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Abstract
The neutron fraction in the very high energy cosmic rays near the Greisen-Zatsepin-Kuzmin (GZK) cutoff energy is analyzed by taking into account the time dilation effect of the neutron decays and also the pion photoproduction behaviors above the GZK cutoff. We predict a non-trivial neutron fraction above the GZK cutoff and a negligibly small neutron fraction below. However, there should be a large antiproton fraction in the high energy cosmic rays below the GZK cutoff in several existing models for the observed cosmic-ray events above and near the GZK cutoff. Such a large antiproton fraction can manifest itself by the muon charge ratio $\mu^+/\mu^-$ in the collisions of the primary nucleon cosmic rays with the atmosphere, if there is no neutron contribution. We suggest to use the muon charge ratio as one of the information to detect the composition of the primary cosmic rays near or below the GZK cutoff.
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