Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X(5), -X(5), and E(5) symmetries are considered. The dynamical criteria of quantum chaos-the basis state fragmentation width and the wave function entropy-are studied for the (η, χ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed.