Abstract
A large number of bound state properties of the four-body muonium-positronium system MuPs (or μ + e - 2 e +) are determined to high accuracy. Based on these expectation values we predict that the weakly-bound four-body MuPs system has the ‘two-body’ cluster structure Mu + Ps. The two neutral clusters Mu (μ + e −) and Ps (e + e −) interact with each other by the attractive van der Waals forces. By using our expectation values of the electron-positron delta-functions we evaluated the half-life τ a of the MuPs system against annihilation of the electron-positron pair: τa = 1/Γ ≈ 4.071509 × 10-10 s. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation values is Δ ≈ 23.064(5) MHz.
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