Bound state spectra and properties of the five- and six-body muonic ions and quasi-molecules

The ground bound states in the five-body muonic ions $a b \mu e_2$ (or $(a b \mu e_2)^{-}$), where $(a, b) = (p, d, t)$, are considered for the first time. As follows from accurate numerical computations of these five-body ions they are similar to the negatively charged hydrogen ion H$^{-}$ with a three-particle central quasi-nucleus $a b \mu$ (or $(a b \mu)^{+}$). These five-body ions play some role in the muon-catalyzed fusion of nuclear reaction in liquid deuterium and/or deuterium-tritium mixtures. We also discuss the bound states in the six-body $a b c \mu e_2$ quasi-molecules, where $(a, b, c) = (p, d, t)$. These six-body, two-electron quasi-molecules are of great interest for muon-catalyzed nuclear fusion, since in liquid deuterium and/or deuterium-tritium mixture more than 99 \% of all muon-catalyzed reactions of the $(dd)-$ and $(dt)-$fusion occur in such six-body quasi-molecules: $d d t \mu e_2, d d d \mu e_2$ and $d t t \mu e_2$.