Critical stability of the three-body system (Z, e−, e+)

We studied the stability of the system (Z,e-,e+) as a function of the fixed nuclear charge Z. This system, which can be a model to study more complex systems such as positrons bound to atoms or charged excitons in semiconductors, is stable for Z<1. We studied, using the diffusion Monte Carlo method, its ground-state energy E(Z) as a function of the nuclear charge, giving a rigorous upper bound to the critical charge: Zc<0.421. We fitted the available data to give a nonvariational estimate of the critical charge: 0.418<0.419. We also studied a Pe bound excited state of unnatural parity and estimated its critical charge: 0.54<0.55.