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Asymptotic behavior of the ground state of large atoms

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Asymptotic behavior of the ground state of large atoms JOURNÉES ÉQUATIONS AUX DÉRIVÉES PARTIELLES HEINZ SIEDENTOP Asymptotic behavior of the ground state of large atoms Journées Équations aux dérivées partielles (1989), p. 1-10. <http://www.numdam.org/item?id=JEDP_1989____A10_0> © Journées Équations aux dérivées partielles, 1989, tous droits réservés. L’accès aux archives de la revue « Journées Équations aux dérivées partielles » (http://www. math.sciences.univ-nantes.fr/edpa/), implique l’accord avec les conditions générales d’utili- sation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression sys- tématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi- chier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Asymptotic Behavior of the Ground State of Large Atoms Heinz Siedentop Department of Mathematics Fine Hall Princeton University Princeton, New Jersey 08544 USA June 12, 1989 Abstract We review some results on the behavior of the ground state energy and the ground state density for large atoms as the nuclear charge Z increases to infin- ity. Here the atom is described by various models, namely the Thomas-Fermi, the Thomas-Fermi-Weizsacker, the Fermi-Hellmann, the Hellmann-Weizsacker model, and the Schrodinger equation. 1 Introduction The following results for large atoms, i.e., for large nuclear charge Z and large electron number N keeping the ratio Z / N = a fixed, shall be presented: • Asymptotic behavior of the ground state energy, • Bounds on the execess charge, • Asymptotic behavior of the ground state density. The results will be presented in the context of the following models ordered roughly according to increasing complexity: 1. The Thomas-Fermi model (Thomas [20], Fermi [7, 6]): £TF{P} = / i^w -1^) +1^ * ^ wp^371 (1) P>^ j P < N , (2) q being the number of sp

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