Medium effect on the nuclear modification factor of protons and pions in intermediate-energy heavy ion collisions

Nuclear modification factors $R_{\mathrm{cp}}$ of protons and pions are investigated by simulating Au+Au collisions from $0.8A$ to $1.8A$ GeV in a framework of an isospin-dependent quantum molecular dynamics (IQMD) model. The $R_{\mathrm{cp}}$ of protons rise with an increase in the transverse particle momentum $p_T$ at different beam energies owing to radial flow and the multiple-collision effect. The rate of increase of $R_{\mathrm{cp}}$ is suppressed at higher beam energies. While the $R_{\mathrm{cp}}$ of pions display weaker $p_T$ dependence. By changing the in-medium nucleon-nucleon cross section, the $R_{\mathrm{cp}}$ of protons change a lot, while the $R_{\mathrm{cp}}$ of pions do not. In addition, by deactivating the $N\mathrm{\Delta }\to NN$ and $\pi N\to \mathrm{\Delta }$ channels, the $R_{\mathrm{cp}}$ of protons change slightly in their increasing rates compared with the “original” case (with these two channels). However, the $R_{\mathrm{cp}}$ of pions is shifted down for the “no $N\mathrm{\Delta }\to NN$” case and has an inverse trend for the “no $\pi N\to \mathrm{\Delta }$” case. Based on these observations, we argue that the observable $R_{\mathrm{cp}}$ is a suitable tool to better distinguish in-medium effects of protons and pions.

Figure 1

Comparison of the $\pi$ production cross section of the measurement and our simulations for midrapidity pions in Au+Au collisions at $1A\mathrm{GeV}$. The circle represents the FOPI data of ${\pi }^{-}$ and the square for ${\pi }^{+}$, the red, green, and blue lines represent different types of $\pi$ from our IQMD simulations. In the calculations, $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account and the in-medium correction for NNCS is not used [i.e., $\eta =0$ in Eq. (8)].

Figure 2

$R_{\mathrm{cp}}$ of (a) protons and (b) pions vs $p_T$ at different beam energies. In the calculations, $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account and the in-medium correction for NNCS is not used [i.e., $\eta =0$ in Eq. (8)].

Figure 3

Blast-wave fits to the spectra and their parameters. (a) $p_T$ spectra in Au+Au central collisions at $0.8A$, $1.0A$, $1.2A$, $1.5A$, and $1.8A\mathrm{GeV}$, the solid lines are the blast-wave fits; (b) the blast-wave fitting contours for temperature vs radial flow at different beam energies. In the calculations, $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account and the in-medium correction for NNCS is not used [i.e., $\eta =0$ in Eq. (8)].

Figure 4

Effects of the reduction factor $\eta$ of the in-medium NNCS on $R_{\mathrm{cp}}$ of (a) protons and (b) pions). Four cases of the in-medium NNCS are considered: $\eta =0$, $\eta =0.2$, $\eta =0.5$, and $\eta =0.9$. In the calculations, $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account.

Figure 5

Blast-wave fitting to (a) $p_T$ spectra of protons and (b) their fitting parameters of $\beta$ and $T$ with different in-medium NNCS reduction factors in the centrality of 0–20%. In the calculations, $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account.

Figure 6

Azimuthal angle distribution of ${\pi }_0$ in “original” case, “no $\pi N\to \mathrm{\Delta }$” case, and “no $N\mathrm{\Delta }\to NN$” case and different centralities (0–20%, 20–40%, and 40–80%). In the calculations, the in-medium correction for NNCS is not used [i.e., $\eta =0$ in Eq. (8)]. In the symbols key, “original” means that both the $\pi N\to \mathrm{\Delta }$ and $N\mathrm{\Delta }\to NN$ are taken into account; “no $\pi N\to \mathrm{\Delta }$” means that the $\pi N\to \mathrm{\Delta }$ is turned off, but the $N\mathrm{\Delta }\to NN$ is on; “no $\pi N\to \mathrm{\Delta }$” means that the $\pi N\to \mathrm{\Delta }$ is on and the $N\mathrm{\Delta }\to NN$ is off.

Figure 7

$R_{\mathrm{cp}}$ of (a) protons and (b) pions vs $p_T$ in Au+Au at $1A\mathrm{GeV}$ by the IQMD simulation with soft EOS and MDI for the three cases. In the calculations, the in-medium correction for NNCS is not used [i.e., $\eta =0$ in Eq. (8)].