Adiabatic spectrum for relativistic hydrogen in a strong homogeneous magnetic field

Pierre Duclos (1, 2) , Philippe Briet (1, 2) , Raymond Brummelhuis (3, 4)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 LMR - Laboratoire de Mathématiques de Reims
4 Birckbeck College

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 eigen-values successively descend into the lower part of the continuous spectrum, (-\infty,mc^2]. This phenomenon is for large B roughly periodical in log B.

Mots clés: Dirac; Strong magnetic fields; effective hamiltonian

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Pierre Duclos, Philippe Briet, Raymond Brummelhuis. Adiabatic spectrum for relativistic hydrogen in a strong homogeneous magnetic field. Fifth Workshop on Critical Stability,, Oct 2008, Erice, Italy. pp.179-182, ⟨10.1007/s00601-009-0014-y⟩. ⟨hal-00368395⟩