One-photon and two-photon annihilation of positronium in strong magnetic fields

In the presence of a strong magnetic field (such as those believed to be characteristic of neutron stars:B≳-1012 Gauss) positronium may annihilate through the emission of a single photon, the magnetic field providing the photon momentum. We report on calculations of the one-photon and two-photon annihilation rates for the ground state of positronium, for magnetic fields in the range (1–44)×1012 Gauss, and give, in the two-photon case, the minimum energy half-width of the emission line due to the momentum contributions from the magnetic field. We find that unless neutron stars have magnetic fields in excess of 1013 Gauss, it is unlikely that the one-photon process will be observable.