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In this study, we explore the impact of symmetry energy on the transitions between hadron and quark phases within compact stars. We investigate the properties of potential configurations of quark-hadron hybrid stars using energy-density functional (EDF) models and the flavor SU(2) Nambu–Jona-Lasinio (NJL) model, employing Schwinger’s covariant proper-time regularization scheme. In this theoretical framework, we utilize equations of state (EoSs) of hadronic matter obtained from EDF models to describe the hadronic phase, and the flavor SU(2) NJL model with varying repulsive-vector interaction strengths represents the quark phase. By solving the Tolman–Oppenheimer–Volkoff equation, we examine the mass-radius properties of the hybrid star configurations for different vector interactions and nuclear symmetry energies. Our findings show that the critical density at which the phase transition occurs ranges from 3.6 to 6.7 times the normal nuclear-matter density, depending on the symmetry energy and the strength of the vector coupling (Gv). The value of Gvinfluences the maximum mass of the neutron star (NS). In the absence of a repulsive force, the maximum mass of the NS is only about 1.5 times the mass of the Sun (M⊙). Still, it exceeds 2.0M⊙when the vector coupling constant is approximately half of the attractive scalar coupling constant. Interestingly, quark matter does not impact the canonical mass of NS (1.4M⊙). Therefore, observing the canonical mass of NSs can provide valuable constraints on the EoS of hadronic matter at high densities.

In this present investigation, we explore the elastic scattering of pions with nuclei (π–A), primarily influenced by the Δ(1232) resonance, within the Eikonal–Glauber model. The medium effects are incorporated by considering nuclear-density (ρA) dependent masses of baryons and strong coupling constants. These dependencies are computed and parameterized up to O(ρA2)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 π+-Nscattering 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 4He and 12C targets. Our numerical results demonstrate a favorable agreement with JINR data for the 4He target, accurately reproducing the total cross-section. However, when considering the 12C target, deviations of approximately ≲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 Δresonance to reproduce the data better.