A quickly converging expansion for three-body variational wave functions is obtained by adding to the usual Hylleraas wave-functions terms which express the correct asymptotic behavior. This modified expansion is applied to three problems: the ${\mathrm{H}}^{-}$ ground state; a search for a He-$e^{+}$ bound state; a search for a H-$e^{+}$ scattering resonance below the positronium threshold. The ${\mathrm{H}}^{-}$ calculation shows a marked improvement in convergence over using Hylleraas functions alone. It is also found that there is no H-$e^{+}$ bound state unless the mass of the positron is greater than 2.20 electron masses. Similarly, no positron scattering resonance below positronium threshold exists unless the mass of the positron is less than about 0.7 electron masses.

• Received 6 March 1969

DOI:https://doi.org/10.1103/PhysRev.182.1