Classical theory of the chaotic ionization of highly excited helium atoms

American Journal of Physics

Volumn 64, Issue 8, 1996, Pages 1013-1023

  Sanders, M M ^b   Jensen, R V ^a  

^a WESLEYAN UNIVERSITY   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030520955     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18320     Document Type: Article

References (28)

1. P. M. Koch and K. A. H. van Leeuwen, "The importance of resonances in microwave 'ionization' of excited hydrogen atoms," Phys. Rep. 255, 289-403 (1995), and references therein.
2. R. V. Jensen, S. M. Susskind, and M. M. Sanders, "Chaotic ionization of highly excited hydrogen atoms: Comparison of classical and quantum theory with experiment," Phys. Rep. 201, 1-56 (1991), and references therein.
3. M. M. Sanders and R. V. Jensen, "Classical theory of the chaotic ionization of highly excited hydrogen atoms," Am. J. Phys. 64, 21-31 (1996).
4. D. R. Mariani, W. van de Water, P. M. Koch, and T. Bergeman, "Observation and quasistatic analysis of structure in the microwave ionization of highly excited helium atoms," Phys. Rev. Lett. 50, 1261-1264 (1983).
5. David R. Mariani, "The Ionization of Hydrogen and Helium Atoms by Static and Microwave Electric Fields," Ph.D. thesis, Yale University, New Haven, Connecticut, December 1983.
6. W. van de Water, S. Yoakum, K. A. H. van Leeuwen, B. E. Sauer, L. Moorman, E. J. Galvez, D. R. Mariani, and P. M. Koch, "Microwave multiphoton ionization and excitation of helium Rydberg atoms," Phys. Rev. A 42, 573-590 (1990).
7. H. Bethe, "Quantenmechanik der Ein-und Zwei-Electronenprobleme," in Handbuch der Physik, Vol. 24 (Springer-Verlag, Berlin, 1933), pp. 342-343.
8. T. P. Hezel, C. E. Burkhardt, M. Ciocca, L.-W. He, and J. J. Leventhal, "Classical view of the properties of Rydberg atoms: Application of the correspondence principle," Am. J. Phys. 60, 329-335 (1992).
9. V. I. Arnold, Mathematical Methods of Classical Mechanics, (Springer-Verlag, New York, 1979).
10. A. J. Lichtenberg and M. A. Lieberman, "Regular and Stochastic Motion," in Applied Mathematical Sciences, (Springer-Verlag, New York, 1983), Vol. 38.
11. I. C. Percival, "Semiclassical theory of bound states," in Advances in Chemical Physics edited by I. Prigogine and Stuart A. Rice (Wiley, New York, 1977), Vol. 26, pp. 1-61.
12. V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Reidel, New York, 1981).
13. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980), 2nd ed.
14. Simpler mean field models have recently been proposed for studying the classical dynamics of nonhydrogenic atoms in strong fields in P. A. Dando, T. S. Monteiro, D. Delande, and K. T. Taylor, "Beyond periodic orbits: An example in nonhydrogenic atoms," Phys. Rev. Lett. 74, 1099-1102 (1995) and B. Hupper, J. Main, and G. Wunner, "Photoabsorption of nonhydrogenic Rydberg atoms in a magnetic field: Effects of core-scattered classical orbits," Phys. Rev. Lett. 74, 2650-2653 (1995). In these cases a simple trial shielding potential with adjustable parameters is chosen for the best fit to the lowest quantum defects. The success of this approach suggests, that for some applications, a detailed model of the nonhydrogenic core potential is not essential, any short range potential that breaks the Coulomb symmetry may suffice.
15. Simpler mean field models have recently been proposed for studying the classical dynamics of nonhydrogenic atoms in strong fields in P. A. Dando, T. S. Monteiro, D. Delande, and K. T. Taylor, "Beyond periodic orbits: An example in nonhydrogenic atoms," Phys. Rev. Lett. 74, 1099-1102 (1995) and B. Hupper, J. Main, and G. Wunner, "Photoabsorption of nonhydrogenic Rydberg atoms in a magnetic field: Effects of core-scattered classical orbits," Phys. Rev. Lett. 74, 2650-2653 (1995). In these cases a simple trial shielding potential with adjustable parameters is chosen for the best fit to the lowest quantum defects. The success of this approach suggests, that for some applications, a detailed model of the nonhydrogenic core potential is not essential, any short range potential that breaks the Coulomb symmetry may suffice.
16. R. J. Damburg and V. V. Kolosov, "Theoretical studies of hydrogen Rydberg atoms in electric fields," in Rydberg States of Atoms and Molecules, edited by F. B. Dunning and R. F. Stebbings, (Cambridge U.P., Cambridge, 1983), pp. 31-69.
17. M. Born, The Mechanics of the Atom (Frederick Ungar, New York, 1960). From lectures delivered at Göttingen, 1923-1924.
18. D. Banks and J. G. Leopold, "Ionization of highly excited atoms by electric fields. I. Classical theory of the critical electric field for hydrogenic ions," J. Phys. B, 11, 37-46 (1978).
19. D. Banks and J. G. Leopold, "Ionization of highly excited atoms by electric fields. II. Classical theory of Stark effect," J. Phys. B 11, 2833-2843 (1978).
20. T. P. Hezel, C. E. Burkhardt, M. Ciocca, and J. J. Leventhal, "Classical view of the Stark effect in hydrogen atoms," Am. J. Phys. 60, 324-328 (1992).
21. M. M. Sanders, "Chaotic Ionization of One and Two Electron Atoms," Ph.D. thesis, Yale University, New Haven, Connecticut, December 1991.
22. A. Sommerfeld, Atomic Structure and Spectral Lines (Methuen, London, 1922), translated by Henry L. Brose.
23. P. Pillet, H. B. van Linden van den Heuvel, W. W. Smith, R. Kachru, N. H. Tran, and T. F. Gallagher, "Microwave ionization of Na Rydberg atoms," Phys. Rev. A 30, 281-294 (1984).
24. T. F. Gallagher, Rydberg Atoms, (Cambridge U.P., New York, 1994), pp. 164-168.
25. E. L. Stiefel and G. Schiefele, Linear and Regular Celestial Mechanics (Springer-Verlag, New York, 1971).
26. F. H. J. Cornish, "The hydrogen atom and the four-dimensional harmonic oscillator" J. Phys. A 17, 323-327 (1984); "Kepler orbits and the harmonic oscillator," J. Phys. A 17, 2191-2197 (1984).
27. F. H. J. Cornish, "The hydrogen atom and the four-dimensional harmonic oscillator" J. Phys. A 17, 323-327 (1984); "Kepler orbits and the harmonic oscillator," J. Phys. A 17, 2191-2197 (1984).
28. O. Rath and D. Richards, "The quadratic Zeeman effect," J. Phys. B 21, 555-571 (1988).