Enhancement of positron-atom annihilation near the positronium formation threshold

The behavior of the positron- 2 gamma annihilation rate on an atomic target near the positronium (Ps) formation threshold is determined. When the positron energy epsilon approaches the threshold epsilon(thr) from below, the effective number of electrons contributing to the annihilation, Z(eff), grows as Z(eff) approximately A/square root of epsilon(thr)-epsilon], where A is related to the size of the Ps formation cross section, sigma(Ps) approximately B square root of epsilon-epsilon(thr)], by A = B square root of 2 epsilon(thr)]/32 pi (in atomic units). Taking account of the finite Ps lifetime eliminates the singularity in Z(eff) and shows that close to threshold the positron annihilation cross section is identical to the para-Ps formation cross section.