The Memory-Function Technique for the Calculation of Pulsed-Gradient NMR Signals in Confined Geometries

✍ Scribed by Daniel Sheltraw; V.M. Kenkre

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 233 KB
• Volume: 122
• Category: Article
• ISSN: 1064-1858
• DOI: 10.1006/jmra.1996.0188

✦ Synopsis

An approximation technique for the calculation of pulsed-gradient experiment. We have also recently initiated a study of the NMR signals in confined spaces is introduced on the basis of a theoretical description of these issues with the help of a new memory-function formalism and compared to the well-known cumuapproach based on equations which are nonlocal in time. lant expansion technique. The validity of the technique is investi-We begin a report on this study in the present paper by gated for the cases of a time-independent field gradient and a gradianalyzing two typical experiments. The first involves the use ent consisting of two pulses of finite duration. It is found that the of a time-independent applied magnetic-field gradient and validity is governed by the ratio of two characteristic times: the time the second involves the use of two gradient pulses.

for the spins to traverse the dimensions of the confining space Our approach, which may be called the memory approach, through diffusion and the reciprocal of the extreme difference beis based on the application of projection operators (14, 15) tween values of the precession frequency of the spin. Oscillations in the time evolution of the signal for the constant gradient, as well to the evolution equation of the system density matrix. Alas oscillations in the (gradient) field dependence for the two-pulse though projection operators have been applied to the problem gradient, which are both characteristic of the exact signals, are preof spins diffusing in a constant magnetic-field gradient predicted by the new technique but not by the cumulant technique. The viously ( 16), a Markoffian approximation, which destroys cumulant results are shown to arise as an approximate consequence the memory-function nature of the equation, has been made.

of the memory results.