Background: The low-lying level structures of deformed odd-odd nuclei away from the region of stability have been sparsely characterized due to low cross-section yields in reactions, short half-lives, and lack of dedicated studies. One such interesting case is the odd-odd rare-earth light-mass isotope ${}^{162}\mathrm{Lu}$, where, except for the ground state (gs) $J^{\pi }=1^{-}\{\pi 1/2^{+}[411\downarrow ]\otimes \nu 3/2^{-}[521\uparrow ]\}$, assignments of other low-lying levels are unknown or ambiguous. The nucleus is reported to have two low-lying isomeric states with uncertain assignments of spin-parity, level energy, and orbital configuration without specific information on the individual $\beta$-decay branchings.

Purpose: This work uses the well-tested empirical two-quasiparticle rotor model (TQRM) with explicit inclusion of the residual neutron-proton interaction to deduce the low-energy spectrum of ${}^{162}\mathrm{Lu}$ and thereby characterize the isomeric states. Following the characterization of ${}^{162}\mathrm{Lu}$, a similar trend of isomers in neighboring odd-odd ${}^{164,166,168}\mathrm{Lu}$ isotopes is analyzed.

Methods: The empirical three-step TQRM calculations estimate the spin-parities, orbital configurations, and energies of the physically admissible two-quasiparticle (2qp) states in the odd-odd system. Experimental energies of the single-particle (1qp), proton ($p$), and neutron ($n$) states close to the Fermi surface in the mass region of interest are taken as inputs. The spin-parities of the low-lying 2qp bandheads are determined by coupling of the 1qp $p$ and $n$ orbitals while the level energies are calculated using the TQRM energy expressions. $\beta$-decay selection rules are employed for mapping the favored $\beta$-branching of the gs and isomers to select daughter levels.

Results: The 1.5 min isomer in ${}^{162}\mathrm{Lu}$ is deduced to have $J^{\pi }=4^{-}\{\pi 5/2^{+}[402\uparrow ]\otimes \nu 3/2^{-}[521\uparrow ]\}$, with estimated level energy $E_x \approx 62$ keV. The 1.9 min isomer is characterized for the first time with $J^{\pi }=6^{+}\{\pi 9/2^{-}[514\uparrow ]\otimes \nu 3/2^{-}[521\uparrow ]\}$ and energy $E_x \approx 160$ keV. Based on these assignments, individual $\beta$-decay branches of the gs and the two isomers to the daughter levels in ${}^{162}\mathrm{Yb}$ are proposed. The study is extended to neighboring isotopes ${}^{164,166,168}\mathrm{Lu}$. A candidate for the isomer, tentatively proposed in an earlier study of ${}^{164}\mathrm{Lu}$, is identified as $J^{\pi }=4^{-}\{\pi 5/2^{+}[402\uparrow ]\otimes \nu 3/2^{-}[521\uparrow ]\}$ with $E_x \approx 52$ keV. The excitation energy of the $J^{\pi }=3^{+}$ isomer in ${}^{168}\mathrm{Lu}$, currently listed with a large uncertainty, is deduced as $E_x \approx 100$ keV, significantly improving its value.

Conclusions: The low-lying levels of ${}^{162}\mathrm{Lu}$ were constructed using the empirical TQRM calculations. The spin-parities, orbital configurations, and level energies of the two low-lying isomers were estimated, and their $\beta$ decay pathways were proposed for the first time. Isomers in the neighboring odd-odd isotopes were also studied. These proposed assignments can be used as location guides for in-depth experimental studies.

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• Beta decay
• Electromagnetic transitions
• Energy levels
• Isomer decays
• Nuclear spin & parity
• Nuclear structure & decays
• 150 ≤ A ≤ 189