Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle

  • Rafael Benguria
  • Elliott H. Lieb


It is well known that ionized atoms cannot be both very negative and stable. The maximum negative ionization is only one or two electrons, even for the largest atoms. The reason for this phenomenon is examined critically and it is shown that electrostatic considerations and the uncertainty principle cannot account for it. The exclusion principle plays a crucial role. This is shown by proving that when Fermi statistics is ignored, then the degree of negative ionization is at least of order z, the nuclear charge, when z is large.


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  1. 1.
    M. B. Ruskai, Commun. Math. Phys. 82, 457 (1982).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    I. M. Sigal, Commun. Math. Phys. 85, 309 (1982).MathSciNetADSMATHCrossRefGoogle Scholar
  3. See also Mathematical Problems in Theoretical Physics, Lecture Notes in Theoretical Physics Vol. 153 ( Springer-Verlag, Berlin, 1982 ), pp. 149–156.Google Scholar
  4. 3.
    M. B. Ruskai, Commun. Math. Phys. 85, 325 (1982).MathSciNetADSCrossRefGoogle Scholar
  5. 4.
    I. M. Sigal, Institute Mittag-Leffler Report No. 12, 1982 (unpublished).Google Scholar
  6. 5.
    R. Benguria, H. Brezis, and E. H. Lieb, Commun. Math. Phys. 79, 167 (1981).MathSciNetADSMATHCrossRefGoogle Scholar
  7. 6.
    E. H. Lieb, Rev. Mod. Phys. 53, 603 (1981).MathSciNetADSCrossRefGoogle Scholar
  8. 7.
    M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, Phys. Rev. A 16, 1782 (1977).MathSciNetADSCrossRefGoogle Scholar
  9. 8.
    E. H. Lieb, Density Functionals for Coulomb Systems, in Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on His 75th Birthday, edited by A. Shimony and H. Feshbach ( MIT Press, Cambridge, Mass., 1982 ), pp. 111–149.Google Scholar
  10. 9.
    E. H. Lieb, Phys. Lett. 70A, 444 (1979).MathSciNetCrossRefGoogle Scholar
  11. 10.
    S. Oxford and E. H. Lieb, Int. J. Quantum Chem. 19, 427 (1981).CrossRefGoogle Scholar
  12. 11.
    E. H. Lieb, Rev. Mod. Phys. 48, 553 (1976).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rafael Benguria
    • 1
  • Elliott H. Lieb
    • 2
  1. 1.Departamento de FisicaUniversidad de ChileSantiagoChile
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityUSA

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