SIMPLE SOLUTIONS OF THE TORREY-BLOCH EQUATIONS IN THE NMR-STUDY OF MOLECULAR-DIFFUSION

A simple technique for solving the Torrey-Bloch equations appearing in the calculation of the NNR signal under gradient fields is presented. It is applicable to arbitrary time dependence of the gradient field t o arbitrary initial distribution of spins, and to spin motion on discr ete lattices as well as in the continuum under conditions of unrestric ted diffusion. Known results are recovered as particular cases and new results are presented, The discrete lattice results are shown to be s imilar to known results for restricted diffusion in the continuum. Als o presented is a surprising equivalence between results for a simple t wo-site hopping model and earlier expressions for the NMR signal for s pins undergoing restricted diffusion in a continuum. (C) 1997 Academic Press.