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 μ+/μ− 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.Comment: 5 LaTex page