Abstract
An equation describing the multiexponential longitudinal and transverse relaxation of quadrupolar nuclei, including the effects of chemical exchange in the limit of fast exchange, is derived. It is difficult to produce analytical solutions for nuclei with spins greater than 3/2, but the equation is in a form convenient for numerical solution, and such solutions are presented for both the longitudinal and transverse relaxation of nuclei with spins 5/2 and 7/2 in the absence of chemical exchange, and for the case of two-site exchange where one site is in the extreme narrowing limit. Longitudinal relaxation may be described approximately by a single exponential in all cases. However, the transverse relaxation generally must be described as the sum of three and four exponentials for the spin 5/2 and spin 7/2 cases, respectively, the amplitudes of which vary with the correlation time in the absence of exchange, and also with the ratio of the lifetimes of the nucleus in each state when two-site exchange is considered.
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