Antihydrogen $(\bar{\mathrm{H}})$ and muonic antihydrogen $({\bar{\mathrm{H}}}_{\mu })$ formation in low energy three-charge-particle collisions

Abstract

A few-body formalism is applied for computation of two different three-charge-particle systems. The first system is a collision of a slow antiproton, $\bar{\mathrm{p}}$, with a positronium atom: Ps$=(e^{+}{e}^{-})$ $-$ a bound state of an electron and a positron. The second problem is a collision of $\bar{\mathrm{p}}$ with a muonic muonium atom, i.e. true muonium $-$ a bound state of two muons one positive and one negative: Ps${}_{\mu }=({\mu }^{+}{\mu }^{-})$. The total cross section of the following two reactions: $\bar{\mathrm{p}}+(e^{+}{e}^{-})\to \bar{\mathrm{H}}+e^{-}$ and $\bar{\mathrm{p}}+({\mu }^{+}{\mu }^{-})\to {\bar{\mathrm{H}}}_{\mu }+{\mu }^{-}$, where $\bar{\mathrm{H}}=(\bar{\mathrm{p}}{e}^{+})$ is antihydrogen and ${\bar{\mathrm{H}}}_{\mu }=(\bar{\mathrm{p}}{\mu }^{+})$ is a muonic antihydrogen atom, i.e. a bound state of $\bar{\mathrm{p}}$ and ${\mu }^{+}$, are computed in the framework of a set of coupled two-component Faddeev-Hahn-type (FH-type) equations. Unlike the original Faddeev approach the FH-type equations are formulated in terms of only two but relevant components: ${\Psi }_1$ and ${\Psi }_2$, of the system's three-body wave function $\Psi$, where $\Psi ={\Psi }_1+{\Psi }_2$. In order to solve the FH-type equations ${\Psi }_1$ is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of, for example, the $({\mu }^{+}{\mu }^{-})$ atom eigenfunctions. At the same time ${\Psi }_2$ is expanded in terms of the output channel two-body wave functions, that is in terms of ${\bar{\mathrm{H}}}_{\mu }$ atom eigenfunctions.

32 pages (preprint), 2 tables, and 9 figures

References in corpus (5)

• Muonic hydrogen and MeV forces
• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• Evaporative Cooling of Antiprotons to Cryogenic Temperatures
• The Production and Discovery of True Muonium in Fixed-Target Experiments
• Why three-body physics do not solve the proton radius puzzle

Cited by in corpus (1)

• Few-body semiclassical approach to nucleon transfer and emission reactions