Shapes and Shape Phase Transitions in the Interacting Boson Model
The interacting boson approximation (IBA) has been shown to provide a rather successful description of collective nuclear properties. Since the model is formulated in an elegant but rather abstract algebraic way its precise relation to geometrical models like the Bohr-Hamiltonian describing a liquid drop with quadrupole surface oscillations is by no means obvious. Up to now the connection with the geometrical approach has only been made indirectly: it has been inferred on the basis of the similarity of the expressions for energy levels and E2 transition rates that the three dynamical symmetries1,2,3 that occur in IBA, namely SU(5), SU(3) and O(6), correspond (for N → ∞) to the anharmonic vibrator, the axially symmetric rigid rotor and the gamma unstable rotor, respectively. To establish a more direct connection between the two pictures one needs to express the IBA hamiltonian in terms of shape variables, thus allowing one to associate a geometry with the IBA formulation.
KeywordsCoherent State Casimir Operator Dynamical Symmetry Transitional Region Trial Wave Function
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