Low Energy Rydberg States in Dipositronium

Previously the possible resonances in positronium hydride, PsH, [1] were studied, assuming a positronium ion, Ps$^{-}$, interacting with a proton, H$^{+}$, as the prime configuration. This study will look at the first resonances of dipositonium, Ps$_{2}$, in a similar manner. In this situation a variational method is used to determine the radial function of the bound state. First, the model system consisting of Ps$^{-}$ and a positron, e$^{+}$is investigated by including electron exchange but no positron exchange. Then the antisymmetrization of the two positrons is considered giving rise to a non-local potential. The full symmetrization of a system such as Ps$_{2}$ involves not only exchanging electrons and exchanging positrons, but also the charge conjugation of the two interacting ions in our model. Thus, in this second approach we construct a wave function that includes representations of both the Ps$^{-}$ + e$^{+}$ and Ps$^{+}$ + e$^{- }$channels to provide a complete description of this resonant system. From the calculations, the lowest energy singlet Rydberg resonant states are determined. A comparison will be made with results using group-theory analysis [2]. [1] J. Di Rienzi, R. J. Drachman, Phys. Rev. A \textbf{76}, 032705 (2007). [2] J. Usukura and Y. Suzuki, Phys. Rev. A \textbf{66}, 010502(R) (2002); C. G. Bao and T. Y. Shu, Phys. Rev. A \textbf{67}, 042505 (2003).