Detailed spectroscopy of quadrupole and octupole states in ${}^{168}\mathrm{Yb}$

The low-lying positive- and negative-parity states in ${}^{168}\mathrm{Yb}$ have been investigated by means of the $(\alpha ,2\mathrm{n}\gamma )$ fusion evaporation reaction. Using the coincidence method, the level scheme was corrected and extended up to 3 MeV, for both the positive- and negative-parity states. Using the new branching ratios determined in the present experiment, the $K$ quantum number was proposed for two negative-parity bands by direct comparison with the Alaga rule. Like in some other nuclei, one negative-parity band was established, decaying predominantly to the $\gamma$-vibrational band. In a second experiment, the lifetimes of the low-lying excited states up to $J^{\pi }=6^{+}$ in the ground-state band were measured by using the in-beam fast-timing method with the Bucharest mixed high-purity germanium (HPGe) and ${\mathrm{LaBr}}_3$:Ce detector array using the triple-$\gamma$ coincidence method. Reduced $E2$ transition probabilities were extracted from the measured lifetimes and compared with the corresponding observables in neighboring isotopes, showing a smooth behavior with increasing mass. The positive- and negative-parity states as well as $E1$ and $E2$ transition probability ratios revealed by these experiments are compared with the interacting boson model in the $sd$ and $spdf$ boson space, and with the confined beta-soft rotor model, and are found to be in good agreement.

Figure 1

Sample $\gamma$-ray spectra from the ${}^{166}\mathrm{Er}(\alpha ,2n)$ reaction. (a) Total projection spectrum of a symmetric $\gamma \text{−}\gamma$ coincidence matrix; (b) projection of the $\gamma \text{−}\gamma$ matrix gated by the 1039.2 keV $\gamma$ ray $\left(6_{\beta }^{+}\to 6_1^{+}\right)$. The newly observed peak at 310 keV corresponds to an intraband transition in the $\beta$-vibrational band which was selected from a region where multiple $\gamma$ rays belonging to ${}^{169}\mathrm{Yb}$ are present [marked with asterisk in panel (a)].

Figure 2

Part of the level scheme for ${}^{168}\mathrm{Yb}$. New transitions and levels are in red.

Figure 3

(a) Projection to the HPGe axis of a $\gamma \gamma \gamma$ $\left(E_{HPGe}\text{−}{E}_{LaB{r}_3}\text{−}{E}_{LaB{r}_3}\right)$ coincidence cube. (b) Projection to the energy $(\gamma$ rays observed in the ${\mathrm{LaBr}}_3$:Ce detectors) axis of the $E_{\gamma 1}\text{−}{E}_{\gamma 2}\text{−}\Delta T$ cube gated by the 385 keV $\gamma$ ray in the HPGe detectors. (c) Energy projection of the same cube gated by two $\gamma$ rays: 385 keV in HPGe and 299 keV in ${\mathrm{LaBr}}_3$:Ce.

Figure 4

Time distributions for the $2^{+}$ (a), $4^{+}$ (b), and $6^{+}$ (c) states in the ground-state band of ${}^{168}\mathrm{Yb}$. For the $2^{+}$ state (a) the fit to the experimental data with the convoluted exponential decay function is presented (red line). For the other two states [(b) and (c)] the delayed coincidence time spectrum is obtained by considering the difference between the centroids of the distributions for $t_{\mathrm{start}}-t_{\mathrm{stop}}$ (black) and $t_{\mathrm{stop}}-t_{\mathrm{start}}$ (red).

Figure 5

Experimental lifetimes [(a), (c), and (e)] and reduced $E2$ transition probabilities [(b), (d), and (f)] for the low-lying positive-parity states of the yrast band in Yb isotopes ranging from mass 158 to 176; points are experimental results, blue solid lines are IBM calculations, and green dashed lines are CBS calculations. The red points are the experimental values determined in the present experiments. The other experimental values are from Refs. [30, 31, 32, 33, 34, 35, 36, 37, 38]. The calculations reproduce well the experimental trend, showing in general a slight overprediction for the reduced transition probability values in heavier nuclei.

Figure 6

Systematic behavior of the branching ratios for the $J^{\pi }=2^{-}$ state of the $K^{\pi }=2^{-}$ octupole-vibrational band decaying only to the $\gamma$-band (a) or to the $\gamma$ band and ground-state band for all nuclei between Gd $\left(Z=64\right)$ and W $\left(Z=74\right)$. A strong decay pattern is seen in two mass regions, for $A\le 172$ and $A\ge 182$, and it stops abruptly in between. The data for ${}^{168}\mathrm{Yb}$ in panel (b) corresponds to the $4^{-}\to 3_{\gamma }^{+}/4^{-}\to 4_1^{+}$ ratio. The solid line in panel (a) indicates the Alaga rule prediction for the corresponding transitions. The points in panel (b) with a branching ratio equal to zero are placed at 0.1 due to the logarithmic scale.

Figure 7

Experimental excitation energies for the low-lying levels of ${}^{168}\mathrm{Yb}$ in comparison with the present IBM-$spdf$ calculations. The states are grouped in bands and the ground-state band, the $\beta$- and the $\gamma$-bands (for the positive-parity states), and $K^{\pi }=1^{-}$ and $K^{\pi }=2^{-}$ bands (for the negative-parity states) are presented. The band heads for the octupole bands are not known experimentally and are therefore not included in the figure.

Figure 8

Evolution of the relative moment of inertia from Eq. (18) as a function of spin for the ground state band (a), $\beta$-vibrational band (b), and $\gamma$-vibrational band (c) with the predictions of IBM and CBS models.