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

1 May 1989

journal article
research article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 86 (10) , 3464-3465
https://doi.org/10.1073/pnas.86.10.3464

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.