Theory of spectral diffusion decay using an uncorrelated-sudden-jump model

Abstract

The decay behavior of the one-pulse free-induction, two-pulse echo, and three-pulse stimulated-echo signals is calculated for a system of $A$ spins, isolated from each other, whose local field fluctuates because of the uncorrelated flipping of a system of $B$ spins randomly located. The decay behavior is obtained in closed form and is valid for all time. We find that the dipolar line shape, which is the Fourier transform of the free-induction decay, is always narrowed by the flipping of the $B$ spins. The two-pulse echo first decreases as the $B$-spin-flip rate $W$ increases and then increases as $W$ is further increased. Except for the free-induction decay our formulas coincide in the limits of very short and very long times with those calculated by Klauder and Anderson and by Mims.