ENERGY-SPECTRUM OF ULTRA-HIGH ENERGY COSMIC-RAYS WITH EXTRA-GALACTIC ORIGIN

We carried out a numerical calculation for the propagation of ultra-high energy cosmic ray nucleons in the intergalactic space by a Monte-Carlo method. The resulting energy spectrum above 10(18) eV is modified by the interaction of nucleons with the micro wave background (MWB) photons, forming a bump and a cutoff, with position depending on the propagation distance and source distribution. It is found that the treatment of the evolution of the universe and the interactions between cosmic rays and MWB photons is crucial. We also calculated the spectra of neutrinos and gamma rays produced by the interaction of nucleons with MWB photons. The flux of these particles strongly depends on propagation distance, cosmological evolution parameter and the maximum energy of the cosmic rays. The possibility to detect the secondary neutrinos is also discussed.