Nuclear Quadrupole Resonance by Nuclear Induction: Theory and Experiment; with an Extension of the Theory to Absorption Methods

Abstract

A theory is presented for nuclear quadrupole resonance (NQR) by means of nuclear induction and is extended to absorption methods. Based on the Bloch-type equations of Bloom, Robinson, and Volkoff, the theory is derived for the case $I=1$, $\ensuremath{\eta}=0$. For the induction method to work, a small magnetic field must remove the degeneracy of the $m=\ifmmode\pm\else\textpm\fi{}1$ levels; in practice this is done by an audio-frequency modulation field. Phase-sensitive detection methods are then used to minimize noise. The theory predicts the effect of modulation field, static magnetic field, and rf field on the slow-passage induction signal. Theory and experiment agree that magnetic fields (modulating or static) broaden the line, but for low enough fields, the true NQR derivative line is observed. Sufficiently large static fields introduce complex structure into the line shape. The effect of rf is given by a modified form of the Bloembergen-Purcell-Pound saturation curves. Experiments on polycrystal hexamethylenetetramine yield good agreement with all aspects of the theory. The extension of the theory to single-coil (absorption) NQR methods predicts that sinusoidal magnetic modulation and phase-sensitive detection will produce zero signal in a single-coil experiment. In addition it yields the proper line shapes for Zeeman modulation and frequency modulation methods and predicts the effects of modulation amplitude and magnetic fields in both cases. A brief qualitative discussion of cases other than $I=1$, $\ensuremath{\eta}=0$ indicates that the induction method can be used for half-integral spins with any $\ensuremath{\eta}$, but that it is applicable to integral spins only when $\ensuremath{\eta}$ is small. In other words the induction method can be used for any case to which the Zeeman-modulated absorption method is applicable.