What Are the Conditions for Exponential Time-Cubed Echo Decays?

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Abstract:

Diffusion of precessing spins through a constant field gradient is well-known to produce two distinctive features: an exp(-bt3) decay of the echo amplitude in response to two pulses and a much slower decay of the Carr–Purcell echo train. These features will appear whenever the spin frequency is described by a continuous random-walk. The present work shows that this may also occur in the presence of motions with long correlation times c—continuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than c. Thus, time-cubed 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 spacing  whenever the correlation time c is long; the slower Carr–Purcell 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 c and the frequency noise must consist of nearly continuous variations, as opposed to step-like changes. These criteria define the range of physical parameters for which time-cubed decays will be observable.

Document Type: Research Article

Affiliations: 1: Department of Physics, Knox College, Galesburg, Illinois, 61401 2: Department of Physics–1105, Washington University, One Brookings Drive, St. Louis, Missouri, 63130-4899

Publication date: August 1, 1999

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