Quantum rotor and its SU(3) realization
Abstract
A simple FORTRAN program called ROTXSU3, which determines eigenvalues of the quantum rotor and the corresponding algebraic SU(3) model Hamiltonian, is introduced. General analytic expressions for matrix elements of the two Hamiltonians are given. These results are used to establish the equivalence of the SU(3) and rotor theories in the min(λ,μ) ≫ L limit, where λ and μ are SU(3) representation labels and L is the angular momentum. The results can also be used to study group expansion and deformation mechanism since T5×SO(3), the symmetry group of the quantum rotor, is a contraction of SU(3). A mapping between eigenvalues of the invariant operators of the two theories gives a relationship between the parameters of their Hamiltonians. This mapping also leads to a shell-model interpretation of the β and γ shape variables of the collective model. © 1988.