Antihydrogen (H?) and muonic antihydrogen (H?μ) formation in low energy three-charge-particle collisions

摘要

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, p?, with a positronium atom: Ps= (e~+e-)-a bound state of an electron and a positron. The second problem is a collision of p? with a muonic muonium atom, i.e. true muoniuma bound state of two muons one positive and one negative: Ps_μ = (μ~+ + μ~-). The total cross section of the following two reactions: p? + (e~+e~-) → H? + e~- and p? + (μ~+ + μ~-) → H?_μ~+ μ~-, where H = (p?e~+) is antihydrogen and H?_μ = (p?μ~+) is a muonic antihydrogen atom, i.e. a bound state of p? and μ~+, are computed in the framework of a set of coupled two-component FaddeevHahn-type (FH-type) equations. Unlike the original Faddeev approach the FH-type equations are formulated in terms of only two but relevant components: ψ_1 and ψ_2, of the system's three-body wave function ψ, where ψ= ψ_1 + ψ_2. In order to solve the FH-type equations -1 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 ψ_2 is expanded in terms of the output channel two-body wave functions, that is in terms of H? _μ 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.