Decay of positronium in strong magnetic fields

We investigate the decay of bound electron-positron pairs (positronium) in strong magnetic fields (of order 10¹² Gauss, which are assumed for neutron stars) on the basis of a correct treatment of the two-body problem, thus improving previous work by Carr and Sutherland (1978). We find that, even in the presence of a strong magnetic field, the decay of the ground state of positronium must be momentum conserving, whereby the possibility of the one-photon decay is ruled out. We calculate the transition rate for the two-photon annihilation process which turns out to be larger than the field free transition rate by a factor (1/)² B/B _cr (where is the electromagnetic coupling constant, andB _cr=m _e ² c ²/(e)=4.41×10¹³ Gauss).