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

Abstract

The energy-, density-, and isospin-dependent $\Delta$-formation cross section ${\sigma }_{N\pi \to \Delta }^{\ast }$ and $\Delta$-decay width are calculated based on the relativistic BUU approach in which the effective mass splitting of nucleon and $\Delta$ baryons in isospin-asymmetric matter is considered by the inclusion of the $\delta$ meson exchange in the effective Lagrangian density. With the density-dependent couplings for baryons of F. Hofmann et al., the ${\sigma }_{N\pi \to \Delta }^{\ast }$ 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 $\Delta$ pole mass, the $\Delta$-decay width is also weakly dependent on density. The mass splitting effect of differently charged nucleon and $\Delta$ baryons on ${\sigma }_{N\pi \to \Delta }^{\ast }$ are found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard $\Delta$ production channel $NN\to N\Delta$. Further, the largest mass-splitting influence is seen in the ${\pi }^{-}p\to {\Delta }^0$ and ${\pi }^{+}n\to {\Delta }^{+}$ channels but not in the production of ${\Delta }^{-}$ and ${\Delta }^{++}$ isobars.

11 pages, 5 figures

References in corpus (7)

• Big-Bang Nucleosynthesis
• Symmetry energy from elliptic flow in 197Au + 197Au
• Systematics of central heavy ion collisions in the 1A GeV regime
• Comparison of heavy-ion transport simulations: Collision integral in a box
• In-medium effects on particle production in heavy ion collisions
• The width of the $\Delta$-resonance at two loop order in baryon chiral perturbation theory
• The effect of Lorentz-like force on collective flows of K${}^{+}$ in Au+Au collisions at 1.5 GeV/nucleon}{The effect of Lorentz-like force on collective flows of $K^{+}$ in Au+Au collisions at 1.5 GeV/nucleon

Cited by in corpus (3)

• Application of machine learning in the determination of impact parameter in the ${}^{132}$Sn+${}^{124}$Sn system
• In-medium nucleon-nucleon cross sections from relativistic ab initio calculations
• Nucleon-$\Delta$ elastic cross section in isospin-asymmetric nuclear medium with inclusion of scalar-isovector $\delta$ meson field