Hyperfine Structure and Nuclear Moments of Promethium-147 and Promethium-151

Abstract

The atomic-beam magnetic-resonance method has been used to measure the hyperfine structure of the ${}_{}{}^6{}_{}{}^{}H_{\frac{7}{2}}^{}{}_{}{}^{}$ level in two promethium isotopes. The spins of these isotopes have been verified to be $I\left({\mathrm{Pm}}^{147}\right)=\frac{7}{2}$ and $I\left({\mathrm{Pm}}^{151}\right)=\frac{5}{2}$. The electronic splitting factor ($g_J$) has been measured for the ${}_{}{}^6{}_{}{}^{}H_{\frac{7}{2}}^{}{}_{}{}^{}$ level and is found to be $g_J=-0.8279\mathrm{}\left(4\right)\mathrm{}$, in good agreement with the predicted value. The hyperfine constants and the nuclear moments inferred from them are found to be for ${\mathrm{Pm}}^{147}$: $\mathrm{}\left|A\right|=447.1\mathrm{}\left(9.3\right)\mathrm{} \mathrm{Mc}/sec, \mathrm{}\left|B\right|=267.5\mathrm{}\left(70.8\right)\mathrm{} \mathrm{Mc}/sec, \frac{B}{A}<0,$ $\left|{\mu }_I\mathrm{}\right|=3.2\left(3\mathrm{}\right)\mathrm{} \mathrm{nm}, \mathrm{}\left|Q\right|=0.7\mathrm{}\left(3\right)\mathrm{} \mathrm{b} \frac{Q}{\mu }>0;$ and for ${\mathrm{Pm}}^{151}$: $\mathrm{}\left|A\right|=358\mathrm{}\left(23\right)\mathrm{} \mathrm{Mc}/sec, \mathrm{}\left|B\right|=777\mathrm{}\left(94\right)\mathrm{} \mathrm{Mc}/sec, \frac{B}{A}<0,$ $\left|{\mu }_I\mathrm{}\right|=1.8\left(2\mathrm{}\right)\mathrm{} \mathrm{nm}, \mathrm{}\left|Q\right|=1.9\mathrm{}\left(3\right)\mathrm{} \mathrm{b}, \frac{Q}{\mu }>0.\mathrm{}$ The nuclear moments are corrected for the breakdown of Russell-Saunders coupling. The stated errors include uncertainties in the fields at the nucleus arising from errors in the value of $〈\frac{1}{r^3}〉$ and the neglect of core polarization on the magnetic hyperfine structure. Corrections due to the Sternheimer effect have not been included. The measurements are shown to be consistent with the hypothesis that ${\mathrm{Pm}}^{147}$ is not highly deformed and can be understood from the shell model, but that ${\mathrm{Pm}}^{151}$ is highly deformed and must be interpreted by the collective model.