Effects of the pion-nucleon potential in ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at 1.5 GeV/nucleon

The influence of the pion-nucleon potential on the pion dynamics in ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at 1.5 GeV/nucleon for different centrality intervals is investigated in the framework of the isospin-dependent quantum molecular dynamics model. It is found that the observables related to pions, such as the rapidity distributions, the rapidity dependencies of the directed flow and the elliptic flow, the centrality dependencies of the directed flow and the elliptic flow, and the transverse momentum distribution of the strength function of the azimuthal anisotropy are sensitive to the pion-nucleon potential. The pion multiplicity and the polar-angle distributions of pions are less affected by the pion-nucleon potential. The comparisons to the experimental data, in particular to the rapidity distributions of the directed flow and the elliptic flow, favor the stronger pion-nucleon potential derived from the phenomenological ansatz proposed by Gale and Kapusta [C. Gale and J. Kapusta, Phys. Rev. C 35, 2107 (1987)].

Figure 1

Momentum dependence of the pion energy (a) and the pion optical potential (b) from the free space (solid line), the $\mathrm{\Delta }$-hole model (dashed line), and the Gale-Kapusta model (dotted line) at $\rho =2{\rho }_0$.

Figure 2

(a) Time evolution of pion multiplicity in the central ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon. (b) Excitation function of pion multiplicity. Various sets of the $\pi N$ potential are used in the calculations as indicated.

Figure 3

Rapidity distributions of ${\pi }^{+}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon with different $\pi N$ potentials and centralities as indicated.

Figure 4

Rapidity dependence of the directed flow for ${\pi }^{+}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon.

Figure 5

Rapidity dependence of the directed flow for ${\pi }^{+}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon with the transverse velocity cut $1.0<u_{t0}<4.2$. The experimental data are taken from Ref. [31].

Figure 6

The same as in Fig. 5, but for the results of ${\pi }^{-}$.

Figure 7

Centrality dependence of the midrapidity slope $d{v}_1/d{y}_0$ for ${\pi }^{+}$ (a) and ${\pi }^{-}$ (b) in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon. The cut of $1.0<u_{t0}<4.2$ is used in the calculations. The experimental data are taken from Ref. [31].

Figure 8

Rapidity distributions of the elliptic flow for ${\pi }^{+}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon with two sets of centrality as indicated.

Figure 9

Rapidity distributions of the elliptic flow for ${\pi }^{+}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon. Various $\pi N$ potentials, centralities, and the transverse velocity cut are used in the calculations as indicated. The experimental data are taken from Ref. [31].

Figure 10

The same as in Fig. 9, but for the results of ${\pi }^{-}$.

Figure 11

Centrality dependence of the elliptic flow for ${\pi }^{+}$ (a) and ${\pi }^{-}$ (b) in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon. The cuts of $-1.8<y_0<0$ and $0.8<u_{t0}<4.2$ are used in the calculations. The experimental data are taken from Ref. [31].

Figure 12

Polar angle distributions for ${\pi }^{-}$ in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1 GeV/nucleon with various $\pi N$ potentials and centralities as indicated. The experimental data and the IQMD SM results are from Ref. [31].

Figure 13

The same as in Fig. 12, but for the results in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon with indicated centralities.

Figure 14

Transverse momentum dependence of the strength function of the azimuthal anisotropy in the ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ reaction at 1.5 GeV/nucleon. The various $\pi N$ potentials and centralities are used in the calculations as indicated.