The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory

R. Frank, N. Phan Thanh, H. Van Den Bosch, Communications on Pure and Applied Mathematics 71 (2018) 577–614.


Journal Article | Published | English
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Abstract
We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.
Publishing Year
Date Published
2018-03-01
Journal Title
Communications on Pure and Applied Mathematics
Acknowledgement
We thank the referee for helpful suggestions that improved the presentation of the paper. We also acknowledge partial support by National Science Foundation Grant DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática” (H.V.D.B.).
Volume
71
Issue
3
Page
577 - 614
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Cite this

Frank R, Phan Thanh N, Van Den Bosch H. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 2018;71(3):577-614. doi:10.1002/cpa.21717
Frank, R., Phan Thanh, N., & Van Den Bosch, H. (2018). The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics, 71(3), 577–614. https://doi.org/10.1002/cpa.21717
Frank, Rupert, Nam Phan Thanh, and Hanne Van Den Bosch. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics 71, no. 3 (2018): 577–614. https://doi.org/10.1002/cpa.21717.
R. Frank, N. Phan Thanh, and H. Van Den Bosch, “The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory,” Communications on Pure and Applied Mathematics, vol. 71, no. 3, pp. 577–614, 2018.
Frank R, Phan Thanh N, Van Den Bosch H. 2018. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 71(3), 577–614.
Frank, Rupert, et al. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics, vol. 71, no. 3, Wiley-Blackwell, 2018, pp. 577–614, doi:10.1002/cpa.21717.

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