A detailed analysis of γ-γ annihilation absorption in γ-ray astronomy

Abstract The two-photon annihilation (γ-γ annihilation) is an important absorption mechanism in the theory of radiative transfer in γ-ray astronomy. In this paper, we try to change the known formulae of annihilation cross section given by QED theory in the frame of momemtum center into a new expression in the laboratory reference frame (the observer's frame) by means of relativistic transformation, which is more useful for practical application. Also, we derive a simplified direction-averaged expression for the annihilation cross section σ (ω,ω′) for a general isotropic ambient radiation field and obtain direction-averaged threshold condition of annihilation and the match condition, that have to be satisfied by the energies of two interacting photons, h ω and h ω′ , to ensure the occurrence of annihilation and to achieve the maximum annihilation probability. Finally, we calculate the annihilation absorption coefficients k γγ ( h ω) ∼ h ω for three typical ambient low-frequency radiation fields in astrophysics, i.e. the bremsstrahlung, the black body, and the non-thermal power law field. We further give some detailed physical discussions on the results of our calculation.