Deriving the cosmic ray spectrum from gamma-ray observations

A fundamental problem of cosmic ray (CR) physics is the determination of the average properties of Galactic CRs outside the Solar system. Starting from COS-B data in the 1980's, gamma-ray observations of molecular clouds in the Gloud Belt above the Galactic plane have been used to deduce the Galactic CR energy spectrum. We reconsider this problem in view of the improved precision of observational data which in turn require a more precise treatment of photon production in proton-proton scatterings. We show that the spectral shape $dN/dp∝ p^-2.85$ of CR protons as determined by the PAMELA collaboration in the energy range 80 GeV<pc<230 GeV is consistent with the photon spectra from molecular clouds observed with Fermi-LAT down to photon energies E∼ 1-2 GeV. Adding a break of the CR flux at 3 GeV, caused by a corresponding change of the diffusion coefficient, improves further the agreement in the energy range 0.2-3 GeV.