The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction

Frank, Rupert L. and Siedentop, Heinz and Warzel, Simone (2008) The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction. Communications in Mathematical Physics, 278 (2). pp. 549-566. ISSN 0010-3616. doi:10.1007/s00220-007-0397-x. https://resolver.caltech.edu/CaltechAUTHORS:20170510-160420593

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Abstract

We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the non-relativistic description of atoms. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This allows us to roll the proof back to results for the Schrödinger operator.

Item Type:

Article

Related URLs:

URL	URL Type	Description
http://dx.doi.org/10.1007/s00220-007-0397-x	DOI	Article
http://link.springer.com/article/10.1007%2Fs00220-007-0397-x	Publisher	Article
https://arxiv.org/abs/math-ph/0702056	arXiv	Discussion Paper
http://rdcu.be/rYjX	Publisher	Free ReadCube access

ORCID:

Author	ORCID
Frank, Rupert L.	0000-0001-7973-4688

Additional Information:

© 2007 The authors. Reproduction of this article for non-commercial purposes by any means is permitted. Received: 16 February 2007; Accepted: 02 May 2007; First Online: 21 December 2007. We thank Elliott Lieb and Robert Seiringer for various supportive discussions. R.F. and H.S. thank the Departments ofMathematics and Physics of Princeton University for hospitality while this work was done. The work has been partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.), the U.S. National Science Foundation, grant PHY 01 39984 (H.S.), and the Deutsche Forschungsgemeinschaft, grant SI 348/13-1 (H.S.).

Funders:

Funding Agency	Grant Number
Swedish Foundation for International Cooperation in Research and Higher Education (STINT)	UNSPECIFIED
NSF	PHY-0139984
Deutsche Forschungsgemeinschaft	SI 348/13-1

Subject Keywords:

Heavy atoms, ground state energy, relativistic Coulomb system, Scott correction

Issue or Number:

Classification Code:

1991 Mathematics Subject Classification: 81V45, 81V55, 35Q40, 46N50, 47N50

DOI:

10.1007/s00220-007-0397-x

Record Number:

CaltechAUTHORS:20170510-160420593

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170510-160420593

Official Citation:

Frank, R.L., Siedentop, H. & Warzel, S. Commun. Math. Phys. (2008) 278: 549. doi:10.1007/s00220-007-0397-x

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

77356

Collection:

CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

12 May 2017 18:49

Last Modified:

15 Nov 2021 17:30

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