Ultrahigh energy photons, electrons, and neutrinos, the microwave background, and the universal cosmic-ray hypothesis

The production of ultrahigh energy photons, electrons and neutrinos as the decay products of pions produced in photomeson interactions between cosmic ray nucleons and the blackbody microwave background is discussed in terms of the resultant energy spectra of these particles. Simple asymptotic formulas are given for calculating the ultrahigh energy photon spectrum predicted for the universal cosmic ray hypothesis and the resulting spectra are compared with those obtained previously by numerical means using a different propagation equation for the photons. Approximate analytic solutions for the photon spectra are given in terms of simple power-law energy functions and slowly varying logarithmic functions.