Selection Rule for Electromagnetic Transitions in Nuclear Chiral Geometry

In order to find the selection rules that can be applied to the electromagnetic transitions when the chiral geometry is achieved, a model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation. A quantum number obtained from the invariance of the Hamiltonian is given and the selection rule for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. Among the available candidates for chiral bands of odd-odd nuclei, in which the near degeneracy of two $\mathrm{\Delta }I=1$ bands is observed, the measured electromagnetic properties of the two bands in ${}_{55}^{128}$Cs${}_{73}$ and ${}_{55}^{126}$Cs${}_{71}$ are consistent with the rules, while those of ${}_{59}^{134}$Pr${}_{75}$ and ${}_{57}^{132}$La${}_{75}$ are not.