English

Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acker theory with small nuclear charges

Mathematical Physics 2016-11-11 v2 Analysis of PDEs math.MP

Abstract

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizs\"acker 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

Cite

@article{arxiv.1603.07368,
  title  = {Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acker theory with small nuclear charges},
  author = {Phan Thành Nam and Hanne Van Den Bosch},
  journal= {arXiv preprint arXiv:1603.07368},
  year   = {2016}
}

Comments

Final version, to appear in Mathematical Physics, Analysis and Geometry. Minor clarifications and corrections, a figure added. 30 pages, 1 figure