Theory of Exchange Relaxation of Hyperfine Structure in Electron Spin Resonance

The electron spin exchange interaction between colliding molecules is examined as a possible relaxation mechanism for the hyperfine structure of free-radical molecules in solution. An expression is derived which, under suitable conditions, relates the frequency-dependent susceptibility to a single parameter q, which can be interpreted as the frequency of spin exchanges. For large values of q the absorption narrows to a single line of width σ²q, where σ is the mean square width of the unperturbed spectrum. For small values of q the widths of the individual hyperfine lines are found to depend upon their relative intensities. These results are compared with some recent experiments.