Theory of Saturation in Electron Spin Resonance Spectra

Abstract

A theory of saturation in electron spin resonance spectra exhibiting hyperfine splitting is presented. This theory is used to study the saturation of free radical spectra in solution, and a variety of relaxation processes are investigated. It is shown that motional modulation of the intramolecular electron‐nuclear anisotropic dipole—dipole interaction introduces a relation between the saturation parameters and the hyperfine components that varies symmetrically about the center of the spectrum and causes a smaller degree of relaxation for the components in the central portion of the spectrum than for those in the wings. This relaxation mechanism introduces a greater dependence on nuclear spin state for radicals with several magnetic nuclei than for radicals with only one such nucleus. It is also shown that a cross term between this intramolecular dipolar interaction and motional modulation of the anisotropic g tensor introduces a relaxation that varies linearly from one side of the spectrum to the other. Numerical values of the relaxation‐induced transition probabilities are estimated for the benzene negative ion, and tables are given from which saturation factors can be computed for a variety of conditions for several different spin systems. The relation between the spin‐lattice relaxation time T₁ and the parameters which determine saturation is discussed, and it is pointed out that these quantities are not equivalent in systems exhibiting cross relaxation.