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

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 ${\mathcal{O}}_{\mu }^3$ 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 $B(E3;3_1^{-}\to 0_1^{+})$ transition strength of the isotope ${}^{224}$Th using the semi-microscopic algebraic quartet model (SAQM) based on the proxy-$SU(3)$ scheme.

9 pages, 5 figures. Figures improved

References in corpus (6)

• Improved limit on the permanent electric dipole moment of 199Hg
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Proxy-SU(3) symmetry in heavy deformed nuclei
• The islands of shape coexistence within the Elliott and the proxy-SU(3) Models
• Algebraic models for shell-like quarteting of nucleons
• The proxy-SU(3) symmetry in atomic nuclei