Isotopic dependence of the yield ratios of light fragments from different projectiles and their unified neutron skin thicknesses

The yield ratios of neutron-proton (R(n/p)) and \({^3}\) ${}^3$ H– \({^3}\) ${}^3$ He ( \(R({^3}\textrm{H}/{^3}{\textrm{He}})\) $R({}^3\text{H}/{}^3\text{He})$ ) with reduced rapidity from 0 to 0.5 were simulated at 50 MeV/u even-even \(^{36-56}\) ${}^{36-56}$ Ca + \(^{40}\) ${}^{40}$ Ca, even-even \(^{48-78}\) ${}^{48-78}$ Ni + \(^{58}\) ${}^{58}$ Ni, and \(^{100-139}\) ${}^{100-139}$ Sn (every third isotopes) + \(^{112}\) ${}^{112}$ Sn for full reduced impact parameters using the isospin-dependent quantum molecular dynamics (IQMD) model. The neutron and proton density distributions and root-mean-square radii of the reaction systems were obtained using the Skyrme-Hartree-Fock model, which was used for the phase space initialization of the projectile and target in IQMD. We defined the unified neutron skin thickness as \(\Delta {R_\text {np}}={\langle {r^2}\rangle }_\text {n}^{1/2}-{\langle {r^2}\rangle }_\text {p}^{1/2}\) $\mathrm{\Delta }{R}_{\text{np}}={⟨r^2⟩}_{\text{n}}^{1/2}-{⟨r^2⟩}_{\text{p}}^{1/2}$ , which was negative for neutron-deficient nuclei. The unified \(\Delta {R_\text {np}}\) $\mathrm{\Delta }{R}_{\text{np}}$ values for nuclei with the same relative neutron excess from different isotopic chains were nearly equal, except for extreme neutron-rich isotopes, which is a type of scaling behavior. The yield ratios of the three isotopic chain-induced reactions, which depended on the reduced impact parameter and unified neutron skin thickness, were studied. The results showed that both R(n/p) and \(R({^3}\textrm{H}/{^3}{\textrm{He}})\) $R({}^3\text{H}/{}^3\text{He})$ decreased with a reduced impact parameter for extreme neutron-deficient isotopes; however, they increased with reduced impact parameters for extreme neutron-rich isotopes, and increased with the \(\Delta {R_\text {np}}\) $\mathrm{\Delta }{R}_{\text{np}}$ of the projectiles for all reduced impact parameters. In addition, a scaling phenomenon was observed between \(\Delta {R_\text {np}}\) $\mathrm{\Delta }{R}_{\text{np}}$ and the yield ratios in peripheral collisions from different isotopic chain projectiles (except for extreme neutron-rich isotopes). Thus, R(n/p) and \(R({^3}\textrm{H}/{^3}{\textrm{He}})\) $R({}^3\text{H}/{}^3\text{He})$ from peripheral collisions were suggested as experimental probes for extracting the neutron or proton skin thicknesses of non-extreme neutron-rich nuclei from different isotopic chains.