Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs
$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between these two collision systems and demonstrate that the ratios of ${\rm ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences between $^{96}$Ru and $^{96}$Zr. We also study the nonlinear response coefficients $\chi_{4,22}$, which show insensitivity to the deformation effect.