Stable bound states of e⁺+Li and e⁺+Na

Using model potentials to describe the ionic cores, we have approximated the e⁺+Li and e⁺+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⁺+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⁺+Na with a binding energy of 7 meV and explain why bound states exist for these two systems but not for the e⁺+H system, despite the fact that H^- has a higher binding energy than either Li^- or Na^-. 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.