Phase transitions and quasidynamical symmetry in nuclear collective models. II. The spherical vibrator to gamma-soft rotor transition in an SO(5)-invariant Bohr model

Abstract

A model of a second-order shape phase transition is investigated in the Bohr collective model. The model contains two variable parameters, a mass parameter M and a control parameter α, and is such that when α = 0 the Hamiltonian is that of a harmonic spherical vibrator and when α is large it approaches that of an adiabatically decoupled rotor-vibrator. The results obtained by diagonalization of this Hamiltonian show that the range of α, in which the low-energy states of the model are in a transition region between that of a harmonic spherical vibrator phase (for small α) and that of an adiabatic rotor-vibrator phase (for large α), shrinks as M increases and as M → ∞ a critical point develops at α = 0.5 . The dynamical symmetries associated with the limiting phases of this model, which appear to persist in the small and large α domains, are interpreted as quasidynamical symmetries. For finite values of M, the results closely parallel those of the corresponding phase transition of an interacting boson model, studied in paper I of this series, when the mass M of the collective model is set equal to twice the boson number N of the IBM. The various solvable submodels of the Bohr model are related to corresponding limits of the IBM by contraction maps. Such contraction maps imply a correspondence between subsets of states in the domains of the two models for which a given contraction map applies. Thus, by considering the contraction limit of an IBM Hamiltonian in the Bohr model, one can interpret and even anticipate what the results of an IBM calculation would be in its macroscopic N → ∞ limit. The asymptotic scaling of the spectrum at the critical point and Iachello's critical point symmetry in the Bohr model and IBM are considered from this perspective.