Antihydrogen and muonic antihydrogen 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, , with a positronium atom: Ps=(e+e−)—a bound state of an electron and a positron. The second problem is a collision of with a muonic muonium atom, i.e. true muonium—a bound state of two muons one positive and one negative: Psμ = (μ+μ−). The total cross section of the following two reactions: and , where is antihydrogen and is a muonic antihydrogen atom, i.e. a bound state of and μ+, 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: Ψ1 and Ψ2, of the system's three-body wave function Ψ, where Ψ = Ψ1 + Ψ2. In order to solve the FH-type equations Ψ1 is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of, for example, the (μ+μ−) atom eigenfunctions. At the same time Ψ2 is expanded in terms of the output channel two-body wave functions, that is in terms of atom eigenfunctions. Additionally, a convenient total angular momentum projection is performed. Results for better known low energy μ− transfer reactions from one hydrogen isotope to another hydrogen isotope in the cycle of muon catalyzed fusion (μCF) are also computed and presented.