Muonic Anti-hydrogen $${(\bar{\rm H}_{\mu}})$$ Formation in Low-energy Three-body Reactions

Abstract

A few-body type computation is performed for a three-charge-particle collision with participation of a slow antiproton \({\bar{\rm{p}}}\) and a muonic muonium atom (true muonium), i.e. a bound state of two muons \({(\mu^{+}\mu^{-})}\) in its ground state. The total cross section of the following reaction \({\bar{\rm p}+(\mu^{+}\mu^{-}) \rightarrow \bar{\rm{H}}_{\mu} + \mu^{-}}\), where muonic anti-hydrogen \({\bar{\rm{H}}_{\mu}=(\bar{\rm p}\mu^{+})}\) is a bound state of an antiproton and positive muon, is computed in the framework of a set of coupled two-component Faddeev-Hahn-type equation. A better known negative muon transfer low energy three-body reaction: \({{\rm t}^{+} + ({\rm d}^{+}\mu^{-})\rightarrow ({\rm t}^{+}\mu^{-}) + {\rm d}^{+}}\) is also computed as a test system. Here, t+ is triton and d+ is deuterium.