A study of medium effects in elastic $\pi N$ and $\pi A$ scatterings

The elastic $\pi N$ scattering is investigated for the $I=3/2$ channel dominated by the $\Delta(1232)$ resonance at finite baryon density, employing the effective Lagrangian approach at the tree-level Born approximation. The quark-meson coupling (QMC) model is employed to describe the in-medium baryon properties that are constructed at the quark level, such as the nucleon and $\Delta$ masses, and $\Delta$ full decay width. I reproduce the experimental data of the cross-section in a vacuum as a justification of our approach and then analyze the in-medium total and differential cross-sections as well as proton-spin asymmetry. Following the results of the in-medium elastic $\pi N$ scattering calculation, the elastic $\pi A$ scattering is investigated at finite baryon density in the framework of the Eikonal Glauber model for the light nuclei, $^4\mathrm{He}$ and $^{12}\mathrm{C}$. For the description of the finite nuclei, the Wood-Saxon density profile, and an expansion of the charge distribution as a sum of Gaussians are employed in this study. The nuclear density distribution $\rho_A$, effective baryon mass $m^*_B$, in-medium decay width $\Gamma^*_\Delta$, and in-medium coupling constants $f^*_{\pi NN}$ and $f^*_{\pi N \Delta}$ are analyzed as well as the total cross-section. The results show that the effective baryon mass and cross-sections in the medium decrease as density increases except for the $\Delta$ decay width, which increases as the density increases. The elastic $\pi A$ scattering at the tree-level Born approximation reproduces well the experimental data for $^4\mathrm{He}$ but overestimates for $^{12}\mathrm{C}$. Results for the in-medium $\Delta$ resonance and other findings in this work will be relevant for the relativistic heavy-ion collision experiments.