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Asymptotics for Bosonic atoms

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Abstract

It was proved by Benguria and Lieb that for an atom where the ‘electrons’ do not satisfy the exclusion principle, the critical electron number N c, i.e., the maximal number of electrons the atom can bind, satisfies lim infz→∞Nc/Z ⩾ 1 + γ, where Z is the nuclear charge. Here γ is a positive constant derived from the Hartree model. We complete this result by proving that the correct asymptotics for N c(Z) is indeed z→∞Nc/Z = 1 + γ.

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References

  1. 1.

    BaumgartnerB., On the Thomas-Fermi-von Weizsäcker and Hartree energies as functions of the degree of ionization, J. Phys. A 17, 1593–1602 (1984).

  2. 2.

    BenguriaR. and LiebE. H., Proof of stability of highly negative ions in the absence of the Pauli principle, Phys. Rev. Lett. 50, 1771–1774 (1983).

  3. 3.

    CyconH. L., FroeseR. G., KirschW., and SimonB., Schrödinger Operators, Springer-Verlag, Berlin, Heidelberg, 1987.

  4. 4.

    Fefferman, C. L. and Seco, L. A., Asymptotic neutrality of large ions, Comm. Math. Phys., to appear.

  5. 5.

    Hoffmann-OstenhofM. and Hoffmann-OstenhofT., ‘Schrödinger inequalities’ and asymptotic behavior of the electron density of atoms and molecules, Phys. Rev. A 16, 1782–1785 (1977).

  6. 6.

    LiebE. H., A lower bound for Coulomb energies, Phys. Lett. 70A, 444–446 (1979).

  7. 7.

    LiebE. H., Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53, 603–641 (1981).

  8. 8.

    LiebE. H., Bound on the maximum negative ionization of atoms and molecules, Phys. Rev. A 29, 3018–3028 (1984).

  9. 9.

    LiebE. H. and OxfordS., An improved lower bound on the indirect Coulomb energy, Int. J. Quantum Chem. 19, 427–439 (1981).

  10. 10.

    LiebE. H., SigalI. M., SimonB., and ThirringW., Asymptotic neutrality of large-Z ions, Comm. Math. Phys. 116, 635–644 (1988).

  11. 11.

    Seco, L. A., Sigal, I. M., and Solovej, J. P., Bound on the ionization energy of large atoms, Comm. Math. Phys., to appear.

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Additional information

This work was done while the author was a graduate student at Princeton University supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03.

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Solovej, J.P. Asymptotics for Bosonic atoms. Lett Math Phys 20, 165–172 (1990). https://doi.org/10.1007/BF00398282

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AMS subject classification (1980)

  • 81-XX