Phase transitions in the sdg interacting boson model

A geometric analysis of the sdg interacting boson model is performed. A coherent state is used in terms of three types of deformation: axial quadrupole (β2), axial hexadecapole (β4) and triaxial (γ2). The phase-transitional structure is established for a schematic sdg Hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5)⊗U(9), the (prolate and oblate) deformed SU±(3) and the γ2-soft SO(15) limits. For realistic choices of the Hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.