Higher-rank discrete symmetries in the IBM. III Tetrahedral shapes

TL;DR

This paper derives conditions within the interacting boson model for the emergence of tetrahedral shapes with higher-rank discrete symmetry in nuclear structures, highlighting how specific interactions can induce such shapes.

Contribution

It provides a theoretical framework for realizing tetrahedral symmetry in the sf-IBM by identifying conditions on Hamiltonians and interaction modifications.

Findings

Degenerate minima with tetrahedral symmetry can occur in the classical limit.

Conditions for tetrahedral minima are derived for transitional Hamiltonians.

Modifying two-body f-boson interactions can induce tetrahedral shapes.

Abstract

In the context of the sf-IBM, the interacting boson model with s and f bosons, the conditions are derived for a rotationally invariant and parity-conserving Hamiltonian with up to two-body interactions to have a minimum with tetrahedral shape in its classical limit. A degenerate minimum that includes a shape with tetrahedral symmetry can be obtained in the classical limit of a Hamiltonian that is transitional between the two limits of the model, U_f(7) and SO_{sf}(8). The conditions for the existence of such a minimum are derived. The system can be driven towards an isolated minimum with tetrahedral shape through a modification of two-body interactions between the f bosons. General comments are made on the observational consequences of the occurrence of shapes with a higher-rank discrete symmetry in the context of algebraic models.