Energy surfaces of algebraic models

A procedure to study shapes and stability of algebraic models introduced by Gilmore is presented. According to the time dependent variational principle the coherent states, for algebraic models, are appropriate trial wavefunctions. One calculates the expectation value of the Hamiltonian with respect to the corresponding coherent states to study the energy surfaces of the model. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the catastrophe theory. For one and two-body interactions in the Hamiltonian of the interacting boson model (IBA-1), the critical points are organized through the separatrix. As an example, we apply this separatrix to describe the energy surfaces associated to the dynamical symmetries of the IBA-1, and to the effective Hamiltonians of the Ru, Os and Sm isotopes. (Author)