Zeeman Splitting of Nuclear Quadrupole Resonances

The theory of the Zeeman splitting of the pure quadrupole energy levels for nuclei of half-integral spin is given in a form that is correct for any electric field gradient. The splitting of the spectra is discussed, and also the simplifications that can be made in the theory when the magnetic field is parallel to any of the three principal axes of the electric field gradient. For spin $\frac{3}{2}$ it is shown that the deviation of the gradient from cylindrical symmetry can be determined from the Zeeman spectrum, and detailed calculations are given for this case, along with a discussion of their experimental application.