GAUSSIAN-APPROXIMATION FORMALISM FOR EVALUATING DECAY OF NMR SPIN ECHOES

We present a formalism for evaluating the amplitude of the NMR spin ec ho and stimulated echo as a function of pulse spacings, for situations in which the nuclear spins experience an effective longitudinal magne tic field h(z)(t) resulting from an arbitrary number of independent so urces, each characterized by its own arbitrary time correlation functi on. The distribution of accumulated phase angles for the ensemble of n uclear spins at the time of the echo is approximated as a Gaussian. Th e development of the formalism is motivated by the need to understand the transverse relaxation of Y-89 in YBa2Cu3O7, in which the Y-89 expe riences Cu-63,Cu-65 dipolar fields which fluctuate due to Cu-63,Cu-65 T-1 processes. The formalism is applied successfully to this example, and to the case of nuclei diffusing in a spatially varying magnetic fi eld. Then we examine a situation in which the approximation fails-the classic problem of chemical exchange in dimethylformamide, where the m ethyl protons experience a chemical shift which fluctuates between two discrete values. In this case the Gaussian approximation yields a mon otonic decay of the echo amplitude with increasing pulse spacing, whil e the exact solution yields distinct ''beats'' in the echo height, whi ch we confirm experimentally. In light of this final example the Limit s of validity of the approximation are discussed.