Formation of antihydrogen in three-body antiproton-positron collisions

Abstract

A quantum-mechanical approach is proposed for the formation of antihydrogen $(\overline{H})$ in the ground and excited states $(2s,2p)$ via the mechanism of three-body recombination (TBR) inside a trapped plasma of antiprotons $(\overline{p})$ and positrons $({e}^{+})$ or in the collision between the two beams of them. Variations of the differential as well as the total formation cross sections are studied as a function of the incident energies of both the active and the spectator ${e}^{+}$'s. Significantly large cross sections are found at very low incident energies in the TBR process as compared to other processes leading to antihydrogen. The present $(\overline{H})$ formation cross section decreases with increasing positron energy (temperature) but no simple power law could be predicted for it covering the entire energy range $(\ensuremath{\sim}5--50\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, corroborating the experimental findings qualitatively, the latter being at a much lower energy regime $(\ensuremath{\sim}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. The formation cross sections are found to be much higher for unequal energies of the two ${e}^{+}$'s than for equal energies, as expected physically.