Shape polarization and coexistence of high- three-quasiparticle states in odd-mass isotones
Three-quasiparticle -isomeric states in odd-mass isotones within the mass region are systematically investigated using configuration-constrained potential energy surface calculations. The calculations successfully reproduce the excitation energies and deformations of known high- isomers in the nuclei from Tm to Re. For the nuclei closer to the shell closure (Ir, Au, and Tl), predictions for the configurations of observed and yet-to-be-observed isomers are provided. The results reveal strong shape polarization, where the three-quasiparticle states are driven to larger deformations compared to the often shape-soft or spherical ground states. A particularly rich spectrum of shape coexistence is predicted in Tl, where several high- three-quasiparticle configurations with distinct prolate, oblate, and triaxial shapes are found to coexist at similar excitation energies. Notably, the oblate-deformed configuration at keV is proposed to be responsible for a long-lived isomer. This study provides a comprehensive picture of shape evolution and coexistence in high- multi-quasiparticle states, offering valuable insights for future experimental research.