On the Excess Charge Problem of Atoms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909594541883392 |
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| author | Hundertmark, Dirk Pattakos, Nikolaos Schulz, Marvin Raimund |
| author_facet | Hundertmark, Dirk Pattakos, Nikolaos Schulz, Marvin Raimund |
| contents | 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 $Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Excess Charge Problem of Atoms Hundertmark, Dirk Pattakos, Nikolaos Schulz, Marvin Raimund Mathematical Physics Functional Analysis Spectral Theory Atomic Physics 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 $Z$. |
| title | On the Excess Charge Problem of Atoms |
| topic | Mathematical Physics Functional Analysis Spectral Theory Atomic Physics |
| url | https://arxiv.org/abs/2504.18487 |