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On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms

Published online by Cambridge University Press:  14 November 2011

V. I. Burenkov  and
W. D. Evans
V. I. Burenkov
Affiliation:
School of Mathematics, University of Wales–Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.
W. D. Evans
Affiliation:
School of Mathematics, University of Wales–Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.
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Abstract

The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 5 , 1998 , pp. 993 - 1005
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Bethe, H. A. and Salpeter, E. E.. Quantum mechanics of one- and two-electron atoms. In Handbuch der Physik, XXXV, ed. S. Flugge, pp. 88–436 (Berlin: Springer, 1st edn, 1957).Google Scholar
2Brown, G. E. and Ravenhall, D. G.. On the interaction of two electrons. Proc. Roy. Soc. London, Ser. A 208 (A 1095) (1951), 552–9.Google Scholar
3Evans, W. D., Perry, P. and Siedentop, H.. The spectrum of relativistic one-electron atoms according to Bethe and Salpeter. Commum. Math. Phys. 178 (1996), 733–46.CrossRefGoogle Scholar
4Hardekopf, G. and Sucher, J.. Critical coupling constants for relativistic wave equations and vacuum breakdown in quantum electrodynamics. Phys. Rev. A 31 (1985), 2020–9.CrossRefGoogle ScholarPubMed
5Tix, C.. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall Bull. London Math. Soc. 30 (1998), 283–90.CrossRefGoogle Scholar