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$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at$\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study thegeometry and fluctuations raised from the deformation of the colliding nuclei.Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios betweenthese two collision systems and demonstrate that the ratios of ${\rmac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics andevent-plane correlations, are sensitive to quadrupole and octupoledeformations, which could provide strong constrains on the shape differencesbetween $^{96}$Ru and $^{96}$Zr. We also study the nonlinear responsecoefficients $\chi_{4,22}$, which show insensitivity to the deformation effect.

Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs