REACTION-RATE AND ENERGY-LOSS RATE FOR PHOTOPAIR PRODUCTION BY RELATIVISTIC NUCLEI

We consider the process of e+/- pair production by relativistic nuclei (with Lorentz factors gamma much-greater-than 1) on ambient photons. The process is important for cosmic-ray nuclei in interstellar and intergalactic space as well as in galactic and extragalactic compact objects. The rate of this process is given by an integral of the cross section over the photon angular and energy distribution. In the case of isotropic photons, we perform the angular integration, providing an expression for the rate at given photon energy in the nucleus rest frame. The total rate becomes then a single integral of that rate over the photon energy distribution. We also give formulae for the fractional energy loss (the inelasticity coefficient) of a relativistic nucleus colliding with a photon of a given energy in the rest frame. The total nucleus energy-loss rate due to the process is then given by an integral of the inelasticity coefficient over the photon angular and energy distribution. We obtain the exact asymptotic form of the inelasticity coefficient at high photon energies and give a fit valid at lower energies. Finally, we integrate the nucleus energy-loss rate over the photon angular distribution in the case of isotropic photons and provide simple fits. This extends a result of Blumenthal, who obtained the asymptotic formula in the limit of very high photon energies.