The European Physical Journal D

, Volume 42, Issue 1, pp 1–10 | Cite as

Quadruply excited beryllium-like atoms – a semiclassical model

  • N. SimonovićEmail author
  • P. Grujić
Atomic Physics


The semiclassical spectrum of quadruply highly excited four-electron atomic systems has been calculated for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the circular skeleton orbit approximation, as used in a previous calculation for the triply excited three-electron systems. The full dynamical analysis is carried out within the Hamiltonian theory, accounting for the inertial effects and the complete coupling between different degrees of freedom. Here we present numerical results for energy spectrum of the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation.


31.10.+z Theory of electronic structure, electronic transitions, and chemical binding 31.15.Gy Semiclassical methods 31.25.Jf Electron correlation calculations for atoms and ions: excited states 


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  1. S. Hasegawa, F. Yoshida, L. Matsuoka, F. Koike, S. Fritzsche, S. Obara, Y. Azuma, T. Nagata, Phys. Rev. Lett. 97, 023001 (2006) CrossRefADSGoogle Scholar
  2. H. Nagaoka, Bull. Math. Phys. Soc. Tokyo 2, 140 (1904) Google Scholar
  3. J.W. Nicholson, Month. Not. Roy. Astr. Soc. 72, 49 (1912) ADSGoogle Scholar
  4. Bao Cheng-guang, Phys. Rev. A 47, 1752 (1993) CrossRefADSGoogle Scholar
  5. Bao Chengguang, Duan Yiwu, Phys. Rev. A 49, 818 (1994) CrossRefADSGoogle Scholar
  6. C.G. Bao, J. Phys. B 25, 3725 (1992) CrossRefGoogle Scholar
  7. C.G. Bao, Phys. Lett. A 250, 123 (1998) CrossRefADSGoogle Scholar
  8. C. Nicolaides, N. Pianos, Y. Komninos, Phys. Rev. A 48, 3578 (1993) CrossRefADSGoogle Scholar
  9. Y. Komninos, C. Nicolaides, Phys. Rev. A 50, 3782 (1994). CrossRefADSGoogle Scholar
  10. L. B. Madsen, J. Phys. B. 36, R223 (2003) Google Scholar
  11. P. Grujić, Eur. Phys. J. D 6, 441 (1999) CrossRefADSGoogle Scholar
  12. M. Poulsen, P. Madsen, Phys. Rev. A 72, 042501 (2005) CrossRefADSGoogle Scholar
  13. M. Poulsen, P. Madsen, Phys. Rev. A 71, 062502 (2005) CrossRefADSGoogle Scholar
  14. T. Morishita, C.D. Lin, Phys. Rev. A 71, 012504 (2005) CrossRefADSGoogle Scholar
  15. M. Walter, J.S. Briggs, J.M. Feagin, J. Phys. B. 33, 2907 (2000) CrossRefADSGoogle Scholar
  16. L.B. Madsen, K. Molmer, Phys. Rev. A 64, 060501(R) (2001) CrossRefADSGoogle Scholar
  17. L.B. Madsen, K. Molmer, Phys. Rev. A 65, 022506 (2002) CrossRefADSMathSciNetGoogle Scholar
  18. P. Grujić, J. Phys. B 21, 63 (1988) CrossRefADSGoogle Scholar
  19. N. Simonović, Phys. Rev. A 50, 4390 (1994) CrossRefADSGoogle Scholar
  20. N. Simonović, M. Predojević, V. Panković, P. Grujić (unpublished) Google Scholar
  21. S. Cvejanović, Z.D. Dohčević, P. Grujić, J. Phys. B 23, L167 (1990) Google Scholar
  22. P. Grujić, X Eur. Symp. Dyn. Few-Body Sys., Balatonfuüred, 1986, edited by Gy. Bencze, P. Doleshall, J. Reval (Budapest, 1986), pp. 253–281 Google Scholar
  23. N. Simonović, P. Grujić, in Adv. Math. Study of Atomic Doubly-Excited States, Medellin, Colombia, 1995, edited by J. Mahecha, J. Botero (Universidad de Antioquia, 1996), pp. 107–153 Google Scholar
  24. Y. Kuchiev, V. Ostrovsky, Phys. Rev. A 58, 321 (1998) CrossRefADSGoogle Scholar
  25. G.H. Wannier, Phys. Rev. 90, 817 (1953) zbMATHCrossRefADSGoogle Scholar
  26. N. Norcliffe, in Case Studies in Atomic Physics, Vol. 4, edited by W. McDaniel, M.R.C. McDowell (North-Holland, Amsterdam, 1975), pp. 45-55 Google Scholar
  27. A.F. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, New York, 1992) Google Scholar
  28. L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965) Google Scholar
  29. P. Grujić, J. Phys. B 16, 2567 (1983) CrossRefADSGoogle Scholar
  30. H. Goldstein, Classical Mechanics (Addison-Wesley, London, 1981) Google Scholar
  31. I.M. Gel'fand, Lectures in Linear Algebra (Nauka, Moscow, 1966) (in Russian) Google Scholar
  32. N.S. Simonović, J. Chem. Phys. 124, 014108 (2006) CrossRefADSGoogle Scholar
  33. N.S. Simonović, J.M. Rost, Classical Lifetimes for Quantum Resonances, Twenty Second International Conference on Photonic, Electronic, and Atomic Collisions (XXII ICPEAC), Abstracts of Contributed Papers, edited by S. Datz, M.E. Bannister, H.F. Krause, L.H. Saddiq, D.R. Schultz, C.R. Vane (Rinton Press, 2001), p. 212 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institute of PhysicsBelgradeSerbia

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