Abstract :
The transition from a spherical-vibrator to a deformed-rotor phase is examined in this and succeeding papers in the interacting boson and Bohr–Mottelson collective models. This paper explores the transition from a U(5) to an O(6) phase in the interacting boson model with variation of a control parameter α. As expected from other studies, it is observed that a low-lying state of the model can be assigned to one of three phases: a U(5) phase, an O(6) phase, or a transition phase. It is also shown that the range of values of the control parameter, for which the low-lying states are in the transition phase, shrinks as the dimension of the IBM Hilbert space increases and that a sharp phase transition develops as the infinite-dimensional limit is approached. A detailed examination of the states of the two phases shows that the U(5) symmetry of the α=0 limit is mixed throughout much of the U(5) phase and the O(6) symmetry of the α=1 limit is even more strongly mixed throughout much of the O(6) phase. Nevertheless, it is found that quasidynamical U(5) and O(6) symmetries continue to characterize the phases and provide an explanation of the apparent persistence of these symmetries in the face of strong symmetry-breaking interactions. Thus, the analysis suggests a useful definition of a phase associated with a dynamical symmetry. It also adds a perspective to Landauʹs theory of second-order phase transitions and to Iachelloʹs concept of a critical point symmetry with analytical solutions in the transition region.
