Effects of nuclear symmetry energy and in-medium $NN$ cross section in heavy-ion collisions at beam energies below the pion production threshold

Based on the isospin-dependent Boltzmann–Uehling–Uhlenbeck (IBUU04) transport model, we explored effects of in-medium $NN$ elastic scattering cross section and nuclear symmetry energy on the subthreshold pion production in the ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction. We find that, with the decrease of the incident beam energy, the effects of the in-medium $NN$ elastic scattering cross section on the ${\pi }^{-}/{\pi }^{+}$ ratio are larger than that of the symmetry energy, although the latter may be also larger. While keeping the effect of symmetry energy, the double ratio of ${\pi }^{-}/{\pi }^{+}$ from neutron-rich and neutron-poor reaction systems (with the same mass number of system) ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{128}\mathrm{Pm}+{}^{128}\mathrm{Pm}$ almost fully cancels out the effects of the in-medium $NN$ elastic scattering cross section.

Figure 1

Maximal baryon densities reached in central reaction ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at $E_{\text{beam}}=100$, 200, and 300 MeV/nucleon.

Figure 2

Effects of in-medium $NN$ elastic scattering cross section on the ${\pi }^{-}/{\pi }^{+}$ ratio in central collision ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at $E_{\text{beam}}=100$, 150, 200, 250, and 300 MeV/nucleon, respectively.

Figure 3

Time evolution of ${\pi }^{-}$ and ${\pi }^{+}$ mesons with different symmetry energies ($x=0$, $x=1$) and different $NN$ elastic scattering cross sections (in-medium, free) in the central collision ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at the beam energy of 100 MeV/nucleon.

Figure 4

Same as Fig. 3 but at the beam energy of 200 MeV/nucleon.

Figure 5

Effects of in-medium $NN$ cross section and symmetry energy on ${\pi }^{-}/{\pi }^{+}$ ratio in central collision ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at beam energies of 100 and 200 MeV/nucleon, respectively.

Figure 6

Effects of medium and symmetry energy on the double ${\pi }^{-}/{\pi }^{+}$ ratio from ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Sn}+{}^{100}\mathrm{Sn}$ at the beam energy of 100 MeV/nucleon.

Figure 7

Effects of medium and symmetry energy on the double ${\pi }^{-}/{\pi }^{+}$ ratio from ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{128}\mathrm{Pm}+{}^{128}\mathrm{Pm}$ at the beam energy of 100 MeV/nucleon.