Pairing effect on critical spin in chiral rotation. II. Triaxial deformation dependence

The critical spin ${I}_{c}$ or critical frequency $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$ denotes the minimum spin or rotational frequency required for the onset of aplanar chiral rotation in nuclear systems. The triaxial deformation dependence of the pairing effect on ${I}_{c}$ and $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$ are investigated for the particle-hole configuration $\ensuremath{\pi}(1{h}_{11/2})\ensuremath{\bigotimes}\ensuremath{\nu}{(1{h}_{11/2})}^{\ensuremath{-}1}$, with triaxial deformation parameters $\ensuremath{\gamma}={15}^{\ensuremath{\circ}}$, ${20}^{\ensuremath{\circ}}$, ${25}^{\ensuremath{\circ}}$, ${35}^{\ensuremath{\circ}}$, ${40}^{\ensuremath{\circ}}$, and ${45}^{\ensuremath{\circ}}$, within the particle rotor model. The analyses of the energy-splitting $\mathrm{\ensuremath{\Delta}}E(I)$ between the doublet bands, the probability density profiles $\mathcal{P}(\ensuremath{\theta},\ensuremath{\varphi})$ of the total angular momentum orientation $(\ensuremath{\theta},\ensuremath{\varphi})$, the maximal and average orientation angles ${\ensuremath{\varphi}}_{m}$ and $\overline{\ensuremath{\varphi}}$, as well as the derived rotational frequency $\ensuremath{\hbar}\ensuremath{\omega}(I)$ reveal that with increasing neutron pairing interaction, the critical spin ${I}_{c}$ is delayed for $\ensuremath{\gamma}<{30}^{\ensuremath{\circ}}$, whereas it is advanced for $\ensuremath{\gamma}>{30}^{\ensuremath{\circ}}$. In contrast, the critical frequency $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$ decreases monotonically across all values of $\ensuremath{\gamma}$. These behaviors are further elucidated by analyzing the angular momentum components of both protons and neutrons along the three principal axes.