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$\cdot 10^{9}$ $sec^{-1}$, $\Gamma_{3 \gamma} \approx$ 6.62798$\cdot 10^{6}$ $sec^{-1}$, $\Gamma_{4 \gamma} \approx$ 3.61680$\cdot 10^{3}$ $sec^{-1}$, $\Gamma_{5 \gamma} \approx$ 6.32973 $sec^{-1}$. The hyperfine structure splitting for the ground state in the MuPs system has also been evaluated as $\Delta$ = 23.078 $MHz$

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

“…where δ µ + +− is the expectation value of the triple muon-electron-positron delta-function determined for the ground state of the MuPs system and factor χ is a numerical factor which is approximately equal to the factor ξ in Eq. (7). To produce more accurate formulas for Γ (2) 1γ and exact expressions for the factors ξ in Eqs.…”

“…To produce more accurate formulas for Γ (2) 1γ and exact expressions for the factors ξ in Eqs. (7) and χ in Eq. (9) one needs to perform an adittional analysis.…”

“…Since the MuPs system already contains a positron e + , then these two processes (muonic decay and muon synthesis) can proceed instantly and we can observe a 'self-transition' of MuPs into MuPs. In our earlier paper [7] we have evaluated the probability to observe the muon-positron conversion as one event for ≈ 1 · 10 8 of MuPs systems. This means that currently we cannot observe the muon-positron conversion in MuPs, since the probability of conversion is extremely small and it is still very difficult to create even one MuPs system.…”

Energy levels in muonic helium

“…In atomic physics the trial function ( � , � ) of Hylleraas type or correlated exponential type is often used with success [7,9,10]. This function has the exponential form expressed in terms of the interparticle-distance coordinates.…”

“…In these papers different order corrections to HFS were studied by perturbation theory and on the basis of variational method. The variational method gives high numerical accuracy of the calculation what was demonstrated in [7][8][9][10]. Bound particles in muonic helium have different masses � ≪ � ≪ � .…”