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

Abstract

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