Stability and hyperfine structure of the four- and five-body muon-atomic clusters $a^{+} b^{+} μ^{-} e^{-}$ and $a^{+} b^{+} μ^{-} e^{-} e^{-}$

Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} μ^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $μ^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} μ^{-} e^{-}$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $p^{+} d^{+} μ^{-} e^{-}$ and $p^{+} t^{+} μ^{-} e^{-}$.

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