Journal of Applied Spectroscopy

, Volume 79, Issue 6, pp 962–968 | Cite as

Semiclassical asymmetric top in action–angle variables with binary stereodynamics

  • V. A. Tolkachev

A model is examined for the levels of an asymmetric, rigid top based on action-angle variables and including two basis forms for its rotational stereodynamics, in each of which the analytic expression for the axial action is quantized and does not require matrix diagonalization, is more transparent, and can be used for rapid computations. The maximum (on the order of the rotational constant) deviations of the model energies of the levels from their exact values occur in the separatrix between the basis forms and fall off by orders of magnitude with increasing distance from it. The model shows that the absolute magnitude of the anisotropy in the time averaged cross section of the dipole transition for tops with arbitrary orientation of the transition dipole moment differs greatly in the stereodynamic basis forms. In each of these the anisotropy depends more strongly on the pseudoquantum numbers than on the principal quantum number, and falls off as the latter decreases.


asymmetric top energy level semiclassical model action-angle variables rotational stereodynamics optical cross section anisotropy dipole cross section 


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  1. 1.
    S. M. Colwell, N. C. Handy, and W. H. Miller, J. Chem. Phys., 68, 745–749 (1978).ADSCrossRefGoogle Scholar
  2. 2.
    W. G. Harter and Ch. W. Patterson, J. Chem. Phys., 80, 4241–4261 (1984).ADSCrossRefGoogle Scholar
  3. 3.
    S. D. Augustin and H. Rabitz, J. Chem. Phys., 71, 745–749 (1979).MathSciNetCrossRefGoogle Scholar
  4. 4.
    V. M. Strel’chenya, Vestn. Leningradsk. gos. un-ta., No. 7, 105–108 (1983).Google Scholar
  5. 5.
    D. Huber, E. J. Heller, and W. G. Harter, J. Chem. Phys., 87, 1116–1129 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    V. I. Arnol’d, Usp. Mat. Nauk, 18, 13–39 (1963).Google Scholar
  7. 7.
    B. S. Ray, Zeitschr. Phys., 78, 74 (1932).ADSCrossRefGoogle Scholar
  8. 8.
    C. H. Townes and A. Schawlow, Microwave Spectroscopy, New York, London, Toronto, McGraw-Hill (1955).Google Scholar
  9. 9.
    G. W. King, R. M. Hainer, and P. C. Cross, J. Chem. Phys., 11, 27–42 (1943).ADSCrossRefGoogle Scholar
  10. 10.
    Yu. A. Sadov, Prikl. Mat. Mekh., 5, 962–964 (1970).Google Scholar
  11. 11.
    Yu. A. Arkhangel’skii, Analytic Dynamics of Solids [in Russian], Nauka, Moscow (1970).Google Scholar
  12. 12.
    V. A. Tolkachev and I. N. Kukhto, Opt. Spektrosk., 78, 791–795 (1995).Google Scholar
  13. 13.
    V. A. Tolkachev, Opt. Spektrosk., 79, 601–605 (1995).Google Scholar
  14. 14.
    V. A. Tolkachev, Zh. Prikl. Spektrosk., 66, 758–764 (1999).Google Scholar
  15. 15.
    M. F. Gelin, V. A. Tolkachev, and A. P. Blokhin, Chem. Phys., 255, 111–122 (2000).CrossRefGoogle Scholar
  16. 16.
    M. S. Child, J. Mol. Spectrosk., 53, 280–301 (1974).ADSCrossRefGoogle Scholar
  17. 17.
    V. A. Tolkachev, Zh. Prikl. Spektrosk., 65, 843–849 (1998).Google Scholar
  18. 18.
    V. A. Tolkachev and S. A. Polubisok, Spectr. Lett., 28, 441–450 (1995).ADSCrossRefGoogle Scholar
  19. 19.
    V. A. Povedailo, S. A. Polubisok, and V. A. Tolkachev, Opt. Spektrosk., 80, 70–74 (1996).ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.B. I. Stepanov Institute of PhysicsNational Academy of Sciences of BelarusMinskBelarus

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