Collective flows of pions in Au+Au collisions at energies 1.0 and 1.5 GeV/nucleon

Based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the pion potentials obtained from the in-medium dispersion relation of the $\mathrm{\Delta }$-hole model and from the modified phenomenological approach are further introduced. Both the rapidity $y_0$ and transverse-velocity $u_{t0}$ dependence of directed $v_1$ and elliptic $v_2$ flows of ${\pi }^{+}$ and ${\pi }^{-}$ charged mesons produced from Au+Au collisions at two beam energies of 1.0 and 1.5 GeV/nucleon and within a large centrality region of $0<b_0<0.55$ are scanned. Calculations with pion potentials as well as without considering the pion potential are compared to the newly experimental data released by the FOPI Collaboration at GSI Helmholtzzentrum für Schwerionenforschung. It is found that the directed flow is more sensitive to the pion potential than the elliptic one, and the attractive pion potential from the phenomenological B mode of the phenomenological approach is too strong to describe the flow data and can be safely ruled out. The relatively weak pion potential from the $\mathrm{\Delta }$-hole model can supply a good description for the FOPI data of both flows as functions of both centrality and rapidity. A two-peak structure occurs in the transverse-velocity-dependent directed flow but the elliptic flow drops monotonously with increasing $u_{t0}$. Finally, both $v_1$ and $v_2$ flows with large $u_{t0}$ from semicentral heavy-ion collisions can be taken as sensitive probes for the pion potential.

Figure 1

Momentum dependence of the real part of the pion optical potential at densities $\rho ={\rho }_0$ (a) and $2{\rho }_0$ (b) obtained from the phenomenological formula (phen A and phen B modes) and from the $\mathrm{\Delta }$-hole model.

Figure 2

Rapidity dependence of the directed flows of ${\pi }^{+}$ (a) and ${\pi }^{-}$ (b) charged mesons for Au+Au collisions at 1.5 GeV/nucleon with $0<b_0<0.25$. The scaled transverse velocity cut $1.0<u_{t0}<4.2$ is chosen as well. Calculations with pion potentials from the phen B mode (dotted lines) and the $\mathrm{\Delta }$-hole model (solid lines), and without considering the pion potential (dashed lines) are compared to the FOPI data (scattered stars) taken from Ref. [9]. The directed flow of free protons is also shown by the dash-dotted line with squares.

Figure 3

Centrality dependence of the slope parameter $v_{11}$ of ${\pi }^{+}$ (left) and ${\pi }^{-}$ (right) mesons produced from Au+Au collisions at beam energies 1.0 (upper) and 1.5 GeV/nucleon (bottom). The choice of the $u_{t0}$ and the symbols for various calculations and experimental data are the same as for Fig. 2. The horizontal dashed lines represent unity.

Figure 4

Rapidity dependence of the elliptic flows of ${\pi }^{+}$ [(a)–(c)] and ${\pi }^{-}$ [(d)–(f)] charged mesons for Au+Au collisions at 1.5 GeV/nucleon with centralities $b_0<0.25,0.25<b_0<0.45$, and $0.45<b_0<0.55$ (from left to right). The choice of the $u_{t0}$ and the symbols for various calculations and experimental data are the same as for Fig. 2. The horizontal dashed lines represent unity.

Figure 5

The same as Fig. 4 but for the $u_{t0}$ dependence of the directed flow parameter $v_1$. The rapidity cut $-1.8<y_0<0$ is chosen and, correspondingly, the FOPI experimental data of charged pions are taken from Ref. [9]. In plot (a), the directed flow of free protons is also shown for comparison.

Figure 6

The same as Fig. 5 but for the $u_{t0}$ dependence of the elliptic flow parameter $v_2$ of charged pions.