Line widths of electron resonance spectra in solution

Abstract

The hyperfine lines in the electron resonance spectra of radicals in solution can show marked variations in width, and each line may itself be a sum of Lorentzian components with different relaxation times. In radicals of spin ½, where the anisotropy of the g tensor and the nuclear hyperfine tensors is the dominant cause of relaxation, a theory is given for finding a certain average width of each composite hyperfine line in terms of the inner products of the tensors. The width varies both linearly and quadratically with nuclear spin quantum numbers in a way which agrees qualitatively with previous work by Kivelson. Spectra of several aromatic radicals agree with the theory. The calculations use operator methods based on Bloch’s master equation for the spins. In the simpler problem of relaxation by dipolar electron spin-spin coupling in triplet, quartet, or higher spin states the operator method gives a complete description of the composite line shapes.