Background: Shape coexistence in the $Z\approx 82$ region has been established in mercury, lead, and polonium isotopes. For even-even mercury isotopes with $100\le N\le 106$ multiple fingerprints of this phenomenon are observed, which seems to be no longer present for $N\ge 110$. According to a number of theoretical calculations, shape coexistence is predicted in the ${}^{188}\mathrm{Hg}$ isotope.

Purpose: The aim of this work was to measure lifetimes of excited states in ${}^{188}\mathrm{Hg}$ to infer their collective properties, such as the deformation. Extending the investigation to higher-spin states, which are expected to be less affected by band-mixing effects, can provide additional information on the coexisting structures.

Methods: The ${}^{188}\mathrm{Hg}$ nucleus was populated using two different fusion-evaporation reactions with two targets, ${}^{158}\mathrm{Gd}$ and ${}^{160}\mathrm{Gd}$, and a beam of ${}^{34}\mathrm{S}$ provided by the Tandem-ALPI accelerator complex at the Laboratori Nazionali di Legnaro. The channels of interest were selected using the information from the Neutron Wall array, while the $\gamma$ rays were detected using the GALILEO $\gamma$-ray spectrometer. Lifetimes of excited states were determined using the recoil-distance Doppler-shift method, employing the dedicated GALILEO plunger device.

Results: Lifetimes of the states up to spin $16\hslash$ were measured and the corresponding reduced transition probabilities were calculated. Assuming two-band mixing and adopting, as done commonly, the rotational model, the mixing strengths and the deformation parameters of the unperturbed structures were obtained from the experimental results. In order to shed light on the nature of the observed configurations in the ${}^{188}\mathrm{Hg}$ nucleus, the extracted transition strengths were compared with those resulting from state-of-the-art beyond-mean-field calculations using the symmetry-conserving configuration-mixing approach, limited to axial shapes, and the five-dimensional collective Hamiltonian, including the triaxial degree of freedom.

Conclusions: The first lifetime measurement for states with spin $\ge 6$ suggested the presence of an almost spherical structure above the ${12}_1^{+}$ isomer and allowed elucidating the structure of the intruder band. The comparison of the extracted $B\left(E2\right)$ strengths with the two-band mixing model allowed the determination of the ground-state band deformation. Both beyond-mean-field calculations predict coexistence of a weakly deformed band with a strongly prolate-deformed one, characterized by elongation parameters similar to those obtained experimentally, but the calculated relative position of the bands and their mixing strongly differ.

• Received 22 February 2020
• Accepted 2 July 2020

DOI:https://doi.org/10.1103/PhysRevC.102.014318