Formation of ${\overline{\mathrm{H}}}^{+}$ via electron-assisted three-body attachment of $e^{+}$ to $\overline{\mathrm{H}}$

The formation of positive ions of antihydrogen ${\overline{\mathrm{H}}}^{+}$ via the three-body reaction (i) $e^{+}+e^{-}+\overline{\mathrm{H}}\to e^{-}+{\overline{\mathrm{H}}}^{+}$ is considered. In reaction (i), free positrons $e^{+}$ are incident on antihydrogen $\overline{\mathrm{H}}$ embedded in a gas of low-energy ($\approx$ meV) electrons and, due to the positron-electron interaction, a positron is attached to $\overline{\mathrm{H}}$ whereas an electron carries away the energy excess. We compare reaction (i) with two radiative attachment mechanisms. One of them is (ii) spontaneous radiative attachment, in which the ion is formed due to spontaneous emission of a photon by a positron incident on $\overline{\mathrm{H}}$. The other is (iii) two-center dileptonic attachment which takes place in the presence of a neighboring atom B and in which an incident positron is attached to $\overline{\mathrm{H}}$ via resonant transfer of energy to B with its subsequent relaxation through spontaneous radiative decay. It is shown that reaction (i) can strongly dominate mechanisms (ii) and (iii) for positron energies below 0.1 eV. In addition, it is shown that, at the energies considered, reaction (i) will not be influenced by annihilation and that the reaction $e^{+}+e^{+}+\overline{\mathrm{H}}\to e^{+}+{\overline{\mathrm{H}}}^{+}$ has a vanishingly small rate compared with reaction (i). We also compare the reaction (i) with the formation of ${\overline{\mathrm{H}}}^{+}$ in collisions between an antihydrogen atom and a positronium.

Figure 1

Scheme of three-body attachment with an assisting electron (3BAe).

Figure 2

The ${\overline{\mathrm{H}}}^{+}$ formation rate (per $\overline{\mathrm{H}}$) as a function of the incident positron energy ${\varepsilon }_{k_p}$ for three-body attachment with an assisting electron (solid curve). In addition, we illustrate the corresponding rates for spontaneous radiative attachment (dotted curve) and two-center dileptonic attachment (dashed curve). See text for further details.