Partial dynamical symmetries and shape coexistence in nuclei

TL;DR

This paper introduces a symmetry-based method using partial dynamical symmetries to analyze shape coexistence in nuclei, providing explicit Hamiltonians, spectral features, and transition properties for multiple nuclear shapes.

Contribution

It develops a novel approach employing partial dynamical symmetries to describe shape coexistence, including explicit Hamiltonians and analytic expressions for observables.

Findings

Constructed critical-point Hamiltonians with multiple PDSs.

Analyzed energy surface topology with multiple minima.

Derived analytic expressions for quadrupole moments and E2 rates.

Abstract

We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to a situation when only selected states (or bands of states) of the coexisting configurations preserve the symmetry while other states are mixed. We construct explicitly critical-point Hamiltonians with two or three PDSs of the type U(5), SU(3), ${\overline{\rm SU(3)}}$ and SO(6), appropriate to double or triple coexistence of spherical, prolate, oblate and $\gamma$-soft deformed shapes, respectively. In each case, we analyze the topology of the energy surface with multiple minima and corresponding normal modes. Characteristic features and symmetry attributes of the quantum spectra and wave functions are discussed. Analytic expressions for quadrupole moments and $E2$ rates involving the remaining solvable states are derived and isomeric states are identified by means of selection rules.