A comprehensive systematic study is made for the collective $\beta$ and $\gamma$ bands in even-even isotopes with neutron numbers $N=88$ to 92 and proton numbers $Z=62\left(\mathrm{Sm}\right)$ to 70 (Yb). Data, including excitation energies, $B\left(E0\right)$ and $B\left(E2\right)$ values, and branching ratios from previously published experiments are collated with new data presented for the first time in this study. The experimental data are compared to calculations using a five-dimensional collective Hamiltonian (5DCH) based on the covariant density functional theory (CDFT). A realistic potential in the quadrupole shape parameters $V(\beta ,\gamma$) is determined from potential energy surfaces (PES) calculated using the CDFT. The parameters of the 5DCH are fixed and contained within the CDFT. Overall, a satisfactory agreement is found between the data and the calculations. In line with the energy staggering $S\left(I\right)$ of the levels in the ${2_{\gamma }}^{+}$ bands, the potential energy surfaces of the CDFT calculations indicate $\gamma$-soft shapes in the $N=88$ nuclides, which become $\gamma$ rigid for $N=90$ and $N=92$. The nature of the ${0_2}^{+}$ bands changes with atomic number. In the isotopes of Sm to Dy, they can be understood as $\beta$ vibrations, but in the Er and Yb isotopes the ${0_2}^{+}$ bands have wave functions with large components in a triaxial superdeformed minimum. In the vicinity of ${}^{152}\mathrm{Sm}$, the present calculations predict a soft potential in the $\beta$ direction but do not find two coexisting minima. This is reminiscent of ${}^{152}\mathrm{Sm}$ exhibiting an $X\left(5\right)$ behavior. The model also predicts that the ${0_3}^{+}$ bands are of two-phonon nature, having an energy twice that of the ${0_2}^{+}$ band. This is in contradiction with the data and implies that other excitation modes must be invoked to explain their origin.

• Received 4 July 2018
• Revised 5 June 2019

DOI:https://doi.org/10.1103/PhysRevC.100.044324