Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon

Within a transport model, we study effects of the momentum dependence nuclear symmetry potential on pion observables in central Sn + collisions at 270 MeV/nucleon. To this end, quantity $U_{sym}^{\infty}(\rho_{0})$, i.e., value saturation density $\rho_{0}$ and infinitely large nucleon momentum, is used to characterise potential. It shown that with certain $L$ (i.e., slope energy $\rho_{0}$) characteristic parameter $U_{sym}^{\infty}(\rho_{0})$ affects significantly production $\pi^{-}$ $\pi^{+}$ as well their ratios. Moreover, through comparing charged yields, ratios spectral theoretical simulations for reactions $^{108}$Sn $^{112}$Sn $^{132}$Sn $^{124}$Sn corresponding data S$\pi$RIT experiments, find our results favor constraint $-160^{+18}_{-9}$~MeV, also suggested within range, $62.7<L<93.1$~MeV. In addition, it observable $^{197}$Au 400~MeV/nucleon supports extracted $U_{sym}^{\infty}(\rho_{0})$.