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

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