Spin-Echo Decay of Spins Diffusing in a Bounded Region

Abstract

An approximate expression for the spin-echo-decay envelope is obtained from Torrey's equation for spins diffusing in a magnetic field gradient $G$ and in a region that is small compared with ${(\frac{D}{\ensuremath{\gamma}G})}^{\frac{1}{3}}$ in the direction of the large uniform magnetic field, and large in the directions perpendicular to the field. (Here $D$ is the diffusion constant and $\ensuremath{\gamma}$ the nuclear gyromagnetic ratio.) In a preceding paper, Wayne and Cotts compare this expression with experiment for regions that are large compared with ${(\frac{D}{\ensuremath{\gamma}G})}^{\frac{1}{3}}$ but small enough that the simple spin-echo-decay envelope for an infinitely large region does not apply.