Magnetization modes and evolution matrices for some simple spin systems in anisotropic media

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Abstract
The time evolution of complete sets of coupled magnetization mode variables for the AX2, AX3, and X3 spin one‐half systems are presented. The chosen modes prove to be the natural kinetic variables for free and partially constrained nuclear magnetic relaxation studies in both spacially isotropic and spacially anisotropic environments. The relationship between spacial anisotropy, the concomitant failure of time reversal symmetry, and the appearence of complex valued angular correlation time constants is also discussed. It is rationalized that the absence of time reversal symmetry necessitates the introduction of certain zero frequency phase coherence variables which linearly couple into the magnetization (population) mode variables. Thus, relaxation studies may indeed distinguishbetween degenerate irreducible multiplicities.