Energy Terms and Stability Diagrams for the 2D Problem of Three Charged Particles
Keywords:energy terms, stability diagrams, Coulomb systems, variational approach, Born–Oppenheimer approximation, space dimensionality
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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