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

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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.

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Author notes

  1. Rupert L. Frank

    Present address: Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA

Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Rupert L. Frank

  2. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, München, Germany

    Heinz Siedentop

  3. Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA

    Simone Warzel

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  1. Rupert L. Frank
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  2. Heinz Siedentop
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Correspondence to Heinz Siedentop.

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Frank, R.L., Siedentop, H. & Warzel, S. The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction. Commun. Math. Phys. 278, 549–566 (2008). https://doi.org/10.1007/s00220-007-0397-x

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