Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

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.

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Correspondence to Hanne Van Den Bosch.

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Nam, P.T., Van Den Bosch, H. Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges. Math Phys Anal Geom 20, 6 (2017). https://doi.org/10.1007/s11040-017-9238-0

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Keywords

  • Thomas-Fermi-Dirac-von Weizsäcker Theory
  • Ionization problem
  • Concentration-compactness method

Mathematics Subject Classification (2010)

  • 35Q40