Stability of the five-body bi-positronium ion [formula omitted

Abstract

The stability of the five-body bi-positronium ion Ps 2 e − ( = e 3 − e 2 + ) 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 χ 1 = α β α − β α α and χ 2 = 2 α α β − β α α − α β α possible for the doublet S 2 -state were used. The wave functions with different permutation symmetry between electrons and positrons are used in computations of the Ps 2 e − ion. Such a wave function produces a stable ground state in the Ps 2 e − ion. Analogously, the wave functions with alternative permutation symmetry indicate clearly that the six-body polyelectron system Ps 3 ( = tri-positronium ) is also bound.