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The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory
Author(s) -
Frank Rupert L.,
Nam Phan Thành,
Van Den Bosch Hanne
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21717
Subject(s) - semi empirical mass formula , conjecture , fermi–dirac statistics , fermi gamma ray space telescope , electron , physics , constant (computer programming) , radius , dirac (video compression format) , ionization , product (mathematics) , mathematical physics , quantum mechanics , mathematics , ion , pure mathematics , computer science , geometry , computer security , neutron , fission , neutrino , programming language
We prove that in Thomas–Fermi–Dirac–von Weizsäcker 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.© 2017 Wiley Periodicals, Inc.