Low-lying level structures in $^{162}$Lu

The well-tested empirical two quasiparticle rotor model calculations are used to characterize low-lying isomers in the odd-odd nucleus $^{162}$Lu. Physically admissible 2qp bandheads are obtained to construct the low-energy level structure of the nucleus, assign spin-parity (J$^\pi$), orbital configuration, and level energies (E$_x$), for the gs and the two reported isomers. The spin-parity and orbital configuration of the 1.5 min isomer are confirmed to be J$^\pi$= 4$^-$\{$\pi$5/2$^+$[402$\uparrow$] $\otimes$ $\nu$3/2$^-$[521$\uparrow$]\}. Its level energy has been estimated to be E$_x$ $\thickapprox$ 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$ $\thickapprox$ 157 keV. Based on these assignments, individual $\beta$-decay branches of gs and the two isomers to the daughter levels in $^{162}$Yb are proposed. The study is extended to neighboruing isotopes $^{164,166,168}$Lu. A short-lived isomer, tentatively proposed in a previous study of $^{164}$Lu, is identified as J$^\pi$= 6$^+$\{$\pi$7/2$^+$[404$\downarrow$] $\otimes$ $\nu$5/2$^+$[402$\uparrow$]\} with energy E$_x$ $\thickapprox$ 52 keV. The energy of the J$^\pi$=3$^+$ isomer in $^{168}$Lu, currently listed with large uncertainty, is deduced as E$_x$ $\thickapprox$ 100 keV significantly improving its value.