The NMR of quadrupolar nuclei. Relationship between exact and perturbation solutions for spin 3/2

Nuclei with spin > 1/2 often experience an interaction, called the quadrupole interaction, which can be very strong in NMR terms. For nuclei with half-integral spins, however, the so-called central transition in the NMR spectrum remains relatively narrow. Second-order perturbation theory provides an excellent description, but the classic derivation involves perturbing the energy levels, then constructing the transitions. Recently, we have derived a method for calculating transitions and their energies directly, without requiring any detailed knowledge of wavefunctions, operators or their commutators. This provides a simple derivation of the perturbation result that highlights important physical aspects of the equations.