Atomic-Beam Investigations of Electronic and Nuclear Ground States in the Rare-Earth Region

A number of radioactive isotopes in the rare-earth region have been investigated by using the atomic-beam magnetic-resonance technique. The total electronic angular momentum ($J$) and the atomic $g$ value ($g_J$) have been determined for some low-lying levels in, Pm, Dy, Ho, and Er. These observations are consistent with the following ground-state assignments: Pmi—${\mathrm{}\left(4f\right)\mathrm{}}^5{\mathrm{}\left(6s\right)\mathrm{}}^2$, ${}_{}{}^6{}_{}{}^{}H_{\frac{5}{2}}^{}{}_{}{}^{}$; Dyi—${\mathrm{}\left(4f\right)\mathrm{}}^{10}{\mathrm{}\left(6s\right)\mathrm{}}^2$, ${}_{}{}^5{}_{}{}^{}I_8^{}{}_{}{}^{}$; Hoi—${\mathrm{}\left(4f\right)\mathrm{}}^{11}{\mathrm{}\left(6s\right)\mathrm{}}^2$, ${}_{}{}^4{}_{}{}^{}I_{\frac{15}{2}}^{}{}_{}{}^{}$; and Eri—${\mathrm{}\left(4f\right)\mathrm{}}^{12}{\mathrm{}\left(6s\right)\mathrm{}}^2$, ${}_{}{}^3{}_{}{}^{}H_6^{}{}_{}{}^{}$. The ground-level assignments agree with the Hund's-rule predictions, and the $g$ values approximate the Landé values well. Our present experimental knowledge concerning electronic ground states in the rare-earth region is summarized. The following nuclear spin values have been obtained: ${\mathrm{Pm}}^{149}$, $I=\frac{7}{2}$; ${\mathrm{Pm}}^{151}$, $I=\frac{5}{2}$; ${\mathrm{Gd}}^{159}$, $I=\frac{3}{2}$; ${\mathrm{Tb}}^{160}$, $I=3\mathrm{}$; ${\mathrm{Dy}}^{165}$, $I=\frac{7}{2}$; ${\mathrm{Dy}}^{166}$, $I=0\mathrm{}$; 27-hr ${\mathrm{Ho}}^{166}$, $I=0\mathrm{}$; ${\mathrm{Er}}^{169}$, $I=\frac{1}{2}$; ${\mathrm{Er}}^{171}$, $I=\frac{5}{2}$; and ${\mathrm{Tm}}^{171}$, $I=\frac{1}{2}$. These values are compared with available beta-decay results. Most of these isotopes have large nuclear deformations, and the spin values are discussed in relation to the single-particle energy-level diagrams given by Nilsson. A few results are explained with the shell model.