Pion-nucleus elastic scatterings incorporating medium effects within the Eikonal-Glauber mode

In this present investigation, we explore the elastic scattering of pions with nuclei ($\pi$-$A$), 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 $\lesssim10\%$. 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.