The effective penetration distance of ultrahigh-energy electrons and photons traversing a cosmic blackbody photon gas
The effective average energy loss for an energetic (at least about 10 to the 15th power eV) particle traversing the microwave background radiation is evaluated. Electron-photon transformations by Compton scattering and pair production (in photon-photon collisions) are computed, with the energy loss considered to be carried away by the least energetic of the outgoing particles. Considering the most energetic of the outgoing particles as the high-energy particle, the relative probability and mean time for the particle to be a photon or electron (or positron) is evaluated. The effects of synchrotron losses for electrons and positrons are emphasized and compared with Compton losses to determine a critical energy (for given magnetic field) above which synchrotron losses dominate. Magnetic deflections are also treated for the case where the magnetic field is disordered, having a characteristic 'cell' size.