Return of Collective Rotation in ${}^{157}\mathrm{Er}$ and ${}^{158}\mathrm{Er}$ at Ultrahigh Spin

A new frontier of discrete-line $\gamma$-ray spectroscopy at ultrahigh spin has been opened in the rare-earth nuclei ${}^{157,158}\mathrm{Er}$. Four rotational structures, displaying high moments of inertia, have been identified, which extend up to spin $\sim 65\hslash$ and bypass the band-terminating states in these nuclei which occur at $\sim 45\hslash$. Cranked Nilsson-Strutinsky calculations suggest that these structures arise from well-deformed triaxial configurations that lie in a valley of favored shell energy which also includes the triaxial strongly deformed bands in ${}^{161–167}\mathrm{Lu}$.

Figure 1

Evolution of the nuclear structure of ${}^{158}\mathrm{Er}$ with spin. Excitation energies of a variety of observed structures are plotted with respect to a rigid-rotor reference in order to emphasize the changes that occur along and close to the yrast line. The strongest new high moment-of-inertia band is included, but its exact excitation energy is not known. The inset illustrates the changing shape of ${}^{158}\mathrm{Er}$ with increasing spin within the standard $(\epsilon ,\gamma )$ deformation plane.

Figure 2

Background-subtracted coincident ${\gamma }^5$ spectra illustrating the two strongest sequences observed in (a) ${}^{158}\mathrm{Er}$ and (b) ${}^{157}\mathrm{Er}$. The strong unlabeled peaks represent the low-spin yrast structures in these nuclei. The relative intensity profiles of the new (band 1) sequence in ${}^{158}\mathrm{Er}$ and known structures around the feedout region are shown in the inset in (a).

Figure 3

Dynamic moments of inertia as a function of rotational frequency for the new (band 1) sequences in ${}^{157,158}\mathrm{Er}$, the yrast SD band in ${}^{152}\mathrm{Dy}$ [1], a TSD band in ${}^{163}\mathrm{Lu}$ [2], and the strongly deformed band in ${}^{175}\mathrm{Hf}$ [4].

Figure 4

(a) Calculated deformations for some well-deformed configurations. Axial ($\gamma =0°$) SD configurations involving proton holes in the $g_{9/2}$ $[404]9/2$ orbital are shown for nuclei from ${}^{132}\mathrm{Ce}$ to ${}^{152}\mathrm{Dy}$. Similar axial deformations for configurations involving neutron holes in the $h_{11/2}$ $[505]11/2$ orbital are shown for nuclei from ${}^{152}\mathrm{Dy}$ to ${}^{175}\mathrm{Hf}$. Triaxial ($\gamma \sim 20°$) shapes are also predicted corresponding to a valley of low level density shown in (b) for neutron numbers $N=82–94$. In (a), the solid data points indicate that corresponding experimental bands are established. In (b), single-neutron energies near $N=90$ are shown as a function of deformation for $\gamma =0°$ in the left-hand panel. In the center panel, the elongation is kept constant with ${\epsilon }_2=0.25$, and $\gamma$ is increased to 20°. The strong coupling within the upsloping $N_{\mathrm{osc}}=4$, $n_z=0$ equatorial orbitals causes the $[402]3/2$ and $[400]1/2$ orbitals to split apart so that a region of low level density is created at $\gamma =20°$. This is illustrated in the right-hand panel where ${\epsilon }_2$ is increased.