Internal structure and positron annihilation in the four-body MuPs system

Abstract

A large number of bound state properties of the four-body muonium-positronium system MuPs (or ${\mu }^{+}{e}_2^{-}{e}^{+}$) 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 (${\mu }^{+}{e}^{-}$) 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 ${\tau }_a$ of the MuPs system against annihilation of the electron-positron pair: ${\tau }_a=\frac{1}{\Gamma }\approx 4.071509\cdot 10^{-10}$ $sec$. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation values is $\Delta \approx$ 23.064(5) $MHz$.

References in corpus (2)

• Hyperfine structure and $(e^{-},e^{+})$-pair annihilation in the muonium-positronium MuPs and positronium hydrides
• Positron annihilation in the MuPs system