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.

Comments: 11 pages, 5 figures