Shapes and stability within the interacting boson model: Dynamical symmetries

For algebraic models the coherent states are appropriate trial wave functions to study the energy surfaces of the system. The equilibrium configurations of these functions are classified by means of the separatrix of the catastrophe formalism, which is defined by the bifurcation and Maxwell sets. The bifurcation sets correspond to curves in the parameter space associated to degenerate critical points while the Maxwell sets constitute the locus of points for which the energy surface takes the same value in two or more critical points. As an example we study the energy surfaces associated to the dynamical symmetries of the interacting boson model in the essential parameter space. {} 1996 The American Physical Society.