Large Static Field Research Articles

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

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.

Free nuclear induction

The study of nuclear magnetic resonance or nuclear induction, a recent field of research for which F. Bloch and E. M. Purcell have been awarded the Nobel Prize, has been carried out by a variety of techniques. The usual approach has been to observe the nuclear resonance of an ensemble of nuclear moments in a large static magnetic field as a function of a slow change in this field. Meanwhile, a small radio-frequency field is applied continuously to the nuclear sample in a direction perpendicular to the large field. An alternative method to this steady state or “slow passage” technique is one by which the radio-frequency energy is applied to the sample in the form of short, intense pulses, and nuclear signals are observed after the pulses are removed. The effects which result can be compared to the free vibration or “ringing” of a bell, a term often applied to the free harmonic oscillations of a shocked inductive-capacitive (LC) circuit. The circuit is first supplied with electrical energy from some source, and the supply of energy is suddenly removed. The LC circuit then remains for a time in the “excited state”, and the energy is gradually dissipated into heat, mostly in the circuit resistance. Similarly the atom or nucleus in the excited state can store energy for a time before it is completely dissipated, and in the case discussed here, the free oscillation or precession of an ensemble of nuclear spins in a large static field provides the ringing process.