Phase diagram for a cubic-Q interacting boson model Hamiltonian: Signs of triaxiality

An extension of the Interacting Boson Model that includes the cubic ((Q) over cap x (Q) over cap x (Q) over cap)((0)) term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete (chi-dependent) expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter gamma as a linear combination of cos (3 gamma) and cos(2) (3 gamma) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored: The orders of the phase transition surfaces that define the phase diagram are described, and the possible nuclear equilibrium shapes are established. It is found that for this particular Hamiltonian, contrary to expectations, there is only a very tiny region of triaxiality, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.