Nuclear relaxation in coupled spin systems. A heteronuclear two pulse experiment and a general numerical method for analyzing spin dynamics

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Abstract
A convenient new heteronuclear two pulse nuclear spin relaxation experiment is described. When combined with relaxation experiments already in the literature, each of the interlevel transition probabilities for a system of weakly coupled nuclear spins may be determined. Previous work in coupled spin relaxation has yielded only certain linear combinations of these transition probabilities. The well understood AX spin system was selected to illustrate the method, and sodium formate in D2O solution is used as the specific case. Values for all four interlevel transition probabilities characterizing the spin lattice relaxation of the 1H–13C spin system of the formate ion are obtained. These data yield the first experimental verification of the extreme narrowing condition commonly assumed for small molecules in nonviscous liquids. A general numerical method is described for estimating the relaxation parameters from measurements of the time evolution of nonequilibrium magnetization. The method involves numerical solution of coupled linear homogeneous differential equations with constant coefficients. These coefficients are linear combinations of relaxation parameters. The approach is sufficiently general to allow for a variety of initial conditions which characterize the manner in which the spin system is prepared in its nonequilibrium configuration. Several types of spin perturbations are described in detail.