The static quadrupole moments (SQMs) of nuclear chiral doublet bands are investigated for the first time taking the particle-hole configuration $pi(1h_{11/2}) otimes u(1h_{11/2})^{-1}$ with triaxial deformation parameters in the range $260^circ leq gamma leq 270^circ$ as examples. The behavior of the SQM as a function of spin $I$ is illustrated by analyzing the components of the total angular momentum. It is found that in the region of chiral vibrations the SQMs of doublet bands are strongly varying with $I$, whereas in the region of static chirality the SQMs of doublet bands are almost constant. Hence, the measurement of SQMs provides a new criterion for distinguishing the modes of nuclear chirality. Moreover, in the high-spin region the SQMs can be approximated by an analytic formula with a proportionality to $cosgamma$ for both doublet bands. This provides a way to extract experimentally the triaxial deformation parameter $gamma$ for chiral bands from the measured SQMs.
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