Algebraic benchmark for prolate-oblate coexistence in nuclei

TL;DR

This paper introduces an algebraic, symmetry-based method within the interacting boson model to analyze shape coexistence in nuclei, providing analytic formulas and identifying isomeric states.

Contribution

It develops a novel Hamiltonian that preserves specific symmetries for different nuclear shapes and derives explicit expressions for observables.

Findings

Analytic formulas for quadrupole moments and E2 transition rates.

Identification of isomeric states through symmetry-based selection rules.

A unified framework for prolate, oblate, and spherical shape coexistence.

Abstract

We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $\overline{\rm SU(3)}$ symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and $E2$ rates involving these states are derived and isomeric states are identified by means of selection rules.