Davydov-filippov limit of the IBM

Abstract

The O(6) limit of the interacting boson model (IBM) is studied in connection to the rigid-triaxial-rotor model of Davydov and Filippov (D–F), and the γ unstable model of Wilets and Jean (W–J). The IP^π = 0⁺ deformation potential is calculated as a function of axial asymmetry γ by projecting a -γ-fixed intrinsic state onto the good angular momentum I^π = 0⁺. Although the projected potential has already been reported to have a minimum at γ = 30° for small values of the boson number N, it is shown that the potential resembles a square well at the classical limit: N → ∞. This indicates that the rigid triaxial (D–F) wave function differs at N → ∞ from the γ unstable (W–J) wave function which is the exact solution of the O(6), although these two types of wave functions are known to be identical for smaller N. The projected spectrum with γ = 30° is found to converge at N → ∞ to the D–F spectrum with γ = 30°. Thus the D–F limit of the IBM can be introduced as the “projected” classical limit, although it can no longer be a good approximation to the exact O(6) solution.