Quadrupole moments of coexisting collective shapes at high spin in ${}^{154}\mathbf{Er}$

Four high-spin collective bands have been populated in ${{}_{68}^{154}\mathrm{Er}}_{86}$ via the ${}^{110}\mathrm{Pd}({}^{48}\mathrm{Ti},4n\gamma ){}^{154}\mathrm{Er}$ reaction. Average transition quadrupole moments $Q_{\mathrm{t}}$ have been measured for three of the bands by using the Doppler-shift attenuation method. The strongest band has a value of $Q_{\mathrm{t}}=11.0\pm 1.0e\mathrm{b}$, similar to values found recently for four triaxial strongly deformed (TSD) bands in ${}^{157,158}\mathrm{Er}$. The second band has a value of $Q_{\mathrm{t}}=19.5\pm 3.2e\mathrm{b}$, consistent with a predicted axially symmetric superdeformed (SD) shape, similar in deformation to the ${}^{152}\mathrm{Dy}$ isotone, and is used as a calibration point. The third, new band has a value of $Q_{\mathrm{t}}=9.9\pm 2.2e\mathrm{b}$. The results confirm the unexpectedly large $Q_{\mathrm{t}}$ moments for the favored TSD bands in light erbium isotopes.

Figure 1

Angle-dependent, triple-gated, and background-subtracted coincidence spectra for band 1 of ${}^{154}\mathrm{Er}$. In-band transitions are labeled with their unshifted energies in keV.

Figure 2

Double-gated background-subtracted coincidence spectra for (a) band 2, (b) band 3, and (c) band 4 of ${}^{154}\mathrm{Er}$. A Doppler correction with an average value of $v/c$ has been applied. Transitions are labeled with their energies in keV.

Figure 3

Dynamic moments of inertia for bands in ${}^{154}\mathrm{Er}$ and $N=86$ isotones ${}^{152}\mathrm{Dy}$ and ${}^{153}\mathrm{Ho}$ [19, 20, 21].

Figure 4

Measured fractional Doppler-shift values $F\left(\tau \right)$ shown as a function of $\gamma$-ray energy together with best fit curves for (a) bands 1 and 2 and (b) band 3 in ${}^{154}\mathrm{Er}$. In (b), curves are also shown for the quoted error on $Q_{\mathrm{t}}$. The two horizontal dashed lines indicate the range of initial recoil velocities within the ${}^{110}\mathrm{Pd}$ target layer.

Figure 5

Total energy surfaces for ${}^{154}\mathrm{Er}$ at (a) $I=30$ and (b) $I=60$ for $(\pi ,\alpha )=(+,0)$. The contour line separation is 0.25 MeV with the last contour line approximately 5 MeV above the minimum, which is marked with a star.

Figure 6

Observed effective alignments when band 2 in ${}^{154}\mathrm{Er}$ is compared with the yrast SD band of ${}^{152}\mathrm{Dy}$. Two curves are shown where the spin of the lowest state in ${}^{154}\mathrm{Er}$ is assumed to be 30 (dashed curve) and $32\hslash$ (solid curve). These curves are compared with calculated values (dotted curve) when the two valence protons are in the two signatures of the lowest $\mathcal{N}=4$ and 5 orbitals, respectively.

Figure 7

Calculated TSD configurations at $\gamma <0^{\circ }$ and $\gamma >0^{\circ }$, which might be assigned to band 1. Values of $Q_{\mathrm{t}}$ at $I=40$ are specified for each configuration. It is also demonstrated how a good agreement between the observed band 1, drawn by the solid line, and the calculated bands can be obtained in the two extreme cases of the $\gamma <0^{\circ }$ [7(10),(42)4] configuration and the $\gamma >0^{\circ }$ [6(22),(42)4] configuration but with very different values of the band-head spin $22\hslash$ and $30\hslash$, respectively. The dashed line labeled “Yrast, $\gamma >0^{\circ }$” corresponds to the lowest energy, independent of signature and parity, for the minima with $\gamma \sim {15}^{\circ }–{30}^{\circ },{\varepsilon }_2\sim 0.3–0.4$. The calculated lowest-energy SD configuration with ${\varepsilon }_2=0.6$ is also included.