Secondary nuclear production physics is receiving increased attention given the high-quality measurements of the gamma-ray emissivity of local interstellar gas between ~50 MeV and ~40 GeV, obtained with the Large Area Telescope on board the Fermi space observatory. More than 90% of the gas-related emissivity above 1 GeV is attributed to gamma-rays from the decay of neutral pions formed in collisions between cosmic rays and interstellar matter, with lepton-induced processes becoming increasingly important below 1 GeV.

The elementary kinematics of neutral pion production and decay are re-examined in light of two physics questions: does isobaric production follow a scaling behavior? and what is the minimum proton kinetic energy needed to make a gamma-ray of a certain energy formed through intermediate pi0 production? The emissivity spectrum will allow the interstellar cosmic-ray spectrum to be determined reliably, providing a reference for origin and propagation studies as well as input to solar modulation models. A method for such an analysis and illustrative results are presented.