  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) x
SO(3), which defines basis states with fixed values of the angular momentum L.
The relationship of the latter to $U(6) \subset U(3)x 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.
