Abstract
We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namelyp 2/2m is replaced by (p 2 c 2+m 2 c 4)1/2−mc 2. The electrons are allowed to haveq spin states (q=2 in nature). For one electron and one nucleus instability occurs ifzα>2/π, wherez is the nuclear charge and α is the fine structure constant. We prove that stability occurs in the many-body case ifzα≦2/π and α<1/(47q). For smallz, a better bound on α is also given. In the other direction we show that there is a critical α c (no greater than 128/15π) such that if α>α c then instability always occurs forall positivez (not necessarily integral) when the number of nuclei is large enough. Several other results of a technical nature are also given such as localization estimates and bounds for the relativistic kinetic energy.
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Communicated by A. Jaffe
Work partially supported by U.S. National Science Foundation grant PHY-85-15288-A02
The author thanks the Institute for Advanced Study for its hospitality and the U.S. National Science Foundation for support under grant DMS-8601978
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Lieb, E.H., Yau, HT. The stability and instability of relativistic matter. Commun.Math. Phys. 118, 177–213 (1988). https://doi.org/10.1007/BF01218577
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DOI: https://doi.org/10.1007/BF01218577