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

Abstract

The results of high-precision variational calculations are reported for anumber of bound states in various Coulomb three-body systems, includinghelium and helium-muonic atoms, some adiabatic systems (H2+, D2+ andDT+ions) and muonic molecular ions ppμ, ddμ, ttμ and dtμ. The hyperfinesplittings for the double electron-excited states in the helium-muonic 3He2+ μ−e− and 4He2+ μ−e−atoms have also been determined. The results of this study are significantly moreaccurate than results known from earlier calculations for all considered systemsand states. The approach can be used to determine the bound-state spectra invarious three-body systems to arbitrary high accuracy. We also discuss a numberof complications which are usually detected in high-precision bound-statecalculations of few-body systems.