The classical treatment is opposed by the macroscopic gradients at high magnetic fields (β’7 T) produces multiple nonlinquantum-theoretical approach trying to describe short-as ear stimulated echoes (NOSE) at times n t 1 after the third pulse, well as long-range dipolar interactions on a purely quantumwhere n is an integer and t 1 the interval between the first two mechanical basis (10-12). The spin system considered in pulses. From the classical point of view, these phenomena are due this case extends from the molecular scale up to the dimento the demagnetizing field produced by the spatial modulation of sion of the whole sample. It is clear that the macroscopic the nuclear magnetization arising in the sample after the first two quantum theory must be correct in principle. However, as pulses. In this paper the behavior of NOSE for molecules conin other fields of physics, it is more useful to consider the taining inequivalent uncoupled spins subject to motional averaging classical limit for effects on length scales far beyond those of short-range interactions is reported. As a consequence of the of atoms and molecules . demagnetizing field the interference between the magnetizations of the different spin ensembles leads to beats in the amplitude of This fact has prompted us to employ a semiclassical for-NOSE. A semiclassical formalism describing this dependence is malism (3) for the description of multiple two-pulse as well established and verified in test experiments with the protons in a as three-pulse echoes (1, 3). That is, spin interactions taking methyl acetate sample. α§ 1998 Academic Press place on atomistic length scales are treated using the Liou-Key Words: stimulated echo; multiple echoes; NOSE; demagneville/von Neumann equation, whereas all long-range effects tizing field.
are classically accounted for by considering the demagnetizing field arising from the spatially modulated magnetization.
Note that the length scale limit is well defined: Depending