2021/04/23 by Johannes Kirscher, Brian C. Tiburzi
Mathematics · Physics and Astronomy · #Bound state #Charged particle #Cold Atom Physics and Bose-Einstein Condensates #Excited state #Field (mathematics) #Ion #Landau quantization #Magnetic field #Mathematics #Physics #Quantum electrodynamics #Quantum field theory #Quantum mechanics #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #hep-lat #hep-ph #nucl-th
paper · pdf · doi:10.1016/j.physletb.2021.136462
8 pages, 3 figures, v2 presentation improved, results unchanged
arxiv created 2021/04/23 · openalex publication_date 2021/06/23 · arxiv updated 2021/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a collective Landau-level quantum number incorporating both center-of-mass and relative degrees of freedom. Results are obtained for a system of one charged and one neutral particle, with the interaction chosen to produce a bound state in vanishing magnetic field. Beyond deriving the weak-field expansion of the energy levels, we focus on non-perturbative aspects. In the strong-field limit, or equivalently for a system in the unitary limit, a single bound level with universal binding energy exists. By contrast, excited states are resonances that disappear into the continuum as the magnetic field is raised beyond critical values. A hyperbola is derived that approximates the number of bound levels as a function of the field strength remarkably well.