THE MEMORY-FUNCTION TECHNIQUE FOR THE CALCULATION OF PULSED-GRADIENT NMR SIGNALS IN CONFINED GEOMETRIES

An approximation technique for the calculation of pulsed-gradient NMR signals in confined spaces is introduced on the basis of a memory-func tion formalism and compared to the well-known cumulant expansion techn ique, The validity of the technique is investigated for the cases of a time-independent field gradient and a gradient consisting of two puls es of finite duration, It is found that the validity is governed by th e ratio of two characteristic times: the time for the spins to travers e the dimensions of the confining space through diffusion and the reci procal of the extreme difference between values of the precession freq uency of the spin, Oscillations in the time evolution of the signal fo r the constant gradient, as well as oscillations in the (gradient) fie ld dependence for the two-pulse gradient, which are both characteristi c of the exact signals, are predicted by the new technique but not by the cumulant technique, The cumulant results are shown to arise as an approximate consequence of the memory results. (C) 1996 Academic Press , Inc.