Phase transitions in the $sdg$ interacting boson model

TL;DR

This paper analyzes phase transitions in the $sdg$ interacting boson model using geometric methods, revealing a phase diagram similar to the $sd$ model with no stable triaxial shape transition.

Contribution

It provides a geometric analysis of the $sdg$ interacting boson model and characterizes its phase-transitional structure with a schematic Hamiltonian.

Findings

Phase diagram resembles the $sd$ model.

No transition to a stable triaxial shape.

Phase transitions occur between dynamical symmetries.

Abstract

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 ($\beta_2$), axial hexadecapole ($\beta_4$) and triaxial ($\gamma_2$). The phase-transitional structure is established for a schematic $sdg$ hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical ${\rm U}(5)\otimes{\rm U}(9)$, the (prolate and oblate) deformed ${\rm SU}_\pm(3)$ and the $\gamma_2$-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.