Delta Decay in Nuclear Medium

Proton-nucleus collisions, where the beam proton gets excited to the delta resonance and then decays to p$\pi ^+$, either inside or outside the nuclear medium, are studied. Cross-sections for various kinematics for the (p,p$' \pi ^+$) reaction between 500 MeV and 1 GeV beam energy are calculated to see the effects of the nuclear medium on the propagation and decay of the resonance. The cross-sections studied include proton energy spectra in coincidence with the pion, four momentum transfer distributions, and the invariant p$\pi^+$ mass distributions. We find that the effect of the nuclear medium on these cross-sections mainly reduces their magnitudes. Comparing these cross-sections with those considering the decay of the delta outside the nucleus only, we further find that at 500 MeV the two sets of cross-sections have large differences, while by 1 GeV the differences between them become much smaller.