Abstract
A Thomas-Fermi-Weizsäcker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the lower bound on the critical value of the fine structure constant, α, is raised from 0.016 to 0.77 (the critical value is known to be less than 2.72). When α = 1/137, the largest nuclear charge is 59 (compared to the known optimum value 87). A part from this, our method is simple, for it parallels the original Lieb-Thirring proof of stability of nonrelativistic matter, and it adds another perspective on the subject.
Work partially by U.S. National Science Foundation grant PHY95-13072.
Work partially supported by U.S. National Science Foundation grant DMS95-00840.
Work partially supported by European Union, grant ERBFMRXCT960001.
© 1996 by the authors. Reproduction of this article, in its entirety, by any means is permitted for non-commercial purposes provided that full reference to the original source of publication is made.
This paper appeared in Helvetica Physica Acta vol. 69, no. 5/6, 974–984 (1996). Three typographical errors that appeared in the original paper and in the second edition of this ’selecta’ have been corrected here.
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This article is dedicated to our colleagues, teachers, and coauthors Klaus Hepp and Walter Hunziker on the occasion of their sexagesimal birthdays. Their enthusiasm for quantum mechanics as an unending source of interesting physics and mathematics has influenced many.
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Lieb, E.H., Loss, M., Siedentop, H. (2005). Stability of Relativistic Matter via Thomas-Fermi Theory. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27056-6_35
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DOI: https://doi.org/10.1007/3-540-27056-6_35
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