The pair annihilation process in relativistic plasmas

This is the authors' abstract. We don't add key points for this paper.

Exact analytical expressions are derived in the Born approximation for the pair annihilation rate and spectral emissivity from isotropic, monoenergetic electrons and positrons of arbitrary energies. The annihilation rate and spectral emissivity for arbitrary particle distribution functions are given as double integrals. The spectral emissivity is determined exactly for the case where the the positrons (electrons) have a Maxwell-Boltzmann distribution, while the electrons (positrons) are at rest. A discussion is given for the more complicated case in which both the electrons and the positrons have Maxwell-Boltzmann distributions at the same temperature. Asymptotic expressions are derived for the annihilation rate, the cooling rate, and the spectral emissivity at relativistic temperatures. Useful, approximate expressions, valid at temperatures larger than 100-million K, are given for the annihilation rate and the cooling rate.