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

  • V. I. Burenkov (a1) and W. D. Evans (a1)

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.

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1Bethe, H. A. and Salpeter, E. E.. Quantum mechanics of one- and two-electron atoms. In Handbuch der Physik, XXXV, ed. S. Flugge, pp. 88436 (Berlin: Springer, 1st edn, 1957).
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.
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.
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.
5Tix, C.. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall Bull. London Math. Soc. 30 (1998), 283–90.

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

  • V. I. Burenkov (a1) and W. D. Evans (a1)

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