Semiclassical approaches to atoms in external fields

  • Jörg Main
Conference paper
First Online:
Part of the Lecture Notes in Physics book series (LNP, volume 485)

Abstract

Applying closed-orbit theory to the recurrence spectra of atoms in magnetic fields, one can interpret most, but not all, structures semiclassically in terms of hydrogenic closed classical orbits. Here we also report semiclassical approaches to phenomena in hydrogenic and nonhydrogenic atoms which can not be explained within conventional closed orbit theory. In particular, we analyze various types of catastrophes at bifurcations of orbits and discuss the role of ghost orbits living in complex phase space. Unphysical divergences of semiclassical recurrence amplitudes near bifurcations are removed by uniform semiclassical approximations which are completely determined by classical parameters of the real orbits and complex ghosts. For nonhydrogenic atoms we investigate the scattering of trajectories at the ionic core and interpret unidentified structures in nonhydrogenic spectra in terms of families of core-scattered closed orbits.

Keywords

Bifurcation Point Closed Orbit Saddle Node Bifurcation Period Doubling Bifurcation Nonhydrogenic Atom 
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References

  1. Abramowitz M. and Stegun I. A. (1964): Handbook of Mathematical Functions, Natl. Bureau of StandardsGoogle Scholar
  2. Beims M. W. and Alber G. (1993): Phys. Rev. A 48, 3123CrossRefADSGoogle Scholar
  3. Berry M. V. and Mount K. E. (1972): Rep. Prog. Phys. 35, 315–397CrossRefADSGoogle Scholar
  4. Berry M. V. and Upstill C. (1980) in Progress in Optics, Vol. 18, ed. E. Wolf, North-Holland, p. 257–346Google Scholar
  5. Bogomolny E. B. (1989): Sov. Phys. JETP 69, 275Google Scholar
  6. Connor J. N. L. (1976): Mol. Phys. 31, 33CrossRefMathSciNetMATHADSGoogle Scholar
  7. Courtney M., Jiao H., Spellmeyer N., and Kleppner D. (1994): Phys. Rev. Lett. 73, 1340CrossRefADSGoogle Scholar
  8. Courtney M., Spellmeyer N., Jiao H., and Kleppner D. (1995): Phys. Rev. A 51, 3604CrossRefADSGoogle Scholar
  9. Courtney M., Jiao Hong, Spellmeyer N., Kleppner D., Gao J., and Delos J. B. (1995): Phys. Rev. Lett. 74, 1538CrossRefADSGoogle Scholar
  10. Delande D., Taylor K. T., Halley M. H., van der Veldt T., Wassen W., Hogervorst W. (1994): J. Phys. B 27, 2771CrossRefADSGoogle Scholar
  11. Dando P. A., Monteiro T. S., Delande D., and Taylor K. T. (1995): Phys. Rev. Lett. 74, 1099CrossRefADSGoogle Scholar
  12. Du M. L. and Delos J. B. (1988): Phys. Rev. A 38, 1896 and 1913CrossRefADSGoogle Scholar
  13. Edmonds A. R. (1970): J. Phys. (Paris) Colloq. C4 31, 71Google Scholar
  14. Friedrich H. and Wintgen D. (1989): Phys. Rep. 183, 37CrossRefADSMathSciNetGoogle Scholar
  15. Gao J., Delos J. B., and Baruch M. (1992): Phys. Rev. A 46, 1449CrossRefADSGoogle Scholar
  16. Gao J. and Delos J. B. (1992): ibid 46, 1455CrossRefADSGoogle Scholar
  17. Garton W. R. S. and Tomkins F. S. (1969): Astrophys. J. 158, 839CrossRefADSGoogle Scholar
  18. Gutzwiller M. (1990): Chaos in Classical and Quantum Mechanics (Springer, New York)MATHGoogle Scholar
  19. Holle A., Wiebusch G., Main J., Hager B., Rottke H., and Welge K. H. (1986a): Phys. Rev. Lett. 56, 2594CrossRefADSGoogle Scholar
  20. Holle A., Wiebusch G., Main J., Welge K. H., Zeller G., Ertl T., and Ruder H. (1986b): Z. Phys. D 5, 279CrossRefADSGoogle Scholar
  21. Holle A., Main J., Wiebusch G., Rottke H., and Welge K. H. (1988): Phys. Rev. Lett. 61, 161CrossRefADSGoogle Scholar
  22. Hüpper B., Main J., and Wunner G. (1995): Phys. Rev. Lett. 74, 2650 and (1996): Phys. Rev. A 93, 744CrossRefADSGoogle Scholar
  23. Kuś M., Haake F., and Delande D. (1993): Phys. Rev. Lett. 71, 2167CrossRefADSGoogle Scholar
  24. Main J., Wiebusch G., Holle A., and Welge K. H. (1986): Phys. Rev. Lett. 57, 2789CrossRefADSGoogle Scholar
  25. Main J., Wiebusch G., and Welge K. H. (1991): Comm. At. Mol. Phys. 25, 233–251Google Scholar
  26. Main J., Wiebusch G., Welge K. H., Shaw J., and Delos J. B. (1994): Phys. Rev. A 49, 847CrossRefADSMATHGoogle Scholar
  27. Main J. and Wunner G. (1997): Phys. Rev. A 55, 1743CrossRefADSGoogle Scholar
  28. Mao J. M. and Delos J. B. (1992): Phys. Rev. A 45, 1746CrossRefADSGoogle Scholar
  29. Monteiro T. S. and Wunner G. (1990): Phys. Rev. Lett. 65, 1100CrossRefADSGoogle Scholar
  30. Ozorio de Almeida A. M. and Hannay J. H. (1987): J. Phys. A 20, 5873CrossRefADSMathSciNetMATHGoogle Scholar
  31. Pearcey T. (1946): Phil. Mag. 37, 311MathSciNetGoogle Scholar
  32. Peters A. D., Jaffé C., and Delos J. B. (1994): Phys. Rev. Lett. 73, 2825CrossRefADSGoogle Scholar
  33. Poston T. and Steward I. N. (1978): Catastrophe theory and its applications (Pitman, London)MATHGoogle Scholar
  34. Raithel G., Held H., Marmet L., and Walther H. (1994): J. Phys. B 27, 2849CrossRefADSGoogle Scholar
  35. Sadovskií D. A., Show J. A., and Delos J. B. (1995): Phys. Rev. Lett. 75, 2120; Sadovskií D. A. and Delos J. B. (1996): preprint (submitted to Phys. Rev. E)CrossRefADSGoogle Scholar
  36. Stiefel E. L. and Scheifele G. (1971): Linear and Regular Celestial Mechanics (Springer)Google Scholar
  37. van der Veldt T., Vassen W., and Hogervorst W. (1993): Europhys. Lett. 21, 903ADSCrossRefGoogle Scholar
  38. Wintgen D., Holle A., Wiebusch G., Main J., Friedrich H., and Welge K. H. (1986): J. Phys. B 19, L557Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Jörg Main
    • 1
  1. 1.Institut für Theoretische Physik IRuhr-Universität BochumBochumGermany

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