A six-dimensional Davidson potential, introduced within the framework of the interacting vector boson model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the $\mathrm{Sp}(12,R)\supset \mathrm{SU}(1,1)\times \mathrm{SO}(6)$ reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of $\mathrm{SO}(6)$ are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

• Received 26 May 2005

DOI:https://doi.org/10.1103/PhysRevC.72.014314