Hyperfine Structure and Nuclear Moments of Promethium-148 and Erbium-165

Abstract

The hyperfine structure of the ${}_{}{}^6{}_{}{}^{}H_{\frac{7}{2}}^{}{}_{}{}^{}$ level in 5.3-day ${\mathrm{Pm}}^{148}$ and the ${}_{}{}^3{}_{}{}^{}H_6^{}{}_{}{}^{}$ level in 10-h ${\mathrm{Er}}^{165}$ have been measured by atomic-beam magnetic resonance. The spins of these isotopes have been verified to be $I\left({\mathrm{Pm}}^{148}\right)=1\mathrm{}$ and $I\left({\mathrm{Er}}^{165}\right)=\frac{5}{2}$. The electronic $g$ factor for the ${}_{}{}^6{}_{}{}^{}\mathrm{H}_{\frac{7}{2}}^{}{}_{}{}^{}$ level in ${\mathrm{Pm}}^{148}$ is found to be $g_J=-0.8278\mathrm{}\left(1\right)\mathrm{}$. The hyperfine constants and inferred nuclear moments are, $\{\mathrm{for} {\mathrm{Pm}}^{148}:,\mathrm{A}=+1038\mathrm{}(75)\mathrm{} \frac{\mathrm{Mc}}{sec},,B=-98\mathrm{}(103)\mathrm{} \frac{\mathrm{Mc}}{sec},\}\{{\mu }_I=+2.07\mathrm{}(21)\mathrm{} \mathrm{nm},,Q=+0.2\mathrm{}(2)\mathrm{} \mathrm{b};\}\{\mathrm{and}\mathrm{for} {\mathrm{Er}}^{165}:, \mathrm{}|A|=195\mathrm{}(6)\mathrm{} \frac{\mathrm{Mc}}{sec},,\mathrm{}|B|=3502\mathrm{}(115)\mathrm{} \frac{\mathrm{Mc}}{sec},,\frac{B}{A}<0,\}\left\{\right|{\mu }_I\mathrm{}|=0.65(3\mathrm{})\mathrm{} \mathrm{nm},,\mathrm{}|Q|=2.2\mathrm{}(1)\mathrm{} \mathrm{b},,Q_{{\mu }_I}>0.\mathrm{}\}$ The nuclear moments of ${\mathrm{Pm}}^{148}$ were calculated from the hyperfine constants and assumptions made concerning the electronic fields at the nucleus; these assumptions include a 2% correction for the breakdown of Russell-Saunders coupling, but do not include corrections for the Sternheimer effect. The stated errors include a 5% uncertainty for $〈\frac{1}{r^3}〉$. The Fermi-Segrè formula and the direct measurement of the magnetic moment of ${\mathrm{Er}}^{167}$ were used to calculate the dipole moment of ${\mathrm{Er}}^{165}$. The quadrupole moment of ${\mathrm{Er}}^{165}$ has not been corrected for the Sternheimer effect. The measurements indicate that ${\mathrm{Pm}}^{148}$ may be described by the shell model, but that ${\mathrm{Er}}^{165}$ is deformed and must be interpreted by the collective model.