S -wave resonances of the negative positronium ion and stability of a system of two electrons and an arbitrary positive charge

We have used a Pekeris-type wave function, expressed on a Sturmian basis in terms of perimetric coordinates, in conjunction with the complex coordinate rotation method, to obtain well-converged estimates of the positions and widths of various ¹Sᵉ and ³Sᵉ resonances of Ps. Calculations employing bases with one and two length scales were performed. We compare our results to earlier estimates. We also discuss the minimum positive charge that a particle of arbitrary mass must possess in order to bind two electrons.