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

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 -- by relatively simple technical means -- to results for the Schrödinger operator.

arXiv comment17 pages

References in corpus (3)

• A new coherent states approach to semiclassics which gives Scott's correction
• The large-Z behaviour of pseudo-relativistic atoms
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• The Scott conjecture for large Coulomb systems: a review
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• On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction
• The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian
• Relativistic Strong Scott Conjecture: A Short Proof
• Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture
• Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic field
• Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field
• Asymptotics of the ground state energy of heavy molecules and related topics. II
• The Magnetic Scott Correction for Relativistic Matter at Criticality