Validity limits of Gaussian approximation in cumulant expansion for diffusion attenuation of spin echo

Cumulant expansion is a way to average out the spin frequency fluctuations, caused by molecular random migration in nonuniform magnetic held, in order to get spin echo attenuation. Since numerous spins have a share in NMR ind uction, the cumulative yield of frequency fluctuations features Gaussian ra ndomness. Thus the cumulant expansion can be terminated by the second term giving the spin echo attenuation related to the time-correlation of molecul ar motion (Stepisnik, Physica B 104 (1981) 350) and to the time-space-corre lation in the case of restricted self-diffusion. The validity limits of thi s approximation is tested by considering the convergence of the cumulant se ries. The estimate of high-order velocity correlations displays that the ga p between the magnetization grating (spin-phase structure) caused by applie d gradient fields has to be much larger than the free path of moving spins. With the spins in confinement, the spin phase structure can be written as composition of plane waves (Stepisnik, J. Phys. 39 (1978) 689; Stepisnik, J . Magn. Res. 131 (1998) 339). The cumulant expansion in Gaussian approximat ion gives the spin echo attenuation as a discord of magnetization grating t hat can exhibit the diffusive diffraction patterns of porous structure (Coy , Callaghan, J. Chem. Phys. 101 (1994) 4599). Advantage of method is its ab ility to be implemented with any general gradient pulse sequence, i.e., the gradient pulses can violate the short pulse approximation that is required with the propagator method. (C) 1999 Elsevier Science B.V. All rights rese rved.