Properties and hyperfine structure of helium-muonic atoms

Basic geometrical and dynamical properties of the ³He²⁺μ^-e^- and ⁴He²⁺μ^-e^- helium-muonic atoms are determined from high-precision, variational calculations. Only the bound ground states with $L=0$ are discussed. The estimated hyperfine splitting between 1/2S and 3/2S states in the ³He²⁺μ^-e^- atom is Δν=4166.389 MHz. The analogous result for the hyperfine splitting between ⁰S and ¹S states in the ⁴He²⁺μ^-e^- atom is Δν=4464.555 MHz. Both obtained figures agree very well with the known experimental values. The evaluated hyperfine splitting for the ⁶Li³⁺μ^-e^- ion is ≈29311.4 MHz and for the ⁷Li³⁺μ^-e^- ion is ≈36790.8 MHz.