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

TL;DR

This paper calculates the density- and isospin-dependent $ riangle$-formation cross section and decay width using a relativistic BUU model, revealing how effective mass splitting influences these quantities in asymmetric nuclear matter.

Contribution

It introduces a detailed calculation of $ riangle$-formation cross sections and decay widths considering effective mass splitting and density effects in isospin-asymmetric matter, using the relativistic BUU approach.

Findings

$ riangle$-formation cross section varies moderately with density and effective mass considerations.

Decay width is weakly dependent on density near the $ riangle$ pole mass.

Mass splitting effects are most prominent in specific charge channels, notably $ riangle^0$ and $ riangle^+$.

Abstract

The energy-, density-, and isospin-dependent $\Delta$-formation cross section $\sigma_{N\pi \rightarrow \Delta}^*$ 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 $\sigma_{N\pi \rightarrow \Delta}^*$ 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 $\sigma_{N\pi \rightarrow \Delta}^*$ are found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard $\Delta$ production channel $NN\rightarrow N\Delta$. Further, the largest mass-splitting influence is seen in the $\pi^-p\rightarrow \Delta^0$ and $\pi^+n\rightarrow \Delta^+$ channels but not in the production of $\Delta^-$ and $\Delta^{++}$ isobars.