The density- and isospin-dependent Δ-formation cross section and its decay width

Abstract

The energy-, density-, and isospin-dependent Δ-formation cross section σ*_Nπ→Δ and Δ-decay width are calculated based on the relativistic BUU approach in which the effective mass splitting of nucleon and Δ baryons in isospin-asymmetric matter is considered by the inclusion of the δ meson exchange in the effective Lagrangian density and the density-dependent coupling constants of Hofmann et al. The results show that the σ*_Nπ→Δ is decreased (increased) moderately with increasing density with (without) the consideration of medium modifications on pion mass. Meanwhile, if the invariant mass of the system is not far from the Δ pole mass, the Δ-decay width is also weakly dependent on density. The mass splitting effect of differently charged nucleon and Δ baryons on σ*_Nπ→Δ is found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard Δ production channel NN → NΔ. Further, the largest mass-splitting influence is seen in the π⁻p → Δ⁰ and π⁺n → Δ⁺ channels but not in the production of Δ ⁻ and Δ⁺⁺ isobars.