Nucleon Size Independence of Hadronic Nucleus-Nucleus Cross Sections

Abstract

Recent proposals to constrain the nucleon size using hadronic cross sections ($σ_{\rm AA}$) conflict with collective flow data. I demonstrate this dependence is an artifact of ``geometric inflation,'' where smearing point-like nucleons unintentionally dilutes the nuclear surface. By implementing a self-consistent framework that preserves the global nuclear density, I show that $σ_{\rm AA}$ is essentially insensitive to the nucleon width. This establishes $σ_{\rm AA}$ as a robust probe of the nuclear surface rather than the sub-nucleon scale. Utilizing this property, I extract a neutron skin thickness for $^{208}$Pb of $Δr_{\rm np} \in [0, 0.24]$~fm, providing an unconventional way to constrain the nuclear symmetry energy using high-energy hadronic observables.

Figures (4)

• Figure 1: (Color online). Illustration of geometric inflation. The target Woods–Saxon distribution is compared with the inflated density from uncorrected sampling for $w=0.9$ fm. The corrected sampling distribution, obtained via inverse transform, ensures the physical density matches the target after convolution.
• Figure 2: (Color online). The (effective) Woods–Saxon parameters for the target density ($R,a$), the inflated density ($R_{\rm eff},a_{\rm eff}$, constrained by Eqs. (\ref{['eq:norm']})--(\ref{['eq:rms']})), and the corrected density ($\tilde{R},\tilde{a}$). The black dashed curves represent the analytical approximation in Eq. (\ref{['eq:ana']}).
• Figure 3: (Color online). $\sigma_{\rm AA}$ for $^{208}$Pb+$^{208}$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, computed with the default Woods–Saxon parameters (red dashed curve) and with the Gaussian-kernel–corrected Woods–Saxon parameters (blue solid curve), compared with the horizontal band of ALICE measurements ALICE:2022xir. The blue dashed curve shows the effect of increasing the diffuseness to $a=0.6$ fm.
• Figure 4: (Color online). (a) Thickness function $T_{\rm pp}(b)$ vs impact parameter for different nucleon form-factor approximations with nucleon radius $r_{p} = r_{\rm ch,p}$; (b) corresponding effective parton–parton cross section vs nucleon size. The $\gamma$ parameters relate to the general thickness function formula given in Eq. (\ref{['eq:thick']}).