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 H– ^3 He ( R(^3H/^3He) ) with reduced rapidity from 0 to 0.5 were simulated at 50 MeV/u even-even ^36-56 Ca + ^40 Ca, even-even ^48-78 Ni + ^58 Ni, and ^100-139 Sn (every third isotopes) + ^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 ΔR_np=⟨r^2⟩_n^1/2-⟨r^2⟩_p^1/2 , which was negative for neutron-deficient nuclei. The unified ΔR_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(^3H/^3He) 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 ΔR_np of the projectiles for all reduced impact parameters. In addition, a scaling phenomenon was observed between ΔR_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(^3H/^3He) 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.