Positron annihilation in the MuPs system

Abstract

The life-time of the four-body atomic system MuPs (${\mu }^{+}{e}_2^{-}{e}^{+}$ or muonium-positronium) against positron annihilation has been evaluated as $\tau =\frac{1}{\Gamma }\approx 4.076453\cdot 10^{-10}$ $sec$. Various annihilation rates for MuPs are determined to a good numerical accuracy, e.g., ${\Gamma }_{2\gamma }\approx$ 2.446485$\cdot 10^9$ $se{c}^{-1}$, ${\Gamma }_{3\gamma }\approx$ 6.62798$\cdot 10^6$ $se{c}^{-1}$, ${\Gamma }_{4\gamma }\approx$ 3.61680$\cdot 10^3$ $se{c}^{-1}$, ${\Gamma }_{5\gamma }\approx$ 6.32973 $se{c}^{-1}$. The hyperfine structure splitting for the ground state in the MuPs system has also been evaluated as $\Delta$ = 23.078 $MHz$.