Energy systematics of low-lying collective states within the framework of the interacting vector boson model

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