Scaling of the ground-state energy of relativistic ions in high locally bounded magnetic fields

We consider the pseudorelativistic Chandrasekhar/Herbst operator h H 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 h H is discrete below m (the electron mass). For magnetic fie...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-08, Vol.51 (8), p.082303-082303-14
Main Author: Jakubassa-Amundsen, D. H.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
BEAMS
CHARGED PARTICLES
COULOMB FIELD
ELECTRIC FIELDS
ELECTRIC POTENTIAL
ELECTRON BEAMS
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LEVELS
ENERGY RANGE
Exact sciences and technology
FERMIONS
GROUND STATES
IONS
LEPTON BEAMS
LEPTONS
MAGNETIC FIELDS
Mathematical methods in physics
MATHEMATICAL OPERATORS
Mathematics
PARTICLE BEAMS
Physics
RELATIVISTIC RANGE
Sciences and techniques of general use
Theoretical mathematics
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Summary:We consider the pseudorelativistic Chandrasekhar/Herbst operator h H 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 h H is discrete below m (the electron mass). For magnetic fields in the class B A ( x ) = B ⋅ 1 + τ 2 ( | x 1 | τ + | x 2 | τ ) e z , the ground-state energy of h H decreases according to B 1 / ( 2 + τ ) as B → ∞ for 0 ≤ τ < τ c , where τ c is some critical value, depending on γ .
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3467037