Investigation of excited 0$^+$ states in $^{160}\text{Er}$ populated via the $(p,t)$ two-neutron transfer reaction

The interpretation of low-lying 0$^+$ states in rare-earth nuclei remains a highly-debated topic in nuclear structure. Resolving the nature of these states is particularly difficult due to the presence of shape coexistence which can increase the number of low-lying states, as well as the paucity of data for excited 0$^+$ states. Two-neutron transfer reactions are ideal tools for probing 0$^+ \rightarrow$ 0$^+$ transitions in deformed nuclei. In the present work, excited 0$^+$ states are studied via a series of $(p,t)$ reactions on $^{162,164,166,168}$Er targets at the Maier-Leibnitz Laboratory in Garching, Germany. Reaction products were momentum-analyzed with a Q3D magnetic spectrograph. The results confirm strong population of the 0$^{+}_{2}$ state of 18\% of the ground state strength in $^{160}$Er consistent with the strength observed in other $N=92$ isotones, suggesting a special character for this state which is inconsistent with a $\beta$-vibration interpretation. Preliminary results of the $0^{+}$ strength in the aforementioned $(p,t)$ experiments will be presented and placed into context with similar experiments in the $N = 90$ region, underlining the potential role of the $\sfrac{11}{2}^{-}[505] \nu $ orbital in the observed $0^{+}_2$ state strength.