Hydrodynamic theory of CIDEP and CIDNP

The stochastic Liouville method has been applied to the problem of high field CIDEP and CIDNP. The full equation of motion of the density matrix for the pair of free radicals includes: (1) the spatially isotropic Liouville operator; (2) the diffusion operator; (3) selective recombination of radical pairs from the singlet electronic state; (4) the Heisenberg exchange interaction; (5) secular electronic relaxation processes; and (6) radical scavenging processes. The short range character of radical recombination and Heisenberg exchange relative to the long distance of a diffusive trajectory allows these interactions to be treated effectively as delta functions which operate at a distance corresponding to a chemical bond. Using this delta function model, the equation of motion of the density matrix is soluble exactly for: (1) the z component of the electronic magnetization for a single radical fragment, which is proportional to the intensity of an ESR line; and (2) the nuclear spin level populations of the recombination and scavenged products, which are the indirect observables in the NMR experiment. In the limits of weak electronic relaxation and slow scavenging, the solutions of the problem approach those obtained by Adrian using the Noyes molecular pair theory.