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arXiv · 2504.18487

On the Excess Charge Problem of Atoms

Dirk Hundertmark·Nikolaos Pattakos·Marvin Raimund Schulz
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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 $Z$.

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Dirk Hundertmark, Nikolaos Pattakos, Marvin Raimund Schulz. 2025-04-25. On the Excess Charge Problem of Atoms. https://arxiv.org/abs/2504.18487

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