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 $I\leq 23/2\hbar$. 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 $g_{9/2}$ protons and neutrons play an important role in the description of the collective structure of $^{69}$Ga.