A study of the elastic πN scattering at finite baryon density

In this work, we investigate the elastic πN scattering for the I = 3/2 channel dominated by the Δ(1232) resonance at finite baryon density for the symmetric nuclear matter, employing the effective Lagrangian approach at the tree-level Born approximation. The quark-meson coupling (QMC) model is employed to describe the medium modifications for the in-medium baryon properties that are constructed at the quark level, such as the nucleon and Δ masses, and Δ full decay width. We first reproduce the experimental data of the cross-section in a vacuum and we then analyze various physical observables including the total and differential cross-sections and proton-spin asymmetry in a medium. It turns out that suppression and broadening on the peak of the in-medium cross-section becomes more significant at higher baryon density due to the increase of the decay width in the nuclear medium. Also, we find that beyond the Δ-resonance region s ≳ 1.5 GeV, the elastic cross-section scattering is almost independent of the density. Results for the in-medium Δ resonance will be relevant and useful for the relativistic heavy-ion collisions (RHICs).