Abstract
Let N(Z) denote the number of electrons which a nucleus of charge Z can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove that N(Z)/Z → 1 as Z → ∞.
Research partially supported by the NSERC under Grant NA 7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01
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References
Benguria, R., Lieb, E.: Proof of the stability of highly negative ions in the absence of the Pauli principle. Phys. Rev. Lett. 50, 1771 (1983)
Choquet, G.: Sur la fondements de la théorie finie du potential. C.R. Acad. Sci. Paris 244, 1606 (1957)
Cycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger operators with application to quantum mechanics and global geometry. Berlin, Heidelberg, New York: Springer 1987
Evans, G.: On potentials of positive mass, I. Trans. AMS 37, 226 (1935)
Helms, L.: Introduction to potential theory. New York: Wiley 1966
Lieb, E.: Atomic and molecular ionization. Phys. Rev. Lett. 52, 315 (1984)
Lieb, E.: Bound on the maximum negative ionization of atoms and molecules. Phys. Rev. A29, 3018–3028 (1984)
Lieb, E., Sigal, I. M., Simon, B., Thirring, W.: Asymptotic neutrality of large-Z ions. Phys. Rev. Lett. 52, 994 (1984)
Ruskai, M.: Absence of discrete spectrum in highly negative ions. Commun. Math. Phys. 82, 457–469 (1982)
Ruskai, M.: Absence of discrete spectrum in highly negative ions, II. Commun. Math. Phys. 85, 325–327 (1982)
Sigal, I. M.: Geometric methods in the quantum many-body problem. Nonexistence of very negative ions. Commun. Math. Phys. 85, 309–324 (1982)
Sigal, I. M.: How many electrons can a nucleus bind? Ann. Phys. 157, 307–320 (1984)
Simon, B.: On the infinitude or finiteness of the number of bound states of an N-body quantum System, I. Helv. Phys. Acta 43, 607–630 (1970)
Vasilescu, F.: Sur la contribution du potential á traverse des masses et la démonstration d’une lemme de Kellogg. C.R. Acad. Sci. Paris 200, 1173 (1935)
Zhislin, G.: Discussion of the spectrum of Schrödinger operator for systems of many particles. Tr. Mosk. Mat. Obs. 9, 81–128 (1960)
Baumgartner, B.: On Thomas-Fermi-von Weizsäcker and Hartree energies as functions of the degree of ionisation. J. Phys. A 17, 1593–1602 (1984)
Baxter, J.: Inequalities for potentials of particle systems, Ill. J. Math. 24, 645–652 (1980)
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Lieb, E.H., Sigal, I.M., Simon, B., Thirring, W. (2005). Approximate Neutrality of Large-Z Ions. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27056-6_9
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DOI: https://doi.org/10.1007/3-540-27056-6_9
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