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

Abstract

The energy-, density-, and isospin-dependent $Δ$-formation cross section $σ_{Nπ\rightarrow Δ}^*$ 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. With the density-dependent couplings for baryons of F. Hofmann et al., the $σ_{Nπ\rightarrow Δ}^*$ is decreased (increased) moderately with increasing density with (without) the consideration of the density dependent pion effective 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 $σ_{Nπ\rightarrow Δ}^*$ are found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard $Δ$ production channel $NN\rightarrow NΔ$. Further, the largest mass-splitting influence is seen in the $π^-p\rightarrow Δ^0$ and $π^+n\rightarrow Δ^+$ channels but not in the production of $Δ^-$ and $Δ^{++}$ isobars.