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New Bounds on the Maximum Ionization of Atoms

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Abstract

We prove that the maximum number N c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z 1/3. This improves Lieb’s upper bound N c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).

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  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Phan Thành Nam

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  1. Phan Thành Nam
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Correspondence to Phan Thành Nam.

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Communicated by I. M. Sigal

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Nam, P.T. New Bounds on the Maximum Ionization of Atoms. Commun. Math. Phys. 312, 427–445 (2012). https://doi.org/10.1007/s00220-012-1479-y

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  • DOI: https://doi.org/10.1007/s00220-012-1479-y

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