From NQR to NMR: The complete range of quadrupole interactions

Abstract

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.

Nature of lattice distortions in the cubic double perovskite Ba2NaOsO6

“…The lowering of the symmetry induces a finite EFG, which is a quantity directly observable in a static NMR measurement on a nuclei with finite quadrupole moment, such as 23 Na. Specifically, the parameter extracted from the spectra of such NMR experiments is the quadrupole resonance frequency, defined in terms of V zz , which is the largest principal component of the EFG at the nuclear site, and other intrinsic nuclear properties [12][13][14] . Since the EFG tensor is a traceless rank-two tensor, its components can be determined by analysis of the spectra obtained as the orientation of the magnetic field is rotated with respect to the crystalline axes 12,15 .…”

Numerical simulation of NQR/NMR: Applications in quantum computing

“…As an example of simulation of high-field NMR spectrum of a quadrupolar nucleus, Fig. 5 presents the simulated 23 Na NMR spectrum of NaClO 3 single crystal [46]. In this case, each crystallographically inequivalent 23 Na nucleus gives rise to a triplet, with the central transition (between the states ±1/2, which is not affected by the quadrupole interaction to first-order) flanked by two satellites.…”

From nuclear structure to the quadrupolar NMR interaction and high-resolution spectroscopy

“…A discussion on the transition from the NQR situation to the highfield NMR case can be found in Ref. [21].…”

“…(10),(19)-(21),(24), (32)-(34) one arrives at the definition of the quadrupolar interaction in the principal axis frame of V ab as…”