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Adiabatic spectrum for relativistic hydrogen in a strong homogeneous magnetic field

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Abstract

We study the bound states of relativistic hydrogen-like atoms coupled to strong homogeneous magnetic fields, assuming a fixed, infinitely heavy nucleus. Working in the adiabatic approximation in which the electron is confined to the lowest Landau level, we show that the corresponding Dirac Hamiltonian always has an infinite discrete spectrum accumulating at mc 2, m being the electron mass, and that, as the field strength increases, its eigenvalues successively descend into the lower part of the continuous spectrum, (−∞, −mc 2]. This phenomenon is for large B roughly periodical in log B.

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References

  1. Briet, Ph., Brummelhuis, R., Duclos, P.: Effective hamiltonians for relativistic hydrogen in a strong homogeneous magnetic field (in preparation)

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Authors and Affiliations

  1. Département de Mathématique et Informatique, Université de Reims, FR 3111, BP 1039, 51687, Reims Cedex 2, France

    R. Brummelhuis

  2. School of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, N1PB, UK

    R. Brummelhuis

  3. Centre de Physique Théorique de Marseille UMR 6207, Unité Mixte de Recherche du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et de l’Université du Sud Toulon-Var, Laboratoire affiliéá la FRUMAM, Luminy Case 907, 13288, Marseille Cedex 9, France

    Ph. Briet & P. Duclos

Authors
  1. R. Brummelhuis
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  2. Ph. Briet
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  3. P. Duclos
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Corresponding author

Correspondence to R. Brummelhuis.

Additional information

This article is based on the presentation by R. Brummelhuis at the Fifth Workshop on Critical Stability, Erice, Sicily.

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Brummelhuis, R., Briet, P. & Duclos, P. Adiabatic spectrum for relativistic hydrogen in a strong homogeneous magnetic field. Few-Body Syst 45, 179–182 (2009). https://doi.org/10.1007/s00601-009-0014-y

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  • DOI: https://doi.org/10.1007/s00601-009-0014-y

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