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

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7. Annihilation rate and spectrum

The annihilation rate [FORMULA] 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)

[EQUATION]

[EQUATION]

The spectrum of photons [FORMULA], which are emitted in the annihilation is given by

[EQUATION]

where [FORMULA] is the dimensionless photon energy, [FORMULA] are the arbitrary isotropic particle distributions [FORMULA], [FORMULA] and [FORMULA] are the [FORMULA] number densities and Lorentz factors. An analytical expression for the angle-averaged emissivity per pair of particles,

[EQUATION]

was obtained by Svensson (1982), here [FORMULA] is the differential cross section for emission of a photon with LS energy [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998

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