Effects of pion potential and nuclear symmetry energy on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions at beam energies around the pion production threshold

Within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we studied the effects of the pion potential and the symmetry energy on the pion production in central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions around the pion production threshold. It is found that the pion potential has opposite effects on the value of the ${\pi }^{-}/{\pi }^{+}$ ratio at low and high pion energies. The effect of the pion potential on the total ${\pi }^{-}/{\pi }^{+}$ ratio becomes larger in heavy-ion collisions at beam energies below the pion production threshold. At beam energies below the pion production threshold, with the pion potential, the effect of the symmetry energy on the ${\pi }^{-}/{\pi }^{+}$ ratio becomes smaller compared with that above the pion production threshold.

Figure 1

Density- and momentum-dependent symmetry potential as a function of nucleonic kinetic energy with parameter $x=0,-1$.

Figure 2

Density- and momentum-dependent pion potential. The colored lines labeled by different momenta (MD) are Buss's potential [25]. The black solid line denotes the momentum-independent (MID) potential given by Jun Hong et al. [20]. The left window shows negatively charged pion potential while the right window shows positively charged pion potential.

Figure 3

Isoscalar (left) and isovector (right) potentials of pions (only the $\delta =0.2$ case is shown) used in the IBUU model.

Figure 4

Left: Momentum distribution of $\pi$ meson in the compression stage in the central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at $E_{\mathrm{beam}}=400$ MeV/nucleon. Right: Same as the Left, but for $E_{\mathrm{beam}}=200$ MeV/nucleon.

Figure 5

Left: Effect of pion potential on charged pion ratio ${\pi }^{-}/{\pi }^{+}$ in central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at $E_{\mathrm{beam}}=400$ MeV/nucleon with softer symmetry energy $\left(x=0\right)$. Right: Same as the left, but for stiffer symmetry energy $\left(x=-1\right)$.

Figure 6

Effect of the symmetry energy on the ${\pi }^{-}/{\pi }^{+}$ ratio in central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at $E_{\mathrm{beam}}=400$ MeV/nucleon without (left) and with (right) the pion potential.

Figure 7

Time evolution of the ${\pi }^{-}/{\pi }^{+}$ ratio with and without pion potential for softer $\left(x=0\right)$ and stiffer $\left(x=-1\right)$ symmetry energies.

Figure 8

Same as Fig. 5, but for $E_{\mathrm{beam}}=200$ MeV/nucleon.

Figure 9

Same as Fig. 6, but for $E_{\mathrm{beam}}=200$ MeV/nucleon.

Figure 10

Same as Fig. 7, but for $E_{\mathrm{beam}}=200$ MeV/nucleon.