Non-linear interactions and poly-positronium bound states

The creation of a hypothetical many-electron-positron bound system was suggested as a possible source of the correlated peaks observed in the e+ and e- spectra of various heavy-ion collisions. A new electron-electron interaction was assumed, which becomes large in high-Z nuclear collisions. We investigate energy states of such (e+ e-)sup(n) clusters, bound by scalar and vector Fermi-type interactions. For the bi-positronium system (e+ e-)2 we derive a single-particle equation employing the Hartree-Fock method. The required values of the coupling constants are found to be inconsistent with precision QED experiments. (author)