An upper bound for the number of electrons in a large ion

Abstract

Let E(Z, N) be the ground-state energy of N quantized electrons and a single nucleus of charge Z. For fixed Z, E(Z, N) is independent of N for N ≥ N _critical(Z). Physically, this means that at most N _critical electrons can bind to the nucleus. We prove that N _critical ≤ Z + CZ^a with a = 0.84.

• asymptotic neutrality
• excess charge
• quantum mechanics