited for a finite difference solution of the problem. A single solution to the corresponding matrix equation contains the complete dependence of both CIDNP and CIDEP on all initial separations and spin configurations and it can be obtained in a few seconds on a personal computer.