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Timestamp: 2019-04-25 10:59:34+00:00

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cosmic-ray proton flux described by a power law in kinetic energy.
10 MeV, where the -ray production is energetically in-significant. Both models are in general agreement in thehigh-energy asymptotic regime, with the Kamae et al.model giving fluxes larger by 13% due to the inclusionof diffractive processes. The spectral peak in a F repre-sentation occurs at 500 MeV to 1 GeV for this protonspectrum. The most significant discrepancy in the twomodels is by 30% at the pion production peak near67.5 MeV . Because of the different approaches ofthe models and little improvement in nuclear databasesfrom laboratory studies between model development, thiscomparison indicates that our knowledge of the -rayproduction spectrum in p-p collisions is uncertain, atworst, by 30% near the pion-production peak and is betterthan 15% at * 200 MeV.
FIG. 1 (color online). Production spectra of secondary raysmade in p-p collisions from the models of Dermer  andKamae et al. , using the empirical demodulated cosmic-rayproton spectrum given by Eq. (3).
differential -ray emissivity of local neutral gas , employing ashock-acceleration spectrum, Eq. (4), with s 2:75, for thecosmic-ray proton spectrum, and the models of Dermer and Kamae et al.  for -ray production. The nuclear en-hancement factor k takes the values of 1.45 and 1.84, as labeled.
FIG. 3 (color online). Fermi LAT spectrum of the differential-ray emissivity of Gould belt clouds . It is fit with a shock-acceleration model for the cosmic-ray proton spectrum withs 2:85, using the models of Dermer  and Kamae et al. for -ray production. The models are normalized to the fluxat 1 GeV.
FIG. 4 (color online). Theoretical cosmic-ray proton fluxescompared with recent PAMELA, Fermi LAT, ATIC-2, andHESS measurements of cosmic-ray p, He, C, Fe, and electronand positron fluxes . The shock acceleration spectra aregiven by Eq. (4) with s 2:75 and s 2:85, a power-lawkinetic energy flux j / T2:85, and a flux j / T2:85 are shown,in addition to the demodulated cosmic-ray proton spectrum,Eq. (3), and the best-fit spectrum of Ref. . Solar modulationaccounts for the difference between the measured and theoreticalcosmic-ray proton fluxes at T & 10 GeV=nuc. Papers cited inRef.  report systematic errors for different experiments.
then the 0 ! 2 feature from shock-accelerated cosmicrays should be observed in the spectra of individual SNRs.Indications for such a feature are found in a few middle-aged SNRs , but final confirmation of cosmic-raysources will require detailed spectral calculations involv-ing both shock-accelerated protons and leptons , in-cluding radiative losses and escape and comparison withimproving Fermi LAT data resulting from increasing ex-posure and development of better analysis tools.The author thanks A. Atoyan, J. D. Finke, J. Hewitt, R. J.
and Serpico  explains a supposed low-energy break in apower-law injection momentum spectrum as a result ofadvective effects on cosmic-ray propagation (compareRef. ). Kachelriess and Ostapchenko  claim tofind deviations from a cosmic-ray power-law momentumspectrum at low energy, but their treatment is susceptible tosome of the same criticisms as presented here.
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 As discussed in Ref. , this factor ranges from 1.45 to2.0, with a value of 1.84 favored in the work of M. Mori,Astrophys. J. 478, 225 (1997).
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