Bound on the excess charge of generalized Thomas-Fermi-Weizsäcker functionals

Benguria, Rafael D. und Siedentop, Heinz (2025): Bound on the excess charge of generalized Thomas-Fermi-Weizsäcker functionals. In: Journal of Mathematical Physics, Bd. 66, Nr. 7, 072103

Abstract

We bound the number of electrons Q that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power 5/3 more general powers p are considered. For 3/2 < p < 2 we prove the excess charge conjecture, i.e., that Q is uniformly bounded in the atomic number Z. The case p = 3/2 is critical: the behavior changes from a uniform bound in Z to a linear bound at the critical coupling of the nonlinear term. We also improve the linear bound for all p ≥ 6/5.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0022-2488
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 470903074