Sensitivity of anisotropic flow in Pb+Pb collisions to the neutron skin of $^{208}$Pb at energies available at the CERN Large Hadron Collider
We study the sensitivity of anisotropic flow in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$~TeV to the neutron skin of $^{208}$Pb using the improved string-melting version of a multiphase transport (AMPT) model. By varying the neutron surface diffuseness, we trace the impact of several neutron-skin scenarios from the initial nuclear density profiles and eccentricities to final-state charged-particle production and flow cumulants. A systematic response is observed in both the initial eccentricities and the anisotropic flow, indicating that the neutron-skin-induced geometric effects can survive the full transport evolution. A model-to-data comparison with ALICE measurements disfavors the most compact and most diffuse density profiles within the tested AMPT setup, while the reference and moderate-skin configurations give comparable descriptions. Their similarity reflects a geometric degeneracy in large Pb+Pb collision systems, where the inclusive anisotropic flow is dominated by the effective collision geometry and nuclear size, making it only weakly sensitive to the detailed structure of the neutron surface. These results clarify both the sensitivity and the limitations of using anisotropic flow in relativistic heavy-ion collisions to probe neutron-skin effects.