Upper bound to the critical binding nuclear charge for a three-electron atomic system

The three-electron ground state atomic energy in the Z → 2 limit, where Z is the nuclear charge, is studied using high precision Hylleraas-type calculations, with the objective to investigate the stability of the ground state of the helium negative ion. Finite nuclear mass effects and relativistic corrections are incorporated in the computations. The calculations reveal that the critical binding nuclear charge, Zc, the value below which the three-electron system is no longer stable, is bounded above by Zc = 2.000 001