Abstract
We consider an atom described by Müller theory, which is similar to Hartree–Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most \(Z+C\) electrons, where C is a universal constant. Our proof proceeds by comparison with Thomas–Fermi theory, and a key ingredient is a novel bound on the number of electrons far from the nucleus.
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Acknowledgements
The authors are grateful to Heinz Siedentop for a motivating discussion. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/Doctorado Nacional/2014, Fondecyt Project # 116–0856 and Iniciativa Científica Milenio (Chile) through Millennium Nucleus RC–120002 “Física Matemática” (H.V.D.B.) is acknowledged.
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Communicated by Jan Derezinski.
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Frank, R.L., Nam, P.T. & Van Den Bosch, H. The Maximal Excess Charge in Müller Density-Matrix-Functional Theory. Ann. Henri Poincaré 19, 2839–2867 (2018). https://doi.org/10.1007/s00023-018-0695-1
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DOI: https://doi.org/10.1007/s00023-018-0695-1