Hyperfine splitting and lifetime of the positronium lowest level in a strong electric field

When placed in an external electric field, positronium, which already has a finite lifetime due to annihilation, becomes additionally unstable due to field-induced ionization. Calculations of the ionization rate using ab initio methods show that, compared to annihilation, it becomes dominant in the range of field strengths belonging to over-the-barrier ionization (OBI) regime. On the other hand, the hyperfine splitting of the positronium lowest level decreases in the tunnelling domain, taking at the beginning of the OBI domain a value that is about 20% lower than the field-free value. As the field strength increases further, this splitting varies rather slowly, but here an additional splitting of triplet levels occurs, whose rate is comparable to this variation. Finally, it is demonstrated that the lowest energy levels and ionization rates for the hydrogen atom and positronium, determined within the gross structure, are related to scaling transformations.