The coupled-rotor-vibrator model

Abstract

Some recent advances in the theory of dynamical groups are used to extend and put the CRV model on a more rigorous microscopic foundation. We show that vector-coherent-state theory provides exact rotor expansions of Elliott's su(3) operators as well as boson expansions of the giant-resonance excitation operators. The rotor expansion leads to simple analytic expressions for su(3) matrix elements that are exact in many situations and, in general, accurate to high order in a small parameter L/2 λ + μ, for λ ⩾ μ, and in L/ λ + 2 μ, for λ < μ. These expressions provide useful and accurate hand-calculator alternatives to implementation of the exact algorithms available for the computation of su(3) matrix elements in an so(3) basis. They also provide valuable insights into the physical content of the su(3) model in rotor-model terms. Another recent development shows that the rigid-rotor and SU(3) models can survive the effects of strong representation mixing due, for example, to spin-orbit and other interactions, albeit in a “softened form”. We incorporate this development into the CRV model and show that, as a consequence, nuclear rotational bands and their vibrational excitations have natural microscopic origins in valence-shell su(3) representations with strong renormalization and “softening” due to the effects of coupling to higher shells and representation mixing. Some implications of the results for the microscopic interpretation of rotational spectra in heavy nuclei are discussed.