Spin–lattice relaxation in coupled three spin systems of the A I S type

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Abstract
Relaxation in coupled three spin systems of the AIS type is described by an extension of the two spin case treated by Solomon. The proper linear combinations of spin level populations are presented as normal mode variables in a system of coupled differential equations so that maximum reduction in the number of differential equations is achieved. Decoupling experiments further reduce the AIS problem to a set of equations similar to those encountered in the two and one spin cases. The formalism includes in a natural way dipolar relaxation effects due to cross-correlated motion of internuclear vectors. A theoretical expression is derived to describe these effects. In the normal mode variables these terms group together and relate total magnetization variables with a multiplet relaxation mode. Experimental results on the three spin system 13CHFCl2 are presented in terms of the above formalism.