Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges Journal Article


Author(s): Nam, Phan Thanh; Van Den Bosch, Hanne
Article Title: Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges
Alternate Title: Mathematical Physics Analysis and Geometry
Affiliation IST Austria
Abstract: We study the ionization problem in the Thomas-Fermi-Dirac-von 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: Concentration-compactness method; Ionization problem; Thomas-Fermi-Dirac-von Weizsäcker Theory
Journal Title: Mathematical Physics, Analysis and Geometry
Volume: 20
Issue 2
ISSN: 1572-9656
Publisher: Springer  
Date Published: 2017-06-01
Start Page: Article number: 6
URL:
DOI: 10.1007/s11040-017-9238-0
Notes: We would like to thank Rafael Benguria for motivating discussions. We thank Jianfeng Lu and Felix Otto for helpful correspondence on the translation-invariant 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 27533-N27. H. Van Den Bosch acknowledges support from CONICYT (Chile) through CONICYT– PCHA/Doctorado Nacional/2014 and through Fondecyt Project # 112-0836, and from the Iniciativa Cient´ıfica Milenio (Chile) through the Millenium Nucleus RC–120002 “F´ısica Matem´atica”.
Open access: yes (repository)