## 7. Annihilation rate and spectrumThe annihilation rate for monoenergetic positrons in Maxwell-Boltzmann electron gas can be directly obtained from Eq. (15) by substitution of the annihilation cross section (Jauch & Rohrlich 1976) The spectrum of photons , which are emitted in the annihilation is given by where is the dimensionless photon energy, are the arbitrary isotropic particle distributions , and are the number densities and Lorentz factors. An analytical expression for the angle-averaged emissivity per pair of particles, was obtained by Svensson (1982), here is the differential cross section for emission of a photon with LS energy . © European Southern Observatory (ESO) 1997 Online publication: May 5, 1998 |