Electromagnetic transitions in multiple chiral doublet bands

Multiple chiral doublet bands (M$\chi$D) in the $80$, 130 and $190$ mass regions are studied by the model of $\gamma$=90$^{\circ}$ triaxial rotor coupled with identical symmetric proton-neutron configurations. By selecting the suitable basis, the calculated wave functions are explicitly exhibited to be symmetric under the operator $\hat{A}$, which is defined as rotation by $90^{\circ}$ about 3-axis with the exchange of valance proton and neutron. We found that both $M1$ and $E2$ transitions are allowed between the levels with different values of $A$, while are forbidden between the levels with same values of $A$. Such a selection rule holds true for M$\chi$D in different mass regions.