Time-dependent self-diffusion by NMR spin-echo

Abstract The relation between the NMR spin-echo attenuation in the magnetic field gradient and the velocity autocorrelations of molecular random migration has been derived by using the comulant expansion theorem for averaging stochastic processes. It may explain certain cases of time-dependent diffusion observed in many systems. In the limit of long correlation times it is identical to Torrey's well-known formula for spin echo attenuation due to self-diffusion. The method is used to derive the expression for spin-echo attenuation of diffusion in restricted regions.