Antihydrogen formation via antiproton scattering on positronium between the $e^{-} +\bar {H}(n = 2)$ and $e^{-}+\bar {H}(n = 3)$ thresholds
Résumé
The charge exchange reaction $\bar {\mathrm {p}} + \text {Ps} \rightarrow \mathrm {e}^{-} + \bar {\mathrm {H}} $ , of interest for the future experiments (GBAR, AEGIS, ATRAP, ...) aiming to produce antihydrogen atoms, is investigated in the energy range between the $\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 2)$ and $\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 3)$ thresholds. An ab-initio method based on the solution of the Faddeev-Merkuriev equations is used. Special focus is put on the impact of the Feshbach resonances and the Gailitis-Damburg oscillations, appearing in the vicinity of the $\bar {\mathrm {p}} +\text {Ps}(n = 2)$ threshold, on the $\bar {\mathrm {H}}$ production cross section.