  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.
