Shape polarization and coexistence of high-$K$ three-quasiparticle states in odd-mass $N=106$ isotones

TL;DR

This work addresses how high-$K$ three-quasiparticle states in odd-mass $N=106$ isotones evolve in shape as they approach the $Z=82$ shell closure. It employs a configuration-constrained potential-energy-surface method within a macroscopic–microscopic framework to compute deformations and excitation energies for 1-qp and 3-qp configurations, with unpaired nucleons blocked in specific orbitals. The results show strong shape polarization of the 3-qp states relative to softer ground states and reveal rich shape coexistence in $^{187}$Tl, including a prolate $K^{\pi}=27/2^+$ state and an oblate $K^{\pi}=29/2^+$ state, plus a predicted low-lying $K^{\pi}=25/2^{-}$ configuration that could act as a spin trap. The findings align with available data for lighter isotones and provide concrete predictions to guide future spectroscopic experiments near the $Z=82$ shell closure. Overall, the work advances understanding of how unpaired nucleons drive deformation and shape coexistence in high-$K$ multi-quasiparticle states and offers experimental benchmarks for identifying shape isomerism in neutron-deficient nuclei.

Abstract

Three-quasiparticle $K$-isomeric states in odd-mass $N=106$ isotones within the $A\sim 180$ mass region are systematically investigated using configuration-constrained potential energy surface calculations. The calculations successfully reproduce the excitation energies and deformations of known high-$K$ isomers in the nuclei from $^{175}$Tm to $^{181}$Re. For the nuclei closer to the $Z=82$ shell closure ($^{183}$Ir, $^{185}$Au, and $^{187}$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 $^{187}$Tl, where several high-$K$ three-quasiparticle configurations with distinct prolate, oblate, and triaxial shapes are found to coexist at similar excitation energies. Notably, the oblate-deformed $K^π=29/2^+$ configuration at $E_x = 1839$ keV is proposed to be responsible for a long-lived isomer. This study provides a comprehensive picture of shape evolution and coexistence in high-$K$ multi-quasiparticle states, offering valuable insights for future experimental research.

Figures (2)

• Figure 1: Calculated $\beta_2$ and $\gamma$ deformations for the g.s. and 3-qp states of odd-$A$ nuclei in the $N$=106 isotonic chain. For $Z=69{-}79$, the 3-qp states correspond to the coupling of the 2-qp $K^{\pi}=8^{-}$ configuration $\nu7/2^- [514] \otimes 9/2^+ [624]$ with the g.s. configurations of odd-$A$ nuclei, which are $\pi1/2^{+}[411]$, $\pi7/2^{+}[404]$, $\pi7/2^{+}[404]$, $\pi5/2^{+}[402]$, $\pi1/2^{-}[541]$, and $\pi1/2^{-}[541]$, respectively. For $Z=81$, the 3-qp state is $\pi {11/2}^{-}[505] \otimes \nu \{ {9/2}^{+}[624] \otimes {7/2}^{-}[514] \}$. These 3-qp states correspond to observed high-$K$ isomers.
• Figure 2: Calculated ${ }^{187} \mathrm{Tl}$ potential energy surfaces (PES's) of (a) the near-spherical g.s., (b) the prolate $K^{\pi}=27/2^+$, $\pi 11/2^{-}[505] \otimes \nu \left\{9/2^{+}[624] \otimes 7/2^{-}[514]\right\}$ state, (c) the oblate $K^{\pi}= 29/2^{+}$, $\pi 13/2^{+}[606] \otimes \nu \left\{9/2^{+}[624] \otimes 7/2^{+}[633]\right\}$ state, (d) the triaxial $K^{\pi}= 25/2^{+}$, $\pi 11/2^{-}[505] \otimes \nu \left\{7/2^{+}[633] \otimes 7/2^{-}[503]\right\}$ state. The energy difference between neighboring contours is 100 keV. The black dots denote the minima of PES's.