  More than 90% of the Galactic gas-related gamma-ray emissivity above 1 GeV is
attributed to the decay of neutral pions formed in collisions between cosmic
rays and interstellar matter, with lepton-induced processes becoming
increasingly important below 1 GeV. Given the high-quality measurements of the
gamma-ray emissivity of local interstellar gas between ~50 MeV and ~4 GeV
obtained with the Large Area Telescope on board the Fermi space observatory, it
is timely to re-investigate this topic in detail, including the hadronic
production mechanisms. 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.
