Influence of the nuclear symmetry energy on the collective flows of charged pions

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we studied charged pion transverse and elliptic flows in semicentral ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at 600 MeV/nucleon. It is found that ${\pi }^{+}-{\pi }^{-}$ differential transverse flow and the difference of ${\pi }^{+}$ and ${\pi }^{-}$ transverse flows almost show no effects of the symmetry energy. Their corresponding elliptic flows are largely affected by the symmetry energy, especially at high transverse momenta. The isospin-dependent pion elliptic flow at high transverse momenta thus provides a promising way to probe the high-density behavior of the symmetry energy in heavy-ion collisions at the Facility for Antiproton and Ion Research (FAIR) at GSI, Darmstadt or at the Cooling Storage Ring (CSR) at HIRFL, Lanzhou.

Figure 1

Density dependence of nuclear symmetry energy from the MDI interaction with $x=-2$ (stiff), 0 (medium), and 1 (soft).

Figure 2

Effects of nuclear symmetry energy on the rapidity distributions of ${\pi }^{-}$ and ${\pi }^{+}$ in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at a beam energy of 600 MeV/nucleon with an impact parameter of 7 fm.

Figure 3

Effects of nuclear symmetry energy on the rapidity distribution of the ${\pi }^{-}/{\pi }^{+}$ ratio in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at an incident beam energy of 600 MeV/nucleon with an impact parameter of 7 fm.

Figure 4

Effects of nuclear symmetry energy on the charged pion transverse flows ${\mathrm{\Delta }}^{\prime }{F}_{\pi }^x$ (lower panel) and $\mathrm{\Delta }{F}_{\pi }^x$ (upper panel) as a function of rapidity in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at a beam energy of 600 MeV/nucleon and an impact parameter of 7 fm.

Figure 5

Effects of nuclear symmetry energy on the charged pion directed flow ${\mathrm{\Delta }}^{\prime }{v}_1^{\pi }$ and $\mathrm{\Delta }{v}_1^{\pi }$ as a function of rapidity in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at a beam energy of 600 MeV/nucleon and an impact parameter of 7 fm.

Figure 6

Effects of nuclear symmetry energy on the ${\pi }^{+}-{\pi }^{-}$ differential elliptic flow ${\mathrm{\Delta }}^{\prime }{v}_2^{\pi }$ as a function of transverse momentum in different rapidity regions in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at a beam energy of 600 MeV/nucleon and an impact parameter of 7 fm.

Figure 7

Effects of nuclear symmetry energy on the difference of ${\pi }^{+}$ and ${\pi }^{-}$ elliptic flows $\mathrm{\Delta }{v}_2^{\pi }$ as a function of transverse momentum in different rapidity regions in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at a beam energy of 600 MeV/nucleon and an impact parameter of 7 fm.

Figure 8

Effects of nuclear symmetry energy on the ${\pi }^{-}/{\pi }^{+}$ ratio as a function of transverse momentum in different rapidity regions in the reaction of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at a beam energy of 600 MeV/nucleon and an impact parameter of 7 fm.