Benchmark for the determination of the positronium formation fraction in interstellar media

Relativistic positrons (>1 MeV) are produced from many sources in the Galaxy. Observations of positrons rely on the characteristic gamma-rays emitted from their annihilation with an electron, and the dominant annihilation pathways are determined by low-energy (<1 keV) processes. Thus, detailed information on the transport of positrons from high to low energies is required to accurately determine the propagation of positrons in the interstellar medium. This work considers model cross sections with variable parameters to provide a benchmark for several quantities, including the positronium formation fraction and time to reach subpositronium threshold energies. We simulate these processes using Monte Carlo codes within the cold collisional regime and carefully consider the energy sharing in ionization events that leads us to highlight the need for accurate ionization cross sections, which are differential in energy loss. We include tabulated values so that our benchmark values can be reproduced by other transport codes.