Hello Juho,
Electrons can and do annihilate into two or more photons. Single photon annihilation is forbidden by the laws of conservation of energy and momentum. The relative rates of three-or-more photon annihilations agree well with the calculations of quantum electro-dynamics. The simple picture you have in mind, that of a spiraling trajectory, is a bit old-fashioned and really gives a false impression of what's going on. You really have to use the modern QED theory to get things right.
LeeH
(published on 06/01/2014)
