We investigate the elastic πN scattering for the I = 3/2 channel dominated by the ∆(1232) resonance at finite baryon density ρB for the symmetric nuclear matter, employing the effective Lagrangian approach at the tree-level Born approximation. The quark-meson coupling (QMC) model and linear-density approximation are employed to describe the medium modifications for the in-medium baryon properties, such as the nucleon and ∆ masses, and ∆ full decay width. We first reproduce the experimental data in vacuum by fitting the model parameters, then analyze various physical observables including total and differential cross sections, proton-spin asymmetry in medium. It turns out that the ∆-resonance contribution becomes diminished with respect to ρB, due to the weaker πN -interaction strength in medium. Beyond the ∆-resonance region √ s 1.5 GeV, the cross sections are almost independent of the density. The present results will be useful to understand the role of the ∆ resonance in the neutron-star equation of state (EoS) as well as in relativistic heavy-ion collision experiments.
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