Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom