On the Angular Distribution of Two-Photon Annihilation Radiation

An experimental determination, using anthracene scintillation counters in coincidence, has been made of the departure from antiparallelism of the two photons in the pair annihilation process in an Au absorber. The observed mean angular departure, \ensuremath{\cong}1/137 radians, arises from the motion of the centers of mass of the annihilating pairs; the mean momentum of these is found from the experimental data to be equal to 1.2 mc/137, a value to be compared with a lower limit of 0.8 mc/137 obtained from an included theoretical discussion in which the momentum probability amplitudes of the annihilating electrons and positrons (in the absorbing metal) are estimated and appropriately combined. In these estimates it is shown that the positrons become thermalized by collisions with the vibrating lattice atoms in times considerably shorter than the annihilation time, so that only their zero point motions, together with the zero point motions of the annihilating (valence) electrons, effectively contribute to the momenta of the centers of mass of the annihilating pairs.