Symmetry energy extracted from the S$\pi$RIT pion data in Sn+Sn systems

With the improved particular Isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model (impIBUU) including the nucleon-nucleon short-range correlations, the ratios and yields of $\pi^{-}$ and $\pi^{+}$ in Sn+Sn systems with different asymmetries at 270 MeV/nucleon are studied. It is found that the yields of $\pi^{-}$ and $\pi^{+}$ and their ratios in Sn+Sn systems characterized by different neutron to proton ratios obtained from the very recent S$\pi$RIT pion data, are quite well described by the model, especially when a soft symmetry energy with $L(\rho_{0})$ = 66.75$\pm$24.75 MeV is used. The calculations also clearly demonstrate that the high-momentum tail of the nucleon initialization in momentum space strongly affects the yields and ratios of pion production in Sn+Sn systems with different asymmetries near or below threshold. In addition, given many insoluble theoretical uncertainties in transport models, multi-system experimental measurements with various N/Z asymmetries are proposed to extract the symmetry energy less model-dependently by using heavy-ion collisions.