  Recent experiments on lead (\textrm{$Pb_{82}^{208}$}) nuclei have observed
the celebrated phenomenon of neutron skin-thickness of low energy nuclear
physics. The skin-thickness provides a measure of extension of spatial
distribution of neutrons inside the atomic nucleus than protons. We have
studied the effect of neutron skin-thickness on inclusive prompt photon
production in Pb~+~Pb collisions at the Large Hadron Collider energies. We have
calculated the \textquoteleft central-to-peripheral ratio\textquoteright
($R_\textrm{cp}$) of prompt photon production with and without accounting for
neutron skin effect. The neutron skin causes a characteristic enhancement in
the ratio, in particular at forward rapidity, which is distinguishable in our
calculation. However a very precise direct photon measurement up to large
transverse momenta would be necessary to constrain the feature in experiment.
