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The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction

Frank, Rupert L. and Siedentop, Heinz and Warzel, Simone (2008) The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170512-100456574

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Abstract

We consider relativistic many-particle operators which – according to Brown and Ravenhall – describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas-Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev-Gagliardo-Nirenberg type inequality is established for the critical atomic Brown-Ravenhall operator. Moreover, we prove sharp upper and lower bound on the eigenvalues of the hydrogenic Brown-Ravenhall operator up to and including the critical coupling constant.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/0805.4441arXivDiscussion paper
Additional Information:Last revised 23 Jul 2008 (this version, v2) We thank Elliott Lieb and Robert Seiringer for supportive discussions. H.S. thanks the Departments of Mathematics and Physics of Princeton University and R.F. and S.W. thank the Department of Mathematics of LMU Munich for hospitality while parts of this work were done. We also thank Volker Bach for stimulating questions resulting in several improvements. The work has been partially supported by the Deutscher Akademischer Austauschdienst, grant D/06/49117 (R.F.), the U.S. National Science Foundation, grant PHY 01 39984 (H.S.), the Deutsche Forschungsgemeinschaft, grant SI 348/13-1 (H.S.), and a Sloan Fellowship (S.W.).
Funders:
Funding AgencyGrant Number
Deutscher Akademischer Austauschdienst (DAAD)D/06/49117
NSFPHY-0139984
Deutsche Forschungsgemeinschaft (DFG)SI 348/13-1
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Heavy atoms, ground state energy, relativistic Coulomb system, Scott correction, Brown-Ravenhall operator.
Classification Code:MSC: 81V45, 81V55, 35Q40, 46N50, 47N50
Record Number:CaltechAUTHORS:20170512-100456574
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170512-100456574
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77400
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:34
Last Modified:12 May 2017 23:34

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