Nuclear Quadrupole Resonance in Solid Nitrogen— An Exercise in Quantum Mechanics

Abstract

The field of nuclear quadrupole resonance (NQR) in molecular solids provides a rich new source of instructive, easily varied, workable problems in quantum mechanics. Examples which cover the subject areas of spin, identical versus distinguishable particles, degenerate bound-state perturbation theory, symmetry properties of operators and wavefunctions, and selection rules are presented in an integrated discussion of a current research problem involving NQR of N (I = 1)14 in solid α-N2 enriched in the N15 isotope (I = 12). In this solid, the nuclear quadrupole moments interact with an axially symmetric electric field gradient (EFG), and, to an excellent approximation, each diatomic molecule can be treated as a separate two-spin system in which the nuclear quadrupole energy levels are perturbed by a coupling between the magnetic moments of the nuclei. Spectra obtained from first-order perturbation theory applied to both N14-N14 and N14-N15 molecules are compared with the results of an exact calculation and with experiment. In addition, it is demonstrated simply that in the presence of an asymmetric EFG the dipolar interaction of a spin-1 nucleus with a spin-12 nucleus is completely quenched to first order, while some splitting remains for the spin-1-spin-1 case.