Regular Article - Theoretical Physics
Stability/self-consistency of SU(3) highest-weight irreps
Chiba Institute of Technology, Narashino, 275-0023, Chiba, Japan
Accepted: 23 November 2022
Published online: 29 November 2022
Recently the highest-weight irreducible representations (hw irreps) of the SU(3) symmetry came to attract a lot of attention as dominant spatial configurations of ground states in deformed nuclei from the viewpoint that they are the most symmetric spatial configurations. In thinking of dominant configurations, the stability of the configurations is also important. The stability can be interpreted as the self-consistency of the configurations in the deformed potential produced by themselves. That question is investigated in this report through a simple procedure within the three-dimensional harmonic oscillator (3D-HO) shell model. It has been found that while the hw irreps are always self-consistent up to the midshell, in some cases after the midshell, they become unstable and replaced by the ones with the highest eigen-value of the second Casimir operator through the procedure. These unstable cases have turned out to lie within the islands of shape coexistence recently predicted on the basis of the dual-shell mechanism that includes both the 3D-HO and the spin-orbit(SO) like shells. This can be another effect to boost the shape coexistence in these regions.
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