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PreprintarXiv licencearXiv

Asymptotic Neutrality for the Ionization Conjecture in the Two-Center Thomas-Fermi-Dirac-von Weizsäcker Theory

  • Lu Chen
  • Yong Wu
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Abstract

The ionization conjecture for the Thomas-Fermi-Dirac-von Weizsäcker model asks how many electrons a given nuclear configuration can bind. So far, only the single-center case has been settled by Frank, Nam, and Van Den Bosch, while the original molecular case has still remained open. We advance this conjecture in the two-center case. We prove that for two distinct nuclei of total charge Z, the number N of bound electrons satisfies N≤ Z+C Z153/154(1+log Z)3/8, with constants independent of the nuclear positions and the nuclear charges. The proof relies on a comparison with the neutral Thomas-Fermi density and on localization and exterior L1-estimates coupled through the screened potential. Our results could be extended to molecules with any fixed number K of nuclei.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026asymptotic,
  title = {{Asymptotic Neutrality for the Ionization Conjecture in the Two-Center Thomas-Fermi-Dirac-von Weizsäcker Theory}},
  author = {Lu Chen and Yong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09997},
  eprint = {2610.09997},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09997},
}
RIS
TY  - UNPB
TI  - Asymptotic Neutrality for the Ionization Conjecture in the Two-Center Thomas-Fermi-Dirac-von Weizsäcker Theory
AU  - Lu Chen
AU  - Yong Wu
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.09997
UR  - https://arxiv.org/abs/2610.09997
AB  - The ionization conjecture for the Thomas-Fermi-Dirac-von Weizsäcker model asks how many electrons a given nuclear configuration can bind. So far, only the single-center case has been settled by Frank, Nam, and Van Den Bosch, while the original molecular case has still remained open. We advance this conjecture in the two-center case. We prove that for two distinct nuclei of total charge Z, the number N of bound electrons satisfies N≤ Z+C Z^153/154(1+log Z)^3/8, with constants independent of the nuclear positions and the nuclear charges. The proof relies on a comparison with the neutral Thomas-Fermi density and on localization and exterior L^1-estimates coupled through the screened potential. Our results could be extended to molecules with any fixed number K of nuclei.
ER  -