Free spectator nucleons in ultracentral relativistic heavy-ion collisions as a probe of neutron skin

Abstract

Besides the yield ratio of free spectator neutrons produced in ultracentral $^{96}\mathrm{Zr}$+$^{96}\mathrm{Zr}$ to $^{96}\mathrm{Ru}$+$^{96}\mathrm{Ru}$ collisions [Liu et al., Phys. Lett. B 834, 137441 (2022)], we propose that the yield ratio ${N}_{n}/{N}_{p}$ of free spectator neutrons to protons in a single collision system at the BNL Relativistic Heavy Ion Collider or the CERN Large Hadron Collider can be a more sensitive probe of the neutron-skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ and the slope parameter $L$ of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions of colliding nuclei obtained from Skyrme-Hartree-Fock-Bogolyubov calculations, and on a Glauber model that provides information of spectator matter. The final spectator particles are produced from direct emission, clusterization by a minimum spanning tree algorithm or a Wigner function approach, and deexcitation of heavy clusters by gemini. A larger $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ associated with a larger $L$ value increases the isospin asymmetry of spectator matter and thus leads to a larger ${N}_{n}/{N}_{p}$, especially in ultracentral collisions where the multiplicity of free nucleons are free from the uncertainties of cluster formation and deexcitation. We have further shown that the double ratio of ${N}_{n}/{N}_{p}$ in isobaric collision systems or in collisions by isotopes helps to cancel the detecting efficiency for protons. Effects from nuclear deformation and electromagnetic excitation are studied, and they are found to be subdominant compared to the expected sensitivity to $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$.