Selection rules of electromagnetic transitions for chirality-parity violation in atomic nuclei

The nuclear Chirality-Parity (ChP) violation, a simultaneous breaking of chiral and reflection symmetries in the intrinsic frame, is investigated with a reflection-asymmetric triaxial particle rotor model. A new symmetry for an ideal ChP violation system is found and the corresponding selection rules of the electromagnetic transitions are derived. The fingerprints for the ChP violation including the nearly degenerate quartet bands and the selection rules of the electromagnetic transitions are provided. These fingerprints are examined for ChP quartet bands by taking a two-$j$ shell $h_{11\mathrm{/}2}$ and $d_{5\mathrm{/}2}$ with typical energy spacing for $A=$ 130 nuclei.