Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field
| Autor: | Dmitri Maximovitch Gitman, T. C. Adorno, Anatoly E. Shabad |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
High Energy Physics - Theory lcsh:QC793-793.5 nonperturbative methods Quantum Physics lcsh:Elementary particle physics FOS: Physical sciences General Physics and Astronomy Hydrogen atom Electron Landau quantization Quantum number strong fields Schrödinger equation Magnetic field symbols.namesake High Energy Physics - Theory (hep-th) Atom symbols Physics::Atomic Physics Vacuum polarization Atomic physics Quantum Physics (quant-ph) quantum field theory |
| Zdroj: | Universe Volume 6 Issue 11 Universe, Vol 6, Iss 204, p 204 (2020) |
| Popis: | We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler&ndash Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrö dinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be &alpha /3&pi ¯ &lambda C, where ¯ C is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov&ndash Popov method. |
| Databáze: | OpenAIRE |
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