Annihilation of the electron–positron pairs in polyelectrons

Annihilation of the electron–positron pairs (or (e−, e+)-pairs, for short) in various polyelectrons e+ne−m = e−me+n (where n ⩾ 1 and m ⩾ 1) is considered. In particular, we discuss the three- and 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+2e−3 ion is an unbound system. The closed-form expression is derived for the amplitude-square |M|2 of the three-photon annihilation of (e−, e+)-pair at arbitrary energies of the colliding particles. Analogous amplitude-square |M|2 for the four-photon annihilation is reduced to the form which is convenient for future analytical calculations. A method which can be used to produce macroscopic polyelectrons is briefly discussed.