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

Abstract: Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $$a^{+} b^{+} \mu^{-} e^{-} e<sup>{-}$$. Each of these five-body ions contains two electrons $e<sup>{-}$, one negatively charged muon $\mu<sup>{-}$ 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 $$a^{+} b^{+} \mu^{-} e<sup>{-}$$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $$p^{+} d^{+} \mu^{-} e<sup>{-}$$ and $$p^{+} t^{+} \mu^{-} e<sup>{-}$$.