The Averaged Dynamics of the Hydrogen Atom in Crossed Electric and Magnetic Fields as a Perturbed Kepler Problem

Foundations of Physics

Volumn 31, Issue 2, 2001, Pages 283-326

  Berglund, Nils ^a,b   Uzer, Turgay ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035616475     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017542620404     Document Type: Article

References (53)

1. A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. II (Benjamin Reading, 1975).
2. M. Born, The Mechanics of the Atom (Bell, London, 1927).
3. P. A. Braun and E. A. Solov'ev, "The Stark effect for a hydrogen atom in a magnetic field," Sov. Phys. JETP 59, 38-46 (1984).
4. S. L. Coffey, A. Deprit, B. Miller, and C. A. Williams, "The quadratic Zeeman effect in moderately strong magnetic fields," Ann. N.Y. Acad. Sci. 497, 22-36 (1987).
5. J.-P. Connerade, Highly Excited Atoms (University Press, Cambridge, 1998).
6. J.-P. Connerade, M.-S. Zhan, J. Rao, and K. T. Taylor, "Strontium spectra in crossed electric and magnetic fields," J. Phys. B 32, 2351-2360 (1999).
7. R. J. Damburg and V. V. Kolosov, "Theoretical studies of hydrogen Rydberg atoms in electric fields," in Rydberg States of Atoms and Molecules, R. F. Stebbings and F. B. Dunning, eds. (University Press, Cambridge, 1983).
8. D. Delande and J.-C. Gay, "Quantum chaos and the hydrogen atom in strong magnetic fields," in The Hydrogen Atom, G. F. Bassani, M. Inguscio, and T. W. Hänsch, eds. (Springer, Berlin, 1989).
9. J. B. Delos, S. K. Knudson, and D. W. Noid, "Highly excited states of a hydrogen atom in a strong magnetic field," Phys. Rev. A 28, 7-21 (1983).
10. A. Deprit, "Canonical transformations depending on a small parameter," Celestial Mech. 1, 12-30 (1969).
11. A. Deprit and C. A. Williams, "The Lissajous transformation. IV. Delaunay and Lissajous variables," Celestial Mech. Dynam. Astronom. 51, 271-280 (1991).
12. M. M. Dignam and J. E. Sipe, "Semiconductor superlattice exciton states in crossed electric and magnetic fields," Phys. Rev. B 45, 6819-6838 (1992).
13. P. S. Epstein, Ann. Phys. 50, 489 (1916); 58, 553 (1919).
14. P. S. Epstein, Ann. Phys. 50, 489 (1916); 58, 553 (1919).
15. D. Farrelly, "Motional Stark effect on Rydberg states in crossed electric and magnetic fields," Phys. Lett. A 191, 265-274 (1994).
16. D. Farrelly, T. Uzer, P. E. Raines, J. P. Skelton, and J. A. Milligan, "Electronic structure of Rydberg atoms in parallel electric and magnetic fields," Phys. Rev. A 45, 4738-4751 (1992).
17. E. Flöthmann and K. H. Welge, "Crossed-field hydrogen atom and the three-body Sun-Earth-Moon problem," Phys. Rev. A 54, 1884-1888 (1996).
18. H. Friedrich and D. Wintgen, "The hydrogen atom in a uniform magnetic field - an example of chaos," Phys. Rep. 183, 37-79 (1989).
19. W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 839 (1969).
20. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
21. M. C. Gutzwiller, "Moon-Earth-Sun: The oldest three-body problem," Rev. Mod. Phys. 70, 589-639 (1998).
22. H. Hasegawa, M. Robnik, and G. Wunner, "Classical and quantal chaos in the diamagnetic Kepler problem," Progr. Theoret. Phys. Suppl. 98, 198-286 (1989).
23. J. Henrard, "On a perturbation theory using Lie transforms," Celestial Mech. 3, 107-120 (1970).
24. C. Jaffé, D. F. Farrelly, and T. Uzer, "Transition state in atomic physics," Phys. Rev. A 60, 3338-3850 (1999).
25. B. R. Johnson, J. D. Hirschfelder, and K. H. Yang, "Interaction of atoms, molecules, and ions with constant electric and magnetic fields," Rev. Mod. Phys. 55, 109 (1983).
26. P. M. Koch and K. A. H. van Leeuwen, "The importance of resonances in microwave 'ionization' of excited hydrogen atoms," Phys. Rep. 255, 289-406 (1995).
27. J. Laskar, "The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones," Icarus 88, 266-291 (1990).
28. J. Laskar, "Large scale chaos and marginal stability in the solar system," Celestial Mech. Dynam. Astronom. 64, 115-162 (1996).
29. J. Laskar and P. Robutel, "The chaotic obliquity of the planets," Nature 361, 608-612 (1993).
30. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992).
31. J. Main and G. Wunner, "Ericson fluctuations in the chaotic ionization of the hydrogen atom in crossed magnetic and electric fields," Phys. Rev. Lett. 69, 586-589 (1992).
32. G. Mathys, "The observation of magnetic fields in nondegenerate stars," Fundam. Cosm. Phys. 13, 143-308 (1989).
33. F. Mignard, "Radiation pressure and dust particle dynamics," Icarus 49, 347-366 (1982).
34. C. Neumann et al., "Symmetry breaking in crossed magnetic and electric fields," Phys. Rev. Lett. 78, 4705-4708 (1997).
35. P. J. Redmond, "Generalization of the Runge-Lenz vector in the presence of an electric field," Phys. Rev. B 133, 1352-1353 (1963).
36. G. Raithel, M. Fauth, and H. Walther, "Quasi-Landau resonances in the spectra of rubidium Rydberg atoms in crossed electric and magnetic fields," Phys. Rev. A 44, 1898-1909 (1991).
37. G. Raithel, M. Fauth, and H. Walther, "Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments," Phys. Rev. A 47, 419-440 (1993).
38. J. Rao and K. T. Taylor, "Atoms in crossed fields: Calculations for barium and hydrogen," J. Phys. B 30, 3627-3645 (1997).
39. P. Schmelcher, "Delocalization of excitons in a magnetic field," Phys. Rev. B 48, 14642-14645 (1993).
40. K. Schwarzschild, Sitzungsber. Berl Akad. (1916), p. 548.
41. E. A. Solov'ev, "Second-order perturbation theory for the hydrogen atom in crossed electric and magnetic fields," Sov. Phys. JETP 58, 63-66 (1983).
42. J. L. Tennyson, M. A. Lieberman, and A. J. Lichtenberg, "Diffusion in near-integrable Hamiltonian systems with three degrees of freedom," in Nonlinear Dynamics and the Beam-Beam Interaction, M. Month and J. C. Herrera, eds. (Am. Inst. Phys. Conference Proceedings No. 57 New York, 1979), pp. 272-301.
43. T. Uzer et al., "Celestial mechanics on a microscopic scale," Science 253, 42-48 (1991).
44. T. Uzer and D. Farrelly, "Threshold ionization dynamics of the hydrogen atom in crossed electric and magnetic fields," Phys. Rev. A 52, R2501-R2504 (1995).
45. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems (Springer, Berlin, 1996).
46. J. von Milczewski, G. H. F. Diercksen, and T. Uzer, "Intramanifold chaos in Rydberg atoms in external fields," Phys. Rev. Lett. 73, 2428-2431 (1994).
47. J. von Milczewski, G. H. F. Diercksen, and T. Uzer, "Computation of the Arnol'd Web for the hydrogen atom in crossed electric and magnetic fields," Phys. Rev. Lett. 76, 2890-2893 (1996).
48. J. von Milczewski, D. Farelly, and T. Uzer, "l/r dynamics in external fields: 2D or 3D?," Phys. Rev. Lett. 78, 2349-2352 (1997).
49. J. von Milczewski, D. Farelly, and T. Uzer, "Role of the atomic Coulomb center in ionization and periodic orbit selection," Phys. Rev. A 56, 657-670 (1997).
50. J. von Milczewski and T. Uzer, "Chaos and order in crossed fields," Phys. Rev. E 55, 6540-6551 (1997).
51. J. von Milczewski and T. Uzer, "Canonical perturbation treatment of a Rydberg electron in combined electric and magnetic fields," Phys. Rev. A 56, 220-231 (1997).
52. G. Wiebusch et al., "Hydrogen atom in crossed magnetic and electric fields," Phys. Rev. Lett. 62, 2821-2824 (1989).
53. J. A. Yeazell et al., "Observation of wave packet motion along quasi-Landau orbits," Phys. Rev. Lett. 70, 2884-2887 (1993).