On the Excess Charge Problem of Atoms

Abstract

This paper establishes new bounds on the maximum number of electrons $N_c(Z)$ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \begin{equation*} N_c(Z) < 1.1185Z + O(Z^{1/3}) \end{equation*} with an explicit bound on the lower order term $O(Z^{1/3})$. 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 $Z$ since for bosonic atoms it is known that $\lim N_c(Z)/Z=t_c\approx 1.21$ in the limit of large nuclear charges $Z$.

50 pages, 2 figures