Matching Condition in γ-γ Annihilation Absorption

Two-photon annihilation (γ-γ reaction) is an important absorption mechanism in γ-ray physics and γ-ray astronomy. Using the markedly simplified direction-averaged cross section of annihilation σ(ω, ω’) for a normal isotropic ambient radiation field around the γ-ray source, we obtain a matching condition for the energies of two interacting photons, which ensures the attainment of the maximum annihilation probability. This is a new result that is helpful to obtain a better understanding for the absorption behaviour in the γ-γ annihilation process, and this predicts some possible line-like absorption structures in the emergent γ-ray continuous spectra. Some inferences of the matching condition are also presented.