NMR quadrupole liouvillians for arbitrary spin: Exact symbolic expressions and perturbation solutions

Abstract

The NMR of quadrupolar nuclei with half-integer spins is almost always described by treating the quadrupole interaction with second-order perturbation theory. The standard practice is to perturb the wave functions, then calculate the transitions. In this article, we elaborate on the so-called direct method in which the transitions are calculated directly without the requirement of knowing the operators and the wavefunctions. The method is set up using a set of formulae giving fully symbolic expressions. First of all, this provides a convenient way for a full and exact numerical solution that goes beyond perturbation theory. The other possibility is that it allows us to see the effect of the quadrupole perturbation on the unperturbed transitions. The results are the same, as they must be, but this approach reveals a number of important symmetries. Perturbations will mix the unperturbed transitions, but despite the use of high-order perturbation theory, the mixing is very simple, specific, and controlled by selection rules. This gives a clear physical picture of the physical basis of the effects of perturbation theory. The approach is systematic and general and is easily extended to an arbitrary half-integral spin. © 2013 Wiley Periodicals, Inc.