Asymptotic Neutrality of Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math>Ions

Abstract

Let $N(Z)$ denote the number of electrons that a nucleus of charge $Z$ binds in nonrelativistic quantum theory. It is proved that $\frac{N(Z)}{Z}\ensuremath{\rightarrow}1$ as $Z\ensuremath{\rightarrow}\ensuremath{\infty}$. The Pauli principle plays a critical role.