Energy Spectrum of Cosmic Radiation

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THE spectrum of cosmic radiation has the remarkable property that it is a power function (where p is momentum), in which n has a constant value of about 2.5 for several powers of ten of p. In Fermi's theory, n is given by the ratio τ/T between the time of acceleration τ and the time of absorption (or diffusion) T. This means that the empirical formula is obtained only if one assumes that accidentally τ and T are of the same order of magnitude, and that the ratio is constant over a very wide range of momentum. Neither of these assumptions is plausible.

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ALFVÉN, H., ÅSTRÖM, E. Energy Spectrum of Cosmic Radiation. Nature 181, 330–331 (1958) doi:10.1038/181330b0

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