Background: The neutron-deficient Hg isotopes provide one of the most prominent examples of nuclear shape coexistence. While the even-even nuclei have been extensively investigated, much less is known about how an unpaired neutron influences the evolution of collectivity in the odd-mass isotopes.

Purpose: To determine lifetimes of low-spin states in ${}^{189}\mathrm{Hg}$ and investigate the evolution of collectivity in the rotational band built on the $13/2^{+}$ isomer through comparison with neighboring shape-coexisting Hg isotopes.

Methods: Excited states in ${}^{189}\mathrm{Hg}$ were populated in the ${}^{160}\mathrm{Gd}({}^{34}\mathrm{S},5n){}^{189}\mathrm{Hg}$ fusion-evaporation reaction at a beam energy of 185 MeV. The reaction channel of interest was selected by requiring coincidence with at least one neutron detected in the neutron wall array, while prompt $\gamma$ rays were measured with the GALILEO spectrometer. Lifetimes of low-lying states above the $13/2^{+}$ isomer were measured with the recoil-distance Doppler-shift method using the GALILEO plunger device. The experimental results were compared with total Routhian surface calculations.

Results: Lifetimes of the $17/2^{+}, 21/2^{+}$, and $25/2^{+}$ states were measured for the first time and the corresponding $B$($E2$) strengths were extracted. The excitation energies and transition strengths closely follow the systematics observed in neighboring odd- and even-mass Hg isotopes, supporting the interpretation of the rotational sequence as the coupling of an $i_{13/2}$ neutron to the weakly oblate structures of the neighboring even-even cores. The extracted $B_{4/2}$-type ratio is significantly below unity, extending the occurrence of anomalous transition-strength ratios to this odd-mass nucleus. Total Routhian surface calculations reproduce the weakly oblate equilibrium deformation but not the observed evolution of the transition strengths.

Conclusions: The present results indicate that the $i_{13/2}$-based rotational band largely inherits the structural complexity of the neighboring shape-coexisting even-even Hg nuclei. They further demonstrate that electromagnetic transition strengths provide stringent constraints on the evolution of the underlying wave functions beyond those accessible from excitation energies or static mean-field descriptions alone.

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• Electromagnetic transitions
• Fusion evaporation reactions
• Lifetimes & widths
• Nuclear structure & decays
• 150 ≤ A ≤ 189
• Radiation detectors