pseudoSU3

pseudoSU3 is an approximate symmetry employed in nuclear structure theory to describe collective properties of medium–heavy and rare‑earth nuclei. It emerges when the conventional SU(3) classification of the nuclear shell model is modified by the introduction of pseudospin symmetry. In the pseudospin scheme the single‑particle states with total angular momentum j = ℓ + ½ and j = ℓ – ½ are paired into doublets that behave like a quasi‑spin ½ system, called pseudospin. By redefining the orbital angular momentum to a pseudo‑orbital ℓ̃ = ℓ – 1 for the upper members of the doublets, an approximate SU(3) algebra can be constructed in which these pseudospin partners transform as components of a single SU(3) multiplet.

The pseudoSU3 concept was developed in the 1970s by J.P. Draayer and collaborators to account for the apparent restoration of SU(3)–like degeneracies in nuclei where the physical spin‑orbit force would otherwise destroy the symmetry. It provides a microscopic framework for interpreting rotational bands, quadrupole collectivity, and electromagnetic transition rates in deformed nuclei. Calculations within the pseudoSU3 model reproduce observed energy spectra and B(E2) values with remarkable accuracy, especially for nuclei in the 50–82 and 82–126 neutron shells.

While the symmetry is not exact—pairing interactions and configuration mixing break it—the pseudoSU3 approach offers a powerful tool for connecting shell‑model configurations to collective degrees of freedom. It also furnishes insight into the underlying algebraic structure of nuclear forces and facilitates the comparison with other SU(3)–based models used in hadronic physics.