Vibrational structure and symmetry in $^{110-116}$Cd

We show that a vibrational interpretation and good U(5) symmetry are maintained for the majority of low-lying normal states in $^{110,112,114,116}$Cd isotopes, consistent with the empirical data. The observed deviations from this paradigm are properly treated by an interacting boson model Hamiltonian which breaks the U(5) symmetry in selected non-yrast states, while securing a weak mixing with coexisting SO(6)-like intruder states. The results demonstrate the relevance of the U(5) partial dynamical symmetry notion to this series of isotopes.