The nuclear magnetic moment and atomic hyperfine splitting of the rare ${\mathrm{K}}^{40}$ isotope have been measured by the atomic beam magnetic resonance technique. Detection of ${\mathrm{K}}^{40}$ atoms, from a source of normal potassium, was achieved by employing a conventional surface ionization detector as the ion source for a mass spectrometer, and by utilizing an electron multiplier to count the ${\mathrm{K}}^{40}$ ions. By measuring the frequencies of appropriate lines in the Zeeman pattern, the nuclear moment was determined to be ${\mu }_I=-1.2964\mathrm{}\pm 0.0004$ nuclear magnetons. The hyperfine splitting in the ground state was redetermined, with higher precision than that of previous measurements, to be $\Delta \nu =1285.790\mathrm{}\pm 0.007$ Mc/sec.

The ratio of the nuclear $g$ factors of ${\mathrm{K}}^{39}$ and ${\mathrm{K}}^{40}$ was measured directly by observing, in the same homogeneous magnetic field, $H$, the frequencies of two lines (a doublet) in the Zeeman spectrum of each isotope. The doublet separation of these lines is, in each case, proportional to $2g_I{\mu }_{0}H$, so that the ratio of the doublet splittings yielded directly $\left|\frac{g\left({\mathrm{K}}^{40}\right)}{g\left({\mathrm{K}}^{39}\right)}\right|=1.24346\mathrm{}\pm 0.00024$. From these results and from the previously measured $\Delta \nu \left({\mathrm{K}}^{39}\right)$, the hyperfine structure anomaly of these K isotopes is $\left\{\frac{\left[2I\right({\mathrm{K}}^{40})+1]g\left({\mathrm{K}}^{40}\right)\Delta \nu \left({\mathrm{K}}^{39}\right)}{\left[2I\right({\mathrm{K}}^{39})+1]g\left({\mathrm{K}}^{39}\right)\Delta \nu \left({\mathrm{K}}^{40}\right)}\right\}-1=(0.466\mathrm{}\pm 0.019) \mathrm{percent}.$

The theory of the hyperfine structure anomaly, as developed by A. Bohr and V. F. Weisskopf, has been applied to the interpretation of this result. The predictions of a number of specific models, previously suggested to account for the observed nuclear $g$ factors, have been compared with this experiment and with previous results on the anomalies for the Rb and the abundant K isotopes. The "asymmetric core" model of A. Bohr gives the best over-all agreement, mainly on the basis of the ${\mathrm{K}}^{41}$—${\mathrm{K}}^{39}$ anomaly. In general, all models which are, in their essential features, based on the independent-particle model with spin-orbit coupling, give predictions in fair qualitative agreement with the experiments. The contribution of ${\mathrm{K}}^{40}$ to the hfs anomaly seems, however, to be (fortuitously) insensitive to the differences between the models investigated.

Close

PrevNext

View figure in article