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A shock-accelerated particle flux \propto p^-s, where p is the particle momentum, follows from simple theoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-dependent escape into the Galactic halo.
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Cosmic-ray convective and diffusive escape from the Galaxy in terms of rigidity (momentum per unit charge) to explain the ratio of isotopes in the cosmic-rays was considered, e.g., by F. C. Jones, Astrophys. J. 229
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As discussed in [ 7 ] , this factor ranges from 1.45 – 2.0, with a value of 1.84 favored in the work of M. Mori, Astrophys. J., 478
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The parametrization of the model of Kamae et al. is given by T. Kamae, N. Karlsson, T. Mizuno, T. Abe, and T. Koi, Astrophys. J. 647
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For a historical review of the discovery of cosmic rays, see P. Carlson and A. de Angelis, European Physical Journal H, 35
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For reviews of nonrelativistic shock acceleration, see R. Blandford and D. Eichler, Phys. Rept., 154
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For the physical requirement of multi-zone models in SNR spectral fitting, and the resultant ambiguity to discriminate leptonic and hadronic models, see A. Atoyan and C. D. Dermer, Astrophys. J. Lett. 749
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A. Neronov, D. V. Semikoz, and A. M. Taylor, Phys. Rev. Lett., 108
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2012
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J. Fang and L. Zhang, Monthly Not. Roy. Astron. Soc. 384
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