The narrow-pulse criterion for pulsed-gradient spin-echo diffusion measurements

The narrow-pulse criterion for pulsed-gradient NMR spin-echo diffusion in the presence of impenetrable barriers is examined from an expression by Stepisnik [Physica B 183, 343 (1993)] for the attenuation caused by diffusion in any magnetic-field gradient for various parameters. These parameters are delta, Delta, a, D, and g, where delta and Delta are the duration and the interval between bipolar magnetic-field-gradient pulses, respectively, a is the separation of the impenetrable barriers, D is the diffusion coefficient, and g is the gradient strength. The pulsed-gradient spin-echo (PGSE) experiment is a subclass of this set. The attenuation, with the assumption that the diffusive motion of the spins leads to Gaussian distribution of spin phases, goes to known expressions in the free-diffusion (Delta D/a(2) much less than 1), restricted-diffusion (delta D/a(2) much less than 1 much less than Delta D/a(2)), and rapid-diffusion (1 much less than delta D/a(2)) limits. This general expression is found to be valid for all combinations of Delta and delta provided that gamma delta ga/2 pi = qa much less than 1. A criterion for the applicability of the commonly used narrow-pulse expressions for the signal attenuation is calculated from the fraction F of total attenuation that takes place only during the gradient. An independent check was performed from the shifts of the diffraction minima as a function of increasing pulse widths obtained from the simulation by Blees [J. Magn. Reson. A 109, 203 (1994)]. If the narrow-pulse criterion is valid for F much less than 0.1 or for less than a 5% shift in the second minimum of the diffraction pattern, a sufficient condition for its applicability is delta D/a(2) much less than 0.02, a much more stringent condition than is usually supposed. (C) 1995 Academic Press, Inc.