Spectral Diffusion in Magnetic Resonance

Abstract

Electron spin-spin interaction is discussed for the case of strong hyperfine broadening. The hyperfine interaction is represented by a resonance spectrum of width $\ensuremath{\Delta}\ensuremath{\omega}$ and the electron interactions, which are taken to be dipolar, are treated by time-dependent perturbation theory. A characteristic relaxation time for electron spins, ${\ensuremath{\tau}}_{s}=\frac{\ensuremath{\Delta}\ensuremath{\omega}}{{\ensuremath{\Delta}}^{2}}$, is found, where $\ensuremath{\Delta}$ is a measure of the strength of the dipolar interaction. The time-dependent theory suggests a modification of the Bloch equations to give a phenomenological description of systems of this kind. Spin-spin relaxation is represented by a term which gives diffusion of spin excitation through the resonance spectrum. Slow passage, rapid passage, and free relaxation are considered by using the modified equations.