Harmonic-dependent geometry-to-flow transfer in AMPT Ru+Ru and Zr+Zr isobar collisions

Abstract

We present a fixed-$N_{\rm part}$ study of geometry-to-flow transfer in string-melting AMPT simulations of $^{96}{\rm Ru}+^{96}{\rm Ru}$ and $^{96}{\rm Zr}+^{96}{\rm Zr}$ collisions at $\sqrt{s_{NN}}=200$ GeV. Four nuclear configurations are considered: deformation-only Ru+Ru, deformation-only Zr+Zr, deformation plus neutron skin Ru+Ru and deformation plus neutron skin Zr+Zr. The AMPT/HIJING initialization is modified to include deformed Woods--Saxon densities and, when enabled, separate proton and neutron Woods--Saxon radii and diffuseness parameters (neutron skin effect). We introduce an eccentricity-normalized isobar response double ratio, $D_n=(v_n^{\rm Ru}/v_n^{\rm Zr})/(\varepsilon_n^{\rm Ru}/\varepsilon_n^{\rm Zr})$, evaluated in common participant-number intervals. This observable eliminates the initial-geometry eccentricity ratio, and investigates whether the final-state flow ratio is fully determined by the initial-geometry ratio. We find that the elliptic double ratio is nearly unity, and the triangular double ratio is consistently greater than unity for the two deformation-only and deformation-plus-skin configurations. The positive $D_3-1$ pattern is maintained when varying the $N_{\rm part}$ binning, peripheral-bin treatment, flow $p_T$ range and rapidity/pseudorapidity acceptance. The result identifies a harmonic-dependent AMPT response: Ru/Zr elliptic flow follows leading eccentricity scaling to high accuracy, whereas triangular flow retains a residual response component after the triangularity ratio is divided out.