Resolution-matched nuclear geometry and the nucleon-size ambiguity in relativistic heavy-ion collisions

Nuclear structure theory provides point-nucleon densities, whereas high-energy nuclear collisions probe nuclei through finite-resolution hadronic interactions. This resolution mismatch becomes a physical ambiguity when point densities are embedded in Monte Carlo initial-state models with a finite transverse nucleon profile. A parameter intended to describe the effective interaction range can then also reshape the nuclear surface, blurring the separation between nuclear structure and collision dynamics. I show that this ambiguity can largely account for the strong nucleon-width dependence of the ${}^{208}$Pb+${}^{208}$Pb hadronic cross section ($σ_{\rm AA}$) reported in recent Bayesian analyses. Fixing the folded density that enters the Glauber phase shift removes this ambiguity at the level of nuclear geometry. The corrected cross section becomes nearly insensitive to a Gaussian nucleon width and instead probes the nuclear surface. Within a two-component estimate for ${}^{208}$Pb, the current experimental uncertainty of $σ_{\rm AA}$ translates into a broad neutron-skin interval, $Δr_{\rm np}\in[0,0.21]$ fm. These results reframe $σ_{\rm AA}$ as a surface-sensitive bridge between point-nucleon nuclear structure and finite-resolution high-energy initial conditions, rather than as a standalone nucleon-size observable. This establishes resolution matching as a necessary step for using relativistic heavy-ion collisions as quantitative probes of nuclear structure.