Generalized theoretical treatment of axially symmetric ESR hyperfine centers under slow orientational diffusion motion

The ensemble averaging based on the solution of an isotropic diffusion equation is employed to calculate analytical expressions for angular-dependent motional linewidths and shifts in spectral line position of axially symmetric ESR hyperfine centers, which undergo isotropic, small-angle, slow-orientational diffusion motion. The resultant theoretical expressions are consistent with those calculated by other investigators using different theoretical approaches. As a result of the present calculations, the entire ESR hyperfine spectra associated with slow-tumbling motions can be calculated in polycrystalline/amorphous substances. A detailed investigation of these theoretical spectra supports the validity of the previously proposed simple method of determining experimental rotational correlation times from the behavior of the parallel-edge lines of nitroxide ESR powder spectra.