Antiproton low-energy collisions with Ps-atoms and true muonium atoms (${\mu }^{+}{\mu }^{-}$)

Three-charge-particle collisions with participation of ultra-slow antiprotons ($\bar{\mathrm{p}}$) is the subject of this work. Specifically we compute the total cross sections and corresponding thermal rates of the following three-body reactions: $\bar{\mathrm{p}}+(e^{+}{e}^{-})\to \bar{\mathrm{H}}+e^{-}$ and $\bar{\rm p}+(\mu^+\mu^-) \rightarrow \bar{\rm{H}}_{\mu} + \mu^-$,where$e^-(\mu^-)$ is an electron (muon) and $e^{+}({\mu }^{+})$ is a positron (antimuon) respectively, $\bar{\mathrm{H}}=(\bar{\mathrm{p}}{e}^{+})$ is an antihydrogen atom and ${\bar{\mathrm{H}}}_{\mu }=(\bar{\mathrm{p}}{\mu }^{+})$ is a muonic antihydrogen atom, i.e. a bound state of $\bar{\mathrm{p}}$ and ${\mu }^{+}$. A set of two-coupled few-body Faddeev-Hahn-type (FH-type) equations is numerically solved in the framework of a modified close-coupling expansion approach.