Positron annihilation in the MuPs system

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

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