Shell model calculations for the neutron-rich $N=126{}^{206}\mathrm{Hg}\text{−}{}^{197}\mathrm{Lu} (Z=80-71)$ isotones were performed with two different parametrizations. The one refined to explain the isomerism in ${}^{204}\mathrm{Pt}$ was found to be the only one able to reproduce the more recent data on ${}^{203}\mathrm{Ir}$ and, in general, to give a better reproduction of the nuclei in this region. For more exotic nuclei approaching the $r$-process path, this refined parametrization predicts the existence of isomeric states with spin-parities $5^{-}$ and ${10}^{+}$ in the even-mass isotones and $19/2^{+}$ in the odd-mass isotones. Also, it predicts ground-state spin-parities of $3/2^{+}$ for ${}^{201}\mathrm{Re}$ and $11/2^{-}$ for ${}^{199}\mathrm{Ta}$ and ${}^{197}\mathrm{Lu}$, with low-energy long-lived isomers present. The remaining deficiencies of the interaction are related to the properties of the $\pi d_{5/2}$ orbital and are influenced by octupole collectivity. The presented predictions provide guidance and can be tested in the near future at radioactive-beam facilities.

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• Electromagnetic transitions
• Energy levels
• Isomer decays
• Nuclear structure & decays
• 190 ≤ A ≤ 219
• Shell model