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Current issue   Ukr. J. Phys. 2014, Vol. 59, N 4, p. 439-451
https://doi.org/10.15407/ujpe59.04.0439    Paper

Simenog I.V., Mikhnyuk V.V., Bidasyuk Yu.M.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: ivsimenog@bitp.kiev.ua)

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

Section: General problems of theoretical physics
Language: Ukrainian

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 diagrams and certain anomalies arising in the 2D space are explained qualitatively in the framework of the Born–Oppenheimer adiabatic approximation. The asymptotics of energy terms at large distances obtained for an arbitrary space dimensionality are analyzed, and some approximation 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.

Key words: energy terms, stability diagrams, Coulomb systems, variational approach, Born– Oppenheimer approximation, space dimensionality.


  1. D.I. Bondar, V.Yu. Lazur, I.M. Shvab, and S. Halupka, Zh. Fiz. Dosl. 9, 304 (2005).
  2. D.I. Bondar, M. Gnatich, and V.Yu. Lazur, Teor. Mat. Fiz. 148, 269 (2006).
  3. T.K. Rebane and A.V. Filinskii, Yad. Fiz. 60, 1985 (1997).
  4. I.V. Simenog, Yu.M. Bidasyuk, M.V. Kuzmenko, and V.M.Hryapa, Ukr. Fiz. Zh. 54, 881 (2009).
  5. I.V. Simenog, V.V. Mikhnyuk, and M.V. Kuzmenko, Ukr. Fiz. Zh. 58, 290 (2013).
  6. M.A. Lampert, Phys. Rev. Lett. 1, 450 (1958).
  7. K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993).
  8. I.V. Komarov, L.I. Ponomarev, and S.Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions (Nauka, Moscow, 1976) (in Russian).
  9. L.V. Keldysh, Pis'ma Zh. Eksp. Teor. Fiz. 20, 716 (1979).
  10. Y. Suzuki and K. Varga, Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer, Berlin, 1998).
  11. P. Duclos, P. Stovicek, and M. Tusek, J. Phys. A 43, 474020 (2010).
  12. L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon Press, New York, 1977).
  13. D. Yiwu, Z. Guanghui, B. Chengguang et al., Sci. China A 39, 317 (1996).
  14. D.A. Kirzhnits and F.M. Pen'kov, Zh. Eksp. Teor. Fiz. ` 85, 80 (1983).
  15. L.V. Bruch and J.A. Tjon, Phys. Rev. A 19, 425 (1979).
  16. I.V. Simenog, preprint ITP-80-12E (Institute for Theoretical Physics, Kiev, 1980).