Hyperfine-Structure Separations, Nuclear Magnetic Moments, and Hyperfine-Structure Anomalies of Gold-198 and Gold-199

We have measured the hyperfine-structure separations and nuclear magnetic moments of (2.70-day) ${\mathrm{Au}}^{198}$ and (3.15-day) ${\mathrm{Au}}^{199}$ in the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state, using the atomic-beam magnetic-resonance method. We also measured the ratios of the electronic $g$ factor of gold to those of potassium and cesium. The results are, for ${\mathrm{Au}}^{198} \mathrm{}(I=2\mathrm{})\mathrm{}$, $\Delta \nu =21450.7167\mathrm{}\left(4\right)\mathrm{}$ MHz, ${\mu }_I\left(\mathrm{uncorr}\right)=+0.5842\mathrm{}\left(4\right)\mathrm{}$ nm; and for ${\mathrm{Au}}^{199} (I=\frac{3}{2})$, $\Delta \nu =10962.7227\mathrm{}\left(3\right)\mathrm{}$ MHz, ${\mu }_I\left(\mathrm{uncorr}\right)=+0.2673\mathrm{}\left(7\right)\mathrm{}$ nm. The results for the $g$-factor ratios are: $\frac{g_J\left(\mathrm{Au}\right)}{g_J\left(\mathrm{K}\right)}=1.000504\mathrm{}\left(2\right)\mathrm{}$ and $\frac{g_J\left(\mathrm{Au}\right)}{g_J\left(\mathrm{Cs}\right)}=1.000381\mathrm{}\left(2\right)\mathrm{}$. These values yield the following hyperfine-structure anomalies: ${}_{}{}^{197}{}_{}{}^{}\Delta _{}^{198}{}_{}{}^{}=8.53\mathrm{}\left(8\right)\mathrm{}$% and ${}_{}{}^{197}{}_{}{}^{}\Delta _{}^{199}{}_{}{}^{}=3.7\mathrm{}\left(2\right)\mathrm{}$%. Second-order corrections to the hyperfine structure are shown to be negligible. The nuclear results are interpreted in terms of the shell model, with allowance made for configuration mixing.