NMR of diffusing atoms in a periodic porous medium in the presence of a nonuniform magnetic field

David J. Bergman, Keh Jim Dunn

Research output: Contribution to journalArticlepeer-review

Abstract

A detailed theory is developed for calculating the average time-dependent precessing nuclear spin of an atom diffusing through a porous medium in the presence of a nonuniform aligning field. An expansion in cumulant averages of the phase shift of the precessing spin is set up in terms of the diffusion propagator. For a periodic porous medium, a practical scheme of computation is exhibited which is based upon the diffusion eigenstates. This scheme is used to calculate the second and fourth order cumulants, both numerically and by asymptotic expansions for short and long precession times, when the field inhomogeneity is caused either by susceptibility differences between pore fluid and solid matrix or by an externally imposed field gradient. The results are used to calculate the diffusion effect on the transverse relaxation rate of spin polarization, and to discuss the validity of the Gaussian approximation for the distribution of phase shifts of the precessing spins. (c) 1995 The American Physical Society

Original languageEnglish
Pages (from-to)6516-6535
Number of pages20
JournalPhysical Review E
Volume52
Issue number6
DOIs
StatePublished - 1995

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