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

Abstract

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 $\lesssim 10\%$. 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.

Comments: 8 pages, 4 figures