Stability of the five-body bi-positronium ion Ps2e−

The stability of the five-body bi-positronium ion Ps2e−(=e3−e2+) is considered. It is shown that the predicted stability of the negative bi-positronium ion substantially depends upon permutation symmetry of the total electron-positron wave function used in calculations. In one approach developed in this study we apply trial wave functions with atomic-type permutation symmetry between all identical particles, i.e., between three electrons and between two positrons. In particular, in such computations the two independent electron spin functions χ1=αβα−βαα and χ2=2ααβ−βαα−αβα possible for the doublet S2-state were used. The wave functions with different permutation symmetry between electrons and positrons are used in computations of the Ps2e− ion. Such a wave function produces a stable ground state in the Ps2e− ion. Analogously, the wave functions with alternative permutation symmetry indicate clearly that the six-body polyelectron system Ps3(=tri-positronium) is also bound.