Energy Terms and Stability Diagrams for the 2D Problem of Three Charged Particles

  • I. V. Simenog Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • V. V. Mikhnyuk Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • Yu. M. Bidasyuk Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
Keywords: energy terms, stability diagrams, Coulomb systems, variational approach, Born–Oppenheimer approximation, space dimensionality

Abstract

Symmetric and antisymmetric terms have been obtained in the framework of the variational approach for two-dimensional (2D) Coulomb systems of symmetric trions XXY . Stability di-agrams and certain anomalies arising in the 2D space are explained qualitatively in the frame-work of the Born–Oppenheimer adiabatic approximation. The asymptotics of energy terms at large distances obtained for an arbitrary space dimensionality are analyzed, and some approxi-mation formulas for 2D terms are proposed. An anomalous dependence of multipole moments on the space dimensionality has been found in the case of a spherically symmetric field. The main results obtained for the 2D and 3D problems of two Coulomb centers are compared.

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Published
2018-10-22
How to Cite
Simenog, I., Mikhnyuk, V., & Bidasyuk, Y. (2018). Energy Terms and Stability Diagrams for the 2D Problem of Three Charged Particles. Ukrainian Journal of Physics, 59(4), 439. https://doi.org/10.15407/ujpe59.04.0439
Section
General problems of theoretical physics