Spherical-oblate shape coexistence in $^{94}$Zr from a model-independent analysis

Low-lying states of $^{94}$Zr were investigated via low-energy multi-step Coulomb excitation. From the measured $\gamma$-ray yields, 13 reduced transition probabilities between low-spin states were determined, together with the spectroscopic quadrupole moments of the $2_{1,2}^+$ states. Based on this information, for the first time in the Zr isotopic chain, the shapes of the $0_{1,2}^+$ states including their deformation softness were inferred in a model-independent way using the quadrupole sum rules approach. The ground state of $^{94}$Zr possesses a rather diffuse shape associated with a spherical configuration, while the $0_2^+$ state is oblate and more strongly deformed. The observed features of shape coexistence in $^{94}$Zr are in agreement with Monte-Carlo shell-model predictions, and the present results are vital to refine the IBM-CM description of the Zr isotopes around $A\approx 100$ in terms of an intertwined quantum phase transition.