We consider the rate of ionization of diffuse and molecular clouds in the interstellar medium by Galactic cosmic rays ( GCR ) in order to constrain its low energy spectrum .
We extrapolate the GCR spectrum obtained from PAMELA at high energies ( \geq 200 GeV/ nucleon ) and a recently derived GCR proton flux at 1 \hbox { - - } 200 GeV from observations of gamma rays from molecular clouds , and find that the observed average Galactic ionization rate can be reconciled with this GCR spectrum if there is a low energy cutoff for protons at 10 \hbox { - - } 100 MeV .
We also identify the flattening below a few GeV as being due to ( a ) decrease of the diffusion coefficient and dominance of convective loss at low energy and ( b ) the expected break in energy spectrum for a constant spectral index in momentum .
We show that the inferred CR proton spectrum of \Phi \propto E _ { kin } ^ { -1.7 \pm 0.2 } for E _ { kin } \leq few GeV , is consistent with a power-law spectrum in momentum p ^ { -2.45 \pm 0.4 } , which we identify as the spectrum at source .
Diffusion loss at higher energies then introduces a steepening by E ^ { - \alpha } with \alpha \sim 1 / 3 , making it consistent with high energy measurements .