Atomic and molecular three-body ions with positively charged muons

The properties of some atomic and molecular three-body ions which contain positively charged muons μ⁺ are considered. In particular, the ground states in the muonium ion Mu^- (or μ⁺e^-e^-) and muon-hydrogen molecular p⁺μ⁺e^-,d⁺μ⁺e^-,t⁺μ⁺e^- ions are studied in details. The energies of these systems have been determined to high accuracy: E(Mu^-)=-0.52505480624352632929a.u., E(p⁺μ⁺e^-)=-0.5899037853895877261a.u., E(d⁺μ⁺e^-)=-0.5902553521522464177a.u., and E(t⁺μ⁺e^-)=-0.5903740988926828880a.u. The interparticle distances, δ functions, two-particle cusps, and some other bound-state properties are also presented for all considered systems. The photodetachment of the Mu^- ion is briefly discussed.