Reexamine the nuclear chiral geometry from the orientation of the angular momentum

The paradox on the previous interpretation for the nuclear chiral geometry based on the effective angle has been clarified by reexamining the system with the particle-hole configuration $\pi (1h_{11/2})^1 \otimes \nu(1h_{11/2})^{-1}$ and rotor with deformation parameter $\gamma=30^\circ$. It is found that the paradox is caused by the fact that the angular momentum of the rotor is much smaller than those of the proton and the neutron near the bandhead. Hence, it does not support a chiral rotation interpretation near the bandhead. The nuclear chiral geometry based on the effective angle makes sense only when the angular momentum of the rotor becomes comparable with those of the proton and the neutron at the certain spin region.