Exact solution of the Torrey-Bloch equation for a spin echo in restricted geometries

A. V. Barzykin
Phys. Rev. B 58, 14171 – Published 1 December 1998
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Abstract

An exact analytical solution is presented for the magnetization density of spins diffusing in a bounded region under a steady gradient field and, as a result, for any step-wise gradient pulse sequence, in terms of the Green’s function of the diffusion operator. A simple two-mode approximation to the exact formula is derived and shown to be consistently preferable to any of the existing approximations providing reliable fitting functions for most of the gradient NMR applications.

  • Received 4 September 1998

DOI:https://doi.org/10.1103/PhysRevB.58.14171

©1998 American Physical Society

Authors & Affiliations

A. V. Barzykin

  • National Institute of Materials and Chemical Research, Tsukuba, Ibaraki 305-8565, Japan

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Issue

Vol. 58, Iss. 21 — 1 December 1998

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