From NQR to NMR: The complete range of quadrupole interactions

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Abstract
The theoretical transition energies of a spin 3/2 under a combination of quadrupolar and Zeeman interactions are mapped out as a function of magnetic field. This allows us to follow the spectroscopy continuously from zero magnetic field (NQR, nuclear quadrupole resonance) through to high magnetic field (quadrupole‐perturbed NMR). This calculation is made possible by a theoretical approach that makes maximum use of the angular momentum properties of the spin system. In this approach, the detailed form of the spin operators are not required, only their angular momentum quantum numbers. No commutators need be evaluated, and the method is easily coded for computer calculation. Application of the Wigner‐Eckart theorem and selection rules means that there are only two nonzero reduced matrix elements that are needed for a spin 3/2, and there are explicit formulae for them. In looking at the transition energies, the crucial parameter is the orientation of the quadrupole tensor to the magnetic field. If the angle is nonzero, then the quantization of the spins must shift. At zero field, the quantization is defined by the electric field gradient tensor, which is molecule‐fixed at some arbitrary angle to the magnetic field. This direction of quantization must change as the magnetic field increases, to lie close to the z axis at high field. In the region where the two interactions are comparable, all the familiar rules break down and the response is highly nonlinear. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 22A: 69–78, 2004.