Scaling of the Ground-state Energy of Relativistic Ions in High Locally Bounded Magnetic Fields

Abstract

We consider the pseudorelativistic Chandrasekhar/Herbst operator hH for the description of relativistic one-electron ions in a locally bounded magnetic field. We show that for Coulomb potentials of strength γ < 2/π, the spectrum of hH is discrete below m (the electron mass). For magnetic fields in the class BA(x) = B · 1+τ 2 (|x1| τ + |x2| ) ez , the ground-state energy of hH decreases according to B1/(2+τ) as B →∞ for 0 ≤ τ < τc where τc is some critical value depending on γ.

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Cite this paper

@inproceedings{JakubassaAmundsen2010ScalingOT, title={Scaling of the Ground-state Energy of Relativistic Ions in High Locally Bounded Magnetic Fields}, author={D. H. Jakubassa-Amundsen}, year={2010} }