2008ApJ...674..278K

We present the angular distribution of gamma rays produced by proton-proton interactions in parameterized formulae to facilitate calculations in astrophysical environments. The parameterization is derived from Monte Carlo simulations of the up-to-date proton-proton interaction model and its extension by Kamae and coworkers. This model includes the logarithmically rising inelastic cross section, the diffraction dissociation process, and the Feynman scaling violation. The extension adds two baryon resonance contributions: one representing the Δ(1232) and the other representing multiple resonances around 1600 MeV/c². We demonstrate the use of the formulae by calculating the predicted gamma-ray spectrum for two different cases: the first is a pencil beam of protons following a power law, and the second is a fanned proton jet with a Gaussian intensity profile impinging on the surrounding material. In both cases we find the predicted gamma-ray spectrum to be dependent on the viewing angle.