SU(3) partial dynamical symmetry and nuclear shapes

TL;DR

This paper explores various forms of SU(3) partial dynamical symmetry within the interacting boson model to describe different nuclear shapes and their spectral properties.

Contribution

It provides explicit Hamiltonian constructions with SU(3) partial dynamical symmetry, including higher order terms, for both IBM and IBM-2 frameworks.

Findings

Constructed Hamiltonians with solvable bands for different nuclear shapes

Demonstrated coexistence of prolate and oblate shapes with solvable ground bands

Analyzed aligned proton-neutron shapes with mixed-symmetry bands

Abstract

We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton-neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and $\gamma$ or $\beta$ bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton-neutron shapes with solvable symmetric ground and $\gamma$ bands and mixed-symmetry scissors and $\gamma$ bands.