Proof of the stability of highly negative ions in the absence of the Pauli principle

It is well known that ionized atoms cannot be both very negative and stable. The maximum negative ionization is only one or two electrons, even for the largest atoms. The reason for this phenomenon is examined critically and it is shown that electrostatic considerations and the uncertainty principle cannot account for it. The exclusion principle plays a crucial role. This is shown by proving that when Fermi statistics is ignored, then the degree of negative ionization is at least of order z, the nuclear charge, when z is large.