What are the conditions for exponential time-cubed echo decays?

Diffusion of precessing spins through a constant held gradient is well-know n to produce two distinctive features: an exp(-bt(3)) decay of the echo amp litude in response to two pulses and a much slower decay of the Carr-Purcel l echo train. These features will appear whenever the spin frequency is des cribed by a continuous random-walk. The present work shows that this may al so occur in the presence of motions with long correlation times tau(c)-cont inuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than tau(c). Thus, time-cub ed echo decays will occur in situations other than physical diffusion. The decay rate of the Carr-Purcell echo train is shown to vary with the pulse s pacing tau whenever the correlation time tau(c) is long; the slower Carr-Pu rcell decay compared to the two-pulse echo decay is not unique to diffusion . Simulations are presented that display time-cubed decays. The simulations confirm two important criteria: the echo time must be less than tau(c) and the frequency noise must consist of nearly continuous variations, as oppos ed to step-like changes. These criteria define the range of physical parame ters for which time-cubed decays will be observable. (C) 1999 Academic Pres s.