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In a new application of the algebraic interacting vector boson model (IVBM), we exploit the reduction of its Sp(12,R) dynamical symmetry group to Sp(4, R)⊗ SO(3), which defines basis states with fixed values of the angular momentum L. The relationship of the latter to U(6) ⊂ U(3) ⊗ U(2), which is the rotational limit of the model, means the energy distribution of collective states with fixed angular momentum can be studied. Results for low-lying spectra of rare-earth nuclei show that the energies of collective positive parity states with L=0,2,4,6... lie on second-order curves with respect to the number of collective phonons n or vector bosons N=4n out of which the states are built. The analysis of this behavior leads to insight regarding the common nature of collective states, tracking vibrational as well as rotational features.

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Physical Review C - Nuclear Physics