The relaxation matrices for AX2 and AX3 nuclear spin systems

Abstract

The Redfield relaxation matrices describing the approach to thermal equilibrium of populations of coupled nuclear spin systems of AX₂ and AX₃ types are tabulated for relaxation by any combination of dipolar, shielding, spin-rotation and external fields in the extreme narrowing limit together with scalar coupling to a relaxing or exchanging spin. All cross terms are included. These relaxation matrices were calculated using the superoperator representation of the relaxation equation with basis operators in Liouville space which have the symmetry appropriate to the problem. For the practising N.M.R. spectroscopist we show how these matrices may be used to interpret various types of T ₁ relaxation measurement. Some examples are provided showing how the relaxation of different transitions in a ¹³CH₂ group and the FHF^- ion depends on the relaxation mechanism and on the type of experiment.