Several authors on the internet have asserted that single quantum annihilation cannot take place. Strictly speaking this not true. What they mean is that in a field free environment such cannot take place. But if the positron annihilation takes place in the near vicinity of a heavy nucleus, say Cesium, the recoil of the nucleus enables momentum and energy to be balanced in a single photon annihilation. This was empirically demonstrated in the late 1950's by Lester Sodickson at M.I.T. The write-up is given the Physical Review as L. Sodickson et al, "Single-Quantum Annihilation of Positrons," vol.124 num 6, (Dec., 1961), pp.1851-1861.

One quantum annihilation occurs only on the order of 0.2 of 1% because of the infrequency that a positron makes it to the innermost shell of the electrons of an atom. But despite this small rate it was established that measured occurrence of relatively high energy gamma photons is several times higher than the background radiation in the experimental environment.

Two quanta annihilation is usually thought to be the typical mode but the article notes, "Indeed,under certain conditions of eternal field, annihilation via three quanta emission occurs nearly 75% of the time."

The real physical world is more complex than theoreticians can imagine.