Quadrupole-Octupole Residual Interaction in the Proxy-$SU(3)$ Scheme

TL;DR

This paper extends the $SU(3)$ nuclear model to include octupole interactions, enabling analysis of octupole deformation effects on energy levels and transition strengths in $^{224}$Th.

Contribution

It introduces an octupole-octupole residual interaction within the proxy-$SU(3)$ scheme and applies it to calculate nuclear properties of thorium-224.

Findings

Calculated energy levels of $^{224}$Th

Analyzed $B(E3)$ transition strengths

Extended $SU(3)$ model to include octupole effects

Abstract

The octupole deformation of atomic nuclei is a relevant research area given its implications in the nuclear structure and fundamental physics, however, inclusion of octupole degrees of freedom in the nuclear interaction has been explored little in $SU(3)$ symmetry-based models. In this article we expand the octupole operator $\mathcal{O}^3_\mu$ in the $SU(3)$ second quantization formalism and use it to formulate an octupole-octupole residual interaction $\mathcal{O}^3\cdot \mathcal{O}^3$ which is incorporated in Elliott's model Hamiltonian. We compute the matrix elements of this extended Hamiltonian and use them to calculate energy levels and analyse the $B(E3; 3^-_1\rightarrow 0^+_1)$ transition strength of the isotope $^{224}$Th using the semi-microscopic algebraic quartet model (SAQM) based on the proxy-$SU(3)$ scheme.