Positronium-Ion Decay

We present a precise theoretical prediction for the decay width of the bound state of two electrons and a positron (a negative positronium ion), $\Gamma ({\mathrm{Ps}}^{-})=2.087963(12)/\mathrm{ns}$. We include $O({\alpha }^2)$ effects of hard virtual photons as well as soft corrections to the wave function and the decay amplitude. An outcome of a large-scale variational calculation, this is the first result for second-order corrections to a decay of a three-particle bound state. It will be tested experimentally in the new positronium-ion facility in Garching in Germany.

Figure 1

The main decay channel of ${\mathrm{Ps}}^{-}$ (a), and an example of a corrections to it, the three-photon annihilation (b).