Universal variational expansion for high-precision bound-state calculations in three-body systems. Applications to weakly bound, adiabatic and two-shell cluster systems

The results of high-precision variational calculations are reported for a number of bound states in various Coulomb three-body systems, including helium and helium-muonic atoms, some adiabatic systems (H-2(+), D-2(+) and DT+ ions) and muonic molecular ions ppmu, ddmu, ttmu and dtmu. The hyperfine splittings for the double electron-excited states in the helium-muonic (3)He(2+)mu(-)e(-) and (4)He(2+)mu(-)e(-) atoms have also been determined. The results of this study are significantly more accurate than results known from earlier calculations for all considered systems and states. The approach can be used to determine the bound-state spectra in various three-body systems to arbitrary high accuracy. We also discuss a number of complications which are usually detected in high-precision bound-state calculations of few-body systems.