  A well-established observation in nuclear physics is that in neutron-rich
spherical nuclei the distribution of neutrons extends farther than the
distribution of protons. In this work, we scrutinize the influence of this so
called neutron-skin effect on the centrality dependence of high-$p_{\rm T}$
direct-photon and charged-hadron production. We find that due to the estimated
spatial dependence of the nuclear parton distribution functions, it will be
demanding to unambiguously expose the neutron-skin effect with direct photons.
However, when taking a ratio between the cross sections for negatively and
positively charged high-$p_{\rm T}$ hadrons, even centrality-dependent
nuclear-PDF effects cancel, making this observable a better handle on the
neutron skin. Up to 20~\% effects can be expected for the most peripheral
collisions.
