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

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

2007-02-16

arxiv.org/abs/math-ph/0702056v1

Communications in Mathematical Physics 278, 549-566 (2008)

Physics

Mathematical Physics

17 pages

Scientific paper

10.1007/s00220-007-0397-x

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 -- by relatively simple technical means -- to results for the Schr\"odinger operator.

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