Isomeric states in neutron-rich $Z=76$ isotopes and $N=116$ isotones

We have employed both unpaired (cranked Nilsson-Strutinsky) and paired (cranked Nilsson-Strutinsky-Bogoliubov) cranked Nilsson-Strutinsky calculations to explore the properties of observed and potential isomers within the shape-transitional osmium $(Z=76)$ isotopes and $N=116$ isotones. Our analyses reveal the prevalence of multiquasiparticle prolate and broken-pair triaxial structures in even-even osmium isotopes $(N=112–118)$ and $N=116$ isotones $(Z=72–80)$. In addition, our exploration of $N=116$ isotones identifies potential isomeric states, systematically, including noncollective ${10}^{-}$ and collective ${12}^{+}$ states, constructed upon specific neutron configurations.

Figure 1

Unpaired CNS single-particle Routhians for (a) protons and (b) neutrons for the deformation ${\varepsilon }_2=0.143$, ${\varepsilon }_4=0.041$, and $\gamma =-{120}^{\circ }$. The line types distinguish between different $(\pi ,\alpha )$ combinations: solid lines represent $(+,+1/2)$, dotted lines $(+,-1/2)$, dashed lines $(-,+1/2)$, and dash-dotted lines $(-,-1/2)$. A few important crossings for the present interpretation are highlighted.

Figure 2

Calculated CNSB potential-energy surfaces versus quadrupole deformation ${\varepsilon }_2$ and the triaxiality parameter $\gamma$ of ${}^{192}\mathrm{Os}$ for positive-parity $(+,0)(+,0)I=0$, 10, 12, 18, 20, 22, and 28 states which are interpreted in the text. Contour lines are separated by 0.25 MeV and the $\gamma$ plane is marked at ${15}^{\circ }$ intervals. Dark regions represent low energy and absolute minima are labeled with red dots.

Figure 3

The CNSB $(+,0)(+,0)$ yrast line in ${}^{192}\mathrm{Os}$ compared with the energy at different fixed deformations governed by the minima shown in Fig. 2. The collective prolate state energy is obtained with a minimization starting from $\gamma =0^{\circ }$. The noncollective prolate states are calculated at the deformation of the ${18}^{+}$ state. Experimental ground-state energies are also shown. All energies are minimized at different pairing parameters, $\mathrm{\Delta }$ and $\lambda$, and drawn relative to the rotating liquid drop reference.

Figure 4

Experimental and theoretical energies of the ground state bands in ${}^{188–194}\mathrm{Os}$. The experimental data are taken from Ref. [45]. All energies are minimized at different deformation with a minimization starting at $\gamma =0^{\circ }$ and pairing parameters, $\mathrm{\Delta }$ and $\lambda$. Energies and drawn relative to the rotating liquid drop reference.

Figure 5

The favored CNSB MQP state energies in ${}^{188–194}\mathrm{Os}$ are drawn by full black lines. The unfavored ${12}^{+}$ state energy is also shown in brown lines to compare with Ref. [17]. The experimental energies for ${10}^{-}$ isomers (in red dash lines) and $7^{-}$ isomer (in a blue dash line) are taken from Ref. [46].

Figure 6

The low-lying CNS $(+,0)(+,0)$ configurations in ${}^{192}\mathrm{Os}$ with the collective prolate shape ($-{16}^{\circ }<\gamma <0^{\circ }$), the fixed triaxial shape $(\gamma \approx -{90}^{\circ })$ and also the oblate shape. The experimental $(+,0)$ yrast sequence energies are also drawn. The alignments in each configuration are displayed on the figure. All energies are minimized at different pairing parameters, $\mathrm{\Delta }$ and $\lambda$, and drawn relative to the rotating liquid drop reference.

Figure 7

Spin $I$ versus rotational frequency $\hslash \omega$ for the experimental yrast sequence are compared with calculations for the $(+,0)(+,0)$ CNSB configurations with $\gamma =-{90}^{\circ }$ and $\gamma =0^{\circ }$.