Background: The semimicroscopic algebraic quartet model (SAQM) generates the excitation spectra of shell-like quartets, formed by two protons and two neutrons in a well-defined shell configuration. It is based on the SU(3) symmetry, which is valid only in light nuclei. Algebraic quartet models have been proposed for heavy nuclei, too, but their shell model background is not known.

Purpose: I wish to construct an algebraic approach for the description of shell-like quarteting in heavy nuclei.

Methods: The SAQM is extended based on the pseudo- and proxy-SU(3) symmetries.

Results: The procedure of the generalization is presented. The new models are applied for the description of the energy spectrum and electromagnetic transitions of the low-lying bands of ${}^{224}\mathrm{Th}$.

Conclusions: In the present case the performance of the two approximate symmetries is fairly similar due to the alike nature of the relevant shell orbits. The possibly similar or different results of the two symmetries are discussed.

• Received 22 March 2020
• Accepted 14 April 2020

DOI:https://doi.org/10.1103/PhysRevC.101.054306