Quasi-atomic three- and four-body systems with muonium

Abstract

Properties of some few-body systems which include one positively charged muon ${\mu }^{+}$ and two electrons $e^{-}$ are discussed. In particular, we consider the negatively charged muonium ion Mu${}^{-}$ (or ${\mu }^{+}{e}_2^{-}$) and four-body MuPs (or ${\mu }^{+}{e}_2^{-}{e}^{+}$) systems each of which has only one stable bound (ground) state. The problem of annihilation of the electron-positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is $\Delta \approx$ 23.05758 $MHz$. Another group of interesting four-body neutral systems investigated in this study includes the $p^{+}{\mu }^{+}{e}_2^{-},d^{+}{\mu }^{+}{e}_2^{-}$ and $t^{+}{\mu }^{+}{e}_2^{-}$ `quasi-molecules'. These quasi-molecules are formed in large numbers when positively charged muons slow down in liquid hydrogen, or in liquid deuterium and/or tritium. The properties of these systems are unique, since they occupy an intermediate position between actual two-center molecules and one-center atoms.

arXiv commentPACS number(s): 32.10.Fn, 31.15.A- and 31.15.Ve