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 ⁺ 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 ⁻.