Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

TL;DR

This paper investigates the symmetries of the sdg-IBM concerning octahedral shapes, finding that isolated octahedral minima are absent in dynamical symmetries but can emerge in transitional Hamiltonians or through interaction modifications.

Contribution

It demonstrates the absence of isolated octahedral minima in dynamical symmetries of the sdg-IBM and proposes methods to realize such shapes via transitional Hamiltonians or interaction adjustments.

Findings

No sdg-IBM dynamical symmetry Hamiltonian has an isolated octahedral minimum.

Degenerate minima with octahedral shapes can occur in transitional Hamiltonians.

Modifying g boson interactions can produce isolated octahedral or cubic minima.

Abstract

The symmetries of the sdg-IBM, the interacting boson model with s, d and g bosons, are studied as regards the occurrence of shapes with octahedral symmetry. It is shown that no sdg-IBM Hamiltonian with a dynamical symmetry displays in its classical limit an isolated minimum with octahedral shape. However, a degenerate minimum that includes a shape with octahedral symmetry can be obtained from a Hamiltonian that is transitional between two limits, U_g(9) x U_d(5) and SO_sg(10) x U_d(5), and the conditions for its existence are derived. An isolated minimum with octahedral shape, either an octahedron or a cube, may arise through a modification of two-body interactions between the g bosons. Comments on the observational consequences of this construction are made.