Annihilation of the electron-positron pairs in polyelectrons

Annihilation of the electron-positron pairs (or (e−, e)−pairs, for short) in various polyelectrons e n e− m = e− m e n (where n ≥ 1 and m ≥ 1) is considered. In particular, we discuss the threeand four-photon annihilation of the (e−, e)−pairs in the three-body Ps− ion and four-body bi-positronium system Ps2. It is shown that the five-body e + 2 e − 3 ion is an unbound system. The closed form expression is derived for the amplitude-square | M | 2 of the threephoton annihilation of (e−, e)−pair at arbitrary energies of the colliding particles. Analogous amplitude-square | M | for the four-photon annihilation is reduced to the form which convenient for future analytical calculations. A method which can be used to produce macroscopic polyelectrons is briefly discussed. PACS: 36.10.-k and 36.10.Dr