{
  "id": "0805.4441",
  "version": "v2",
  "published": "2008-05-28T22:01:27.000Z",
  "updated": "2008-07-23T08:49:49.000Z",
  "title": "The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction",
  "authors": [
    "Rupert L. Frank",
    "Heinz Siedentop",
    "Simone Warzel"
  ],
  "comment": "42 pages",
  "journal": "Documenta Math. 14 (2009) 463--516",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-23T08:49:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V45"
    ],
    "keywords": [
      "scott correction",
      "heavy atoms",
      "coupling constant",
      "hydrogenic brown-ravenhall operator",
      "ground state energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.4441F"
    }
  }
}