High-spin structures of the near-spherical nuclei $^{91,92}$Zr

In the present work, we have interpreted recently available experimental data for high-spin states of the near-spherical nuclei $^{91,92}$Zr, using the shell-model calculations within the full $f_{5/2}$, $p_{3/2}$, $p_{1/2}$, $g_{9/2}$ model space for protons and valence neutrons in $g_{9/2}$, $g_{7/2}$, $d_{5/2}$ orbits. We have employed a truncation for the neutrons due to huge matrix dimensions, by allowing one neutron excitation from $g_{9/2}$ orbital to $d_{5/2}$ and $g_{7/2}$ orbitals. Results are in good agreement with the available experimental data. Thus, theoretically, we have identified the structure of many high-spin states, which were tentatively assigned in the recent experimental work. The $^{91}$Zr $21/2^+$ isomer lies at low-energy region due to fully aligned spins of two $g_{9/2}$ protons and one $d_{5/2}$ neutron.