On The Excess Charge Problem of Atoms

D. Hundertmark, N. Pattakos and M.R. Schulz

arXiv:2504.18487 [math-ph]

Abstract: This paper establishes new bounds on the maximum number of electrons that an atom with nuclear charge Z can bind. Specifically, we show that N < 1.1185 Z + Z**( 1/3 ) with an explicit bound on the lower order term Z**( 1/3 ). This result improves long–standing bounds by Lieb and Nam obtained in 1984, respectively 2012. Our bounds show the fundamental difference between fermionic and bosonic atoms for finite since for bosonic atoms it is known that lim N/Z  ≈ 1.21 in the limit of large nuclear charges .