Stable bound states ofe++Liande++Na

Using model potentials to describe the ionic cores, we have approximated the $e^{+}+\mathrm{Li}$ and $e^{+}+\mathrm{Na}$ systems as quasi-three-body problems and performed adiabatic hyperspherical calculations to search for the existence of bound states. We have confirmed the existence of a bound state for $e^{+}+\mathrm{Li}$ that was first predicted by Ryzhikh and Mitroy [Phys. Rev. Lett. 21, 4124 (1997)] with a binding energy of 58 meV. Further, we predict the existence of a stable bound state for $e^{+}+\mathrm{Na}$ with a binding energy of 7 meV and explain why bound states exist for these two systems but not for the $e^{+}+\mathrm{H}$ system, despite the fact that ${\mathrm{H}}^{\mathrm{-}}$ has a higher binding energy than either ${\mathrm{Li}}^{\mathrm{-}}$ or ${\mathrm{Na}}^{\mathrm{-}}.$ Based on this work, we find that it is unlikely that positrons can form stable bound states with any other of the alkali-metal atoms.