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We investigate the evolution of quantal spectra and the corresponding wavefunctions along the [O(6)-U(5)]$\supset$O(5) transition of the interactingboson model. The model is integrable in this regime and its ground state passesthrough a second-order structural phase transition. We show that the wholespectrum as a function of the Hamiltonian control parameter, as well asstructures of all excited states, exhibit rather organized and correlatedbehaviors, that provide deeper insight into the nature of this transitionalpath.Comment: 10 pages, 8 figure

Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics