TAILIEUCHUNG - Đề tài " The ionization conjecture in Hartree-Fock theory "

We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms nevertheless remain bounded. Moreover, we show that in Hartree-Fock theory the radius of an atom (properly defined) is bounded independently of its nuclear charge. Contents 1. Introduction and main results 2. Notational conventions and basic prerequisites 3. Hartree-Fock theory 4. Thomas-Fermi theory . | Annals of Mathematics The ionization conjecture in Hartree-Fock theory By Jan Philip Solovej Annals of Mathematics 158 2003 509 576 The ionization conjecture in Hartree-Fock theory By Jan Philip Solovej Abstract We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely we prove that if the nuclear charge is allowed to tend to infinity the maximal negative ionization charge and the ionization energy of atoms nevertheless remain bounded. Moreover we show that in Hartree-Fock theory the radius of an atom properly defined is bounded independently of its nuclear charge. Contents 1. Introduction and main results 2. Notational conventions and basic prerequisites 3. Hartree-Fock theory 4. Thomas-Fermi theory 5. Estimates on the standard atomic TF theory 6. Separating the outside from the inside 7. Exterior Lx-estimate 8. The semiclassical estimates 9. The Coulomb norm estimates 10. Main estimate 11. Control of the region close to the nucleus proof of Lemma 12. Proof of the iterative step Lemma and of Lemma 13. Proving the main results Theorems and Work partially supported by an EU-TMR grant by a grant from the Danish Research Council and by MaPhySto-Centre for Mathematical Physics and Stochastics funded by a grant from the Danish National Research Foundation. 510 JAN PHILIP SOLOVEJ 1. Introduction and main results One of the great triumphs of quantum mechanics is that it explains the order in the periodic table qualitatively as well as quantitatively. In elementary chemistry it is discussed how quantum mechanics implies the shell structure of atoms which gives a qualitative understanding of the periodic table. In computational quantum chemistry it is found that quantum mechanics gives excellent agreement with the quantitative aspects of the periodic table. It is a very striking fact however that the periodic table is much more periodic than can be explained by the simple shell structure picture. As an example

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