Photon splitting in a strong magnetic field

Abstract

Abstract The process of photon splitting γ → γγ in a strong magnetic field is investigated both below and above the pair creation threshold. The partial amplitudes and the splitting probabilities are calculated taking account of the photon dispersion. We show that the limit of the collinear kinematics which has been used in literature till now is inadequate in the strong magnetic field. We point out the necessity to take into account the large radiative corrections near the cyclotron resonances. We also calculate the probability of the reaction γ → e+ e− γ and show that it is negligibly small in comparison with photon splitting probability above the pair creation threshold. Our results should be used for quantitative studies of the photon splitting role in high-energy astrophysics.