Application of generalized cumulant expansions to the theory of electron spin echo phase memory decay in liquids

A generalized cumulant expansion theory for electron spin relaxation in liquids is presented which describes the phase memory decay found in pulse experiments. It is found that for pulse times τ≫τc, the two-pulse electron spin echo envelope decays exponentially, and for motionally narrowed systems, the phase memory decay rate is given by the elements of the Redfield relaxation matrix. For radicals undergoing slow rotational reorientation, the phase memory time is shown to be sensitive to both the rotational correlation time and the assumed dynamical model for rotational diffusion even for correlation times so long that the cw EPR spectra appear to be rigid. If τ≳τc, the echo envelope is found to decay in a complex, oscillatory manner.