Communications in Mathematical Physics

, Volume 312, Issue 2, pp 427–445 | Cite as

New Bounds on the Maximum Ionization of Atoms



We prove that the maximum number Nc of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z1/3. This improves Lieb’s upper bound Nc < 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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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

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