Theoretical analysis of the extraction of neutron skin thickness from coherent π0 photoproduction off nuclei

Background: Coherent $\ensuremath{\pi}{}^{0}$ photoproduction on heavy nuclei has been suggested as a reliable tool to infer neutron skin thicknesses. To this aim, various experiments have been performed, especially on $^{208}\mathrm{Pb}$.Purpose: We analyze the sensitivity of that reaction process to the nucleonic density, and especially to the neutron skin thickness, for $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$, for which reliable data exist, and on $^{116,124}\mathrm{Sn}$, for which measurements have been performed in Mainz. We study also the role played by the ${\ensuremath{\pi}}^{0}$-nucleus final-state interaction.Methods: A model of the reaction is developed at the impulse approximation considering either plane waves or distorted waves to describe the $\ensuremath{\pi}{}^{0}$-nucleus scattering in the outgoing channel.Results: Our calculations are in good agreement with existing data, especially for $^{208}\mathrm{Pb}$. The sensitivity of the theoretical cross sections to the choice of the nucleonic density is small and below the experimental resolution.Conclusions: Coherent $\ensuremath{\pi}{}^{0}$ photoproduction is mostly an isoscalar observable that bares no practical sensitivity to the neutron skin thickness. To infer that structure observable it should be coupled to other reaction measurements, such as electron scattering, or by comparing experiments performed on isotopes of the same chemical element.