Phase relaxation in a many-body system of diffusing spins: Slow motional limit

Abstract

The echo amplitude decay of a diffusing electron-spin-bearing molecule interacting with a diffusing many-spin bath of proton-containing molecules has been studied theoretically in the slow motional limit. Closed-form asymptotic expressions for the short- and long-time behavior of the echo envelope have been obtained. In contrast to the well-studied fast-motional limit, the echo envelope cannot be described by a simple exponential decay, and its rate exhibits a DT1/3 dependence on the relative translational diffusion coefficient, DT. For low proton concentrations and long pulse delay times, τ, an exponential τ9/8-decay of the echo amplitude is found, whereas for high proton concentrations and short τ’s the decay exhibits an exponential τ3-behavior. These limiting analytical results are compared with the exact numerical solutions to establish their range of validity.