By means of the atomic-beam-magnetic-resonance method we have measured the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ level hfs and the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level $g_J$ factors of the ${\mathrm{Bi}}^{209}$ ${\mathrm{}\left(6p\right)\mathrm{}}^3$ ground configuration. Our experimental results are: $A\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=491.028\mathrm{}\left(1\right)\mathrm{}$ MHz, $B\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=978.639\mathrm{}\left(9\right)\mathrm{}$ MHz, $C\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=0.0193\mathrm{}\left(5\right)\mathrm{}$ MHz, $g_J\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)=0.6654\mathrm{}\left(2\right)\mathrm{}$ and $g_J\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=1.26083\mathrm{}\left(12\right)\mathrm{}$. In order to interpret these measurements, we have examined the fine structure and the hfs of all the ${\mathrm{}\left(6p\right)\mathrm{}}^3$ levels. Our calculations show that the inclusion of spin-spin, orbit-orbit, and spin-other-orbit interactions do not improve the theoretical fit to the observed fine structure intervals. The effects of core polarization and relativity can be estimated by writing the dipole hfs Hamiltonian in the form $\mathcal{H}=2\mathrm{}\mu {\mu }_B\overrightarrow{\mathrm{I}}·\Sigma \stackrel{}{i}[{〈{\mathcal{r}}_l^{-3\mathrm{}}〉}_i{\overrightarrow{\mathrm{I}}}_i-\sqrt{10}{〈{\mathcal{r}}_{\mathrm{sC}}^{-3\mathrm{}}〉}_i{\left(s{C}^2\right)}_l^{\mathrm{}\left(1\right)\mathrm{}}+{〈{\mathcal{r}}_s^{-3\mathrm{}}〉}_i{\overrightarrow{\mathrm{s}}}_i]$ This analysis of the dipole hfs yields a value ${〈{\mathcal{r}}^{-3\mathrm{}}〉}_{6p}\left(\mathrm{hfs}\right)=1.02\mathrm{}\times {10}^{26}$ ${\mathrm{cm}}^2$ compared to the fine structure result ${〈{\mathcal{r}}^{-3\mathrm{}}〉}_{6p}\left(\mathrm{fs}\right)=1.25\mathrm{}\times {10}^{26}$ ${\mathrm{cm}}^2$. With these results we find $Q=-0.383\mathrm{}\left(40\right)\mathrm{}$ b and $\Omega =0.55\mathrm{}\left(3\right)\mathrm{}{\mu }_N\mathrm{b}$.

• Received 24 October 1969

DOI:https://doi.org/10.1103/PhysRevA.1.1330