Two-photon positron–electron annihilation in a strong magnetic field

We consider the two-photon positron and electron annihilation in flight, it means the annihilating particles exhibit the middly relativistic momenta in a super strong magnetic field. Such particles are present in the corona of pulsars and magnetars. The paper presents how the total emission rate for the two-photon process is affected not only by magnetic field but also by the relativistic momentum of the annihilating particles. We found that the momenta influence significantly the total emission rate and the directions of the emitted photons. Additionally, the total emission for the two-photon process is comparable to that for the one-photon process at the momentum of annihilating particles of about m0, where m0 is the electron mass, and the magnetic field close to the critical Schwinger value of 4.41 × 1013 G. The latter is reported as a main annihilation channel in a super strong magnetic field. We calculated also the energetic spectra of annihilating photons emitted, which are also affected by the magnetic field and the momenta of the annihilating particles.