Author(s):

Nam, Phan Thanh; Van Den Bosch, Hanne

Article Title: 
Nonexistence in Thomas FermiDiracvon Weizsäcker theory with small nuclear charges

Alternate Title: 
Mathematical Physics Analysis and Geometry

Affiliation 
IST Austria 
Abstract: 
We study the ionization problem in the ThomasFermiDiracvon Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.

Keywords: 
Concentrationcompactness method; Ionization problem; ThomasFermiDiracvon Weizsäcker Theory

Journal Title:

Mathematical Physics, Analysis and Geometry

Volume: 
20

Issue 
2

ISSN:

15729656

Publisher:

Springer

Date Published:

20170601

Start Page: 
Article number: 6

URL: 

DOI: 
10.1007/s1104001792380

Notes: 
We would like to thank Rafael Benguria for motivating discussions. We thank Jianfeng
Lu and Felix Otto for helpful correspondence on the translationinvariant case and for pointing out
the reference [23] to us. P.T. Nam is supported by the Austrian Science Fund (FWF) under Project Nr.
P 27533N27. H. Van Den Bosch acknowledges support from CONICYT (Chile) through CONICYT–
PCHA/Doctorado Nacional/2014 and through Fondecyt Project # 1120836, and from the Iniciativa
Cient´ıfica Milenio (Chile) through the Millenium Nucleus RC–120002 “F´ısica Matem´atica”.

Open access: 
yes (repository) 