New calculation of the properties of the positronium ion

The positronium negative ion (${\mathrm{Ps}}^{-}$), the system composed of two electrons and a positron, has been reinvestigated theoretically. Using a Hylleraas wave function with two nonlinear parameters and more than 200 linear terms, we have obtained excellent values of binding energy and annihilation lifetime of the particle-stable ${}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ ground state. In addition, we have examined the question of stability of the ${}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ state discussed by Mills, and we agree with his conclusion that the state is probably not stable against breakup into $\mathrm{Ps}\mathrm{}(n=2\mathrm{})+e^{-}$. Improved limits on the critical "positron" mass for binding the ${}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ state have also been obtained.