Tilted-axis-cranking covariant density functional theory for the high-spin spectroscopy in ${}^{69}$Ga

The tilted-axis-cranking covariant density functional theory is applied to investigate the three newly-observed positive-parity bands SI, SII, and SIII in ${}^{69}$Ga. The energy spectra and angular momenta are calculated and compared with the experimental data. For the yrast band SI, pairing correlations play a crucial role for the states with spin $I\le 23\mathrm{/}2\mathrm{\hslash }$. The bands SII and SIII are suggested to be signature partner bands with positive and negative signatures, respectively. The transition probabilities $B(E2)$ for these bands are predicted, and await further experimental verification. By analyzing the angular momentum alignments microscopicly, it is revealed that the $g_{9\mathrm{/}2}$ protons and neutrons play an important role in the description of the collective structure of ${}^{69}$Ga.