Author(s):

Frank, Rupert L; Nam, Phan Thanh; Van Den Bosch, Hanne

Article Title: 
The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory

Affiliation 
IST Austria 
Abstract: 
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 ThomasFermi theory which, as a byproduct, 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.

Journal Title:

Communications on Pure and Applied Mathematics

Volume: 
71

Issue 
3

ISSN:

10970312

Publisher:

WileyBlackwell

Date Published:

20180301

Start Page: 
577

End Page:

614

URL: 

DOI: 
10.1002/cpa.21717

Notes: 
We thank the referee for helpful suggestions that improved the presentation of the paper. We also acknowledge partial support by National Science Foundation Grant DMS1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática” (H.V.D.B.).

Open access: 
yes (repository) 