The Radiofrequency Spectra of the Sodium Halides

Abstract

The radiofrequency spectra of ${\mathrm{Na}}^{23}$Br, ${\mathrm{Na}}^{23}$Cl, and ${\mathrm{Na}}^{23}$I have been investigated by use of the molecular-beam resonance method. In external fields of approximately 10,000 gausses, the spectra are about 1 Mc/sec. wide, continuous, and of a characteristic form with a deep central minimum and two smaller side minima. The central minimum agrees in frequency to 0.2 percent with the Larmor frequency for a decoupled ${\mathrm{Na}}^{23}$ nucleus. At this field the orientation-dependent interaction of the ${\mathrm{Na}}^{23}$ nucleus with the molecule is small compared to the interaction of the nuclear magnetic moment with the external magnetic field. Comparison of the observed spectra with the statistical theory of Feld and Lamb suggests that the effect is due to the interaction of an electric quadrupole moment of the sodium nucleus with the inhomogeneous electric field of the other charges in the molecule. In this theory, the continuous nature of the spectrum is a result of the large number, $2J+1$, of magnetic states of the molecule for large rotational quantum numbers, $J$. The triple minima are characteristic of nuclear spin $\frac{3}{2}$. The spectra were further studied in progressively lower fields. The marked loss of character of the spectra for intermediate fields is explained by extending the analysis of the ${cos}^2(\mathbf{I},\mathbf{J})$ coupling. In the limit of zero field (resonance minima of a type not heretofore observed) a single resonance is observed for each compound at a frequency equal to the frequency difference between the side minima observed in strong fields for the same compound. This is in good agreement with the predictions of Feld and Lamb. These frequencies are 1.22, 1.42, and 0.99 Mc/sec. for NaBr, NaCl, and NaI, respectively. The theory of the behavior of the central minimum as a function of the external field, and the effect of the finite resolution of the apparatus are developed more fully, particularly insofar as they affect the ultimate precision of measurements of nuclear $g$-factors and nuclear quadrupole interactions. The analysis of the spectra indicates the possibility of still an additional interaction of the form $c\mathbf{I}·\mathbf{J}$, whose average value is 0.05 Mc/sec. This is about 25 times larger than the interaction which would be caused by the magnetic field of a charge of one electron rotating at the internuclear distance of the molecule and with its average angular velocity. This possibility is supported by the need for introducing a term of this nature in the Hamiltonian for LiF in order to explain the observed width of 0.5 Mc/sec. for the F resonance.