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

Frank, Rupert L. and Nam, Phan Thành and Van Den Bosch, Hanne (2018) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Communications on Pure and Applied Mathematics, 71 (3). pp. 577-614. ISSN 0010-3640. http://resolver.caltech.edu/CaltechAUTHORS:20170501-083145482

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/cpa.21717DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/cpa.21717/abstractPublisherArticle
https://arxiv.org/abs/1606.07355arXivDiscussion Paper
Additional Information:© 2017 Wiley Periodicals, Inc. Issue online: 17 January 2018; Version of record online: 4 October 2017; Manuscript Received: June 2016. We thank the referee for helpful suggestions which improved the presentation of the paper. Partial support by U.S. National Science Foundation 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.) is acknowledged.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
FWF Der WissenschaftsfondsP 27533-N27
Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)UNSPECIFIED
Iniciativa Científica MilenioRC-120002
Record Number:CaltechAUTHORS:20170501-083145482
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170501-083145482
Official Citation:Frank, R. L., Nam, P. T. and Van Den Bosch, H. (2018), The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory. Comm. Pure Appl. Math., 71: 577–614. doi:10.1002/cpa.21717
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77090
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 May 2017 16:08
Last Modified:02 Feb 2018 16:59

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