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Preprint:
Preprint:
On The Excess Charge Problem of Atoms
On The Excess Charge Problem of Atoms
D. Hundertmark, N. Pattakos and M.R. Schulz
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 .
Supplement to the Preprint
Supplement to the Preprint
This supplement refines the constants obtained in the preprint above. In particular, it determines the optimal values of the constants (\beta_s) for (s \leq 3).
The supplementary appendix will eventually be incorporated into the arXiv version of the preprint.
The main argument of the supplement was developed independently of AI. During a later refinement of the proof, ChatGPT was used as a mathematical research tool and contributed to several simplifications, in particular to the argument concerning preservation of the normalizing moment under weak convergence. All mathematical text was written and the resulting arguments were verified by the authors.
Available on ResearchGate.
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