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Abstract
A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are carried out with the use of the Sturmian expansion of the two-dimensional generalized radial Dirac–Coulomb Green function derived in the paper. It is found that, in contrast to the case of the three-dimensional atom (Stefańska, 2015), in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities) are expressible in terms of elementary algebraic functions of a nuclear charge and electron quantum numbers. The problem considered here is related to the Coulomb impurity problem for graphene in a weak magnetic field.
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Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
ANNALS OF PHYSICS
no. 401,
pages 174 - 192,
ISSN: 0003-4916 - Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Szmytkowski R.: Relativistic two-dimensional hydrogen-like atom in a weak magnetic field// ANNALS OF PHYSICS. -Vol. 401, (2019), s.174-192
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.aop.2018.12.007
- Sources of funding:
-
- Statutory activity/subsidy
- Verified by:
- Gdańsk University of Technology
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