In this present investigation, we explore the elastic scattering of pions with nuclei (π–A), primarily influenced by the \(\Delta\) (1232) resonance, within the Eikonal–Glauber model. The medium effects are incorporated by considering nuclear-density ( \(\rho _A\) ) dependent masses of baryons and strong coupling constants. These dependencies are computed and parameterized up to \(\mathcal {O}(\rho _A^2)\) based on the quark–meson coupling (QMC) model. The Wood–Saxon type density profile is utilized for the bound nucleons within finite nuclei. The element \(\pi ^+\) -N scattering cross-section for the Glauber approach is determined using the conventional effective Lagrangian method. Subsequently, we analyze the total cross-sections for elastic scattering with \(^4\) He and \(^{12}\) C targets. Our numerical results demonstrate a favorable agreement with JINR data for the \(^4\) He target, accurately reproducing the total cross-section. However, when considering the \(^{12}\) C target, deviations of approximately \(\lesssim 10\%\) . We also consider the multiple-scattering effects inside the nucleus approximately, using the single-channel meson-baryon Bethe–Salpeter equation, resulting in the effective width-broadening of the \(\Delta\) resonance to reproduce the data better.
