Eur. Phys. J. D (2015) 69: 50
https://doi.org/10.1140/epjd/e2015-50824-2

Regular Article

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

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6H 5B7, Canada

^a e-mail: afrolov@uwo.ca

Received: 17 November 2014
Received in final form: 7 January 2015
Published online: 19 February 2015

Abstract

A large number of bound state properties of the four-body muonium-positronium system MuPs (or μ⁺e^-₂e⁺) 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: τ_a = 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.