The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory

Abstract

We prove that in Thomas-Fermi-Dirac-von Weizsacker theory, a nucleus of charge Z>0 can bind at most Z+C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.(c) 2017 Wiley Periodicals, Inc.