Interpretation of NMR diffusion measurements in uniform- and nonuniform-field profiles

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Abstract
With the use of Carr-Purcell random-walk methods, approximate expressions have been derived for the spin-echo decay envelope for spins diffusing in a restricted region in the presence of an inhomogeneous field. The sample region considered is a slab with a uniform cross section and plane boundaries. The inhomogeneous field may be either time independent or pulsed and is not required to have a uniform gradient. With consideration of different limits of the final expressions, both restricted and unrestricted diffusion can be treated. Comparison is made of our results with those found by other authors, and suggestions are given which can be used to extend the sensitivity of field-gradient NMR (nuclear magnetic resonance) diffusion measurements.