Astron. Astrophys. 325, 401-413 (1997)

7. Annihilation rate and spectrum

The 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

helpdesk.link@springer.de