Observation of γ vibrations and alignments built on non-ground-state configurations in ${}^{156}\mathrm{Dy}$

The exact nature of the lowest $K^{\pi }=2^{+}$ rotational bands in all deformed nuclei remains obscure. Traditionally they are assumed to be collective vibrations of the nuclear shape in the γ degree of freedom perpendicular to the nuclear symmetry axis. Very few such γ bands have been traced past the usual backbending rotational alignments of high-$j$ nucleons. We have investigated the structure of positive-parity bands in the $N=90$ nucleus ${}^{156}\mathrm{Dy}$, using the ${}^{148}\mathrm{Nd}\left({}^{12}\mathrm{C},4n\right){}^{156}\mathrm{Dy}$ reaction at 65 MeV, observing the resulting γ-ray transitions with the Gammasphere array. The even- and odd-spin members of the $K^{\pi }=2^{+}$γ band are observed up to ${32}^{+}$ and ${31}^{+}$, respectively. This rotational band faithfully tracks the ground-state configuration to the highest spins. The members of a possible γ vibration built on the aligned yrast $S$ band are observed up to spins ${28}^{+}$ and ${27}^{+}$. An even-spin positive-parity band, observed up to spin ${24}^{+}$, is a candidate for an aligned $S$ band built on the seniority-zero configuration of the $0_2^{+}$ state at 676 keV. The crossing of this band with the $0_2^{+}$ band is at $\hslash {\omega }_c=0.28\left(1\right)\mathrm{MeV}$ and is consistent with the configuration of the $0_2^{+}$ band not producing any blocking of the monopole pairing.

Figure 1

Partial level scheme deduced for ${}^{156}\mathrm{Dy}$ from the current paper for positive-parity states. New levels and γ-ray transitions are shown in red whereas their known counterparts from previous in-beam work are shown in black. The widths of the arrows are proportional to the intensities of the transitions.

Figure 2

Summed coincident spectra for the (a) even-spin and (b) odd-spin members of the γ bands obtained from the ${}^{12}\mathrm{C}$- and ${}^{36}\mathrm{S}$- [insets (i) and (ii)] induced reactions. New transitions are colored in red whereas contaminants are denoted by hash (#) symbols. In the insets (i) and (ii), transitions marked by asterisks (*) were included in the gating that produced the coincident spectra.

Figure 3

(a)–(c) Summed coincident spectra for bands 12, 17, and 20, respectively, obtained from the ${}^{12}\mathrm{C}$ data. Transitions corresponding to these newly found structures are labeled in red whereas contaminants are denoted by hash (#) symbols.

Figure 4

Plot of the excitation energy minus a rigid rotor for the positive-parity bands shown in Fig. 1.

Figure 5

(a) and (b) Plots of alignment $i_x$ and Routhians $e^{\prime }$, respectively, for the positive-parity bands in ${}^{156}\mathrm{Dy}$.

Figure 6

Ratios of the $B\left(E2\right)$ values for out-of-band to in-band transitions $R_{E2}=B\left(E2;\mathrm{out}\right)/B\left(E2;\mathrm{in}\right)$ for the γ decays from the γ bands to the ground-state band with the γ decays from bands 17 and 20 to the $S$ band. It is assumed that the out-of-band $J\to (J-1)$ transitions are dominated by the $E2$ component due to the $\Delta K=2$ nature of γ band to ground-state band transitions, so we have neglected any $M1$ components.