Formation of Antihydrogen in Excited States in Antiproton-Positronium Collisions

Abstract

The possibility of producing antihydrogen, $\overline H$ , in the laboratory has been discussed recently in the literature. (Humberston et al 1987 and references cited therein). The proposal is to collide slow (<100keV) antiprotons, $\overline p$ , with positronium atoms, Ps, to produce antihydrogen through the reaction $\overline p + Ps \to \overline H + {e^ - }$ . Humberston et al (1987) have determined the formation cross section for $\overline H$ in its ground state from the previously obtained, accurate calculations of the positronium formation cross section σ(e⁺ + H(1s) → Ps(1s) + p) in low energy positron — hydrogen collisions (Humberston 1986 and references cited therein). These cross sections are related in the well known way:

$$\sigma (\overline p + Ps \to \overline H + {e^ - }) = \sigma (p + Ps \to H + {e^ + }) = k_e^2\sigma ({e^ + } + H \to Ps + p)/k_{Ps}^2$$

Here k_e and k_Ps are the wavenumbers of e⁺ and Ps respectively. In this way Humberston et al (1987) show that the cross section for the formation of antihydrogen in its ground state is substantial, being about 3Ų for antiproton energies <10keV.