On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems

Journal of Chemical Physics

Volumn 124, Issue 14, 2006, Pages

  Takahashi, Satoshi ^a   Takatsuka, Kazuo ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ELECTRONS; HYDROGEN; MOLECULAR PHYSICS; POSITIVE IONS; PROTONS;

ANTIPROTON; BORN-OPPENHEIMER APPROXIMATION; HYDROGEN MOLECULE CATION;

HIGH ENERGY PHYSICS;

EID: 34547926518     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2173997     Document Type: Article

References (73)

1. M. Born and R. Oppenheimer, Ann. Phys. 84, 457 (1927).
2. M. S. Child, Molecular Collison Theory (Academic, New York, 1974);
3. M. S. Child, Semiclassical Mechanics with Molecular Approximations (Claredon, Oxford, 1991).
4. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).
5. J. B. Delos, Rev. Mod. Phys. 53, 287 (1981).
6. H. Nakamura, Nonadiabatic Transition (World Scientific, Singapore, 2002).
7. A. W. Jasper, B. K. Kendrick, C. A. Mead, and D. G. Truhlar, in Modern Trends in Chemical Reaction Dynamics, edited by, X. Yang, and, K. Liu, (World Scientific, Singapore, 2004), p. 329.
8. Y. Arasaki, K. Takatsuka, K. Wang, and V. McKoy, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.90.248303 90, 248303 (2003); Y. Arasaki, K. Takatsuka, K. Wang, and V. McKoy, J. Chem. Phys. 119, 7913 (2003).
9. Y. Arasaki, K. Takatsuka, K. Wang, and V. McKoy, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.90.248303 90, 248303 (2003); Y. Arasaki, K. Takatsuka, K. Wang, and V. McKoy, J. Chem. Phys. 119, 7913 (2003).
10. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, C. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Nature (London) 414, 509 (2001).
11. H. Niikura, F. Lágará, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, Nature (London) 417, 917 (2002).
12. A. Baltuška, Th. Udem, M. Uiberacker, et al., Nature (London) 421, 611 (2003).
13. M. Amano and K. Takatsuka, J. Chem. Phys. 122, 084113 (2005).
14. K. Yamanouchi, Science 295, 1659 (2002).
15. K. Yagi and K. Takatsuka, J. Chem. Phys. 123, 224103 (2005).
16. K. Sakimoto, Phys. Rev. A 71, 062704 (2005).
17. K. Sakimoto, Phys. Rev. A 69, 042710 (2004).
18. K. Sakimoto, J. Phys. B 37, 2255 (2004).
19. S. Kais and Q. Shi, Phys. Rev. A 62, 060502 (2000).
20. O. I. Kartavtsev, A. V. Malykh, and V. P. Permyakov, Phys. Rev. A 70, 022504 (2004).
21. S. Kilic, J.-P. Karr, and L. Hilico, Phys. Rev. A 70, 042506 (2004).
22. E. Lindroth, J. Wallenius, and S. Jonsell, Phys. Rev. A 68, 032502 (2003).
23. M. R. Eskandari and R. Gheisari, Phys. Rev. A 70, 032505 (2004).
24. D. Bakalov, K. Bakalova, V. Korobov, H. J. Monkhorst, and I. Shimamura, Phys. Rev. A 57, 3370 (1998).
25. M. R. Harston, S. Hara, Y. Kino, I. Shimamura, H. Sato, and M. Kamimura, Phys. Rev. A 56, 2685 (1997).
26. Y. Kino, M. R. Harston, I. Shimamura, E. A. F. Armour, and M. Kamimura, Phys. Rev. A 52, 870 (1995).
27. I. Shimamura, Phys. Rev. A 40, 4863 (1989).
28. M. C. Fujiwara, A. Adamczak, J. M. Bailey, et al., Phys. Rev. Lett. 85, 1642 (2000).
29. T. A. Porcelli, A. Adamczak, J. M. Bailey, et al., Phys. Rev. Lett. 86, 3763 (2001).
30. N. Kawamura, K. Nagamine, T. Matsuzaki, et al., Phys. Rev. Lett. 90, 043401 (2003).
31. A. Toyoda, K. Ishida, K. Shimomura, S. N. Nakamura, Y. Matsuda, W. Higemoto, T. Matsuzaki, and K. Nagamine, Phys. Rev. Lett. 90, 243401 (2003).
32. N. Kuroda, H. A. Torii, K. Yoshiki Franzen, et al., Phys. Rev. Lett. 94, 023401 (2005).
33. A. K. Bhatia, Phys. Rev. A 58, 2787 (1998).
34. V. I. Korobov, Phys. Rev. A 61, 064503 (2000).
35. D. M. Bishop, A. M. Frolov, and V. H. Smith, Jr., Phys. Rev. A 51, 3636 (1995).
36. A. M. Frolov, Phys. Rev. A 57, 2436 (1998).
37. A. M. Frolov, Phys. Rev. A 59, 4270 (1999).
38. A. M. Frolov, Phys. Rev. A 67, 064501 (2003).
39. A. M. Frolov, Phys. Rev. E 64, 036704 (2001).
40. K. Sohlberg, R. E. Tuzun, B. G. Sumpter, and D. W. Noid, Phys. Rev. A 57, 906 (1998).
41. Y. Duan, C. Browne, and J.-M. Yuan, Phys. Rev. A 59, 238 (1999).
42. G. Tanner, K. Richter, and J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000).
43. M. P. Strand and W. P. Reinhardt, J. Chem. Phys. 70, 3812 (1979).
44. J. Müller, J. Burgdörfer, and D. W. Noid, J. Chem. Phys. 103, 4985 (1995).
45. M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989); M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990); L. E. Reichl, The Transition to Chaos (Springer, New York, 1992); K. Nakamura, Quantum Chaos (Cambridge University Press, Cambridge, 1993).
46. M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989); M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990); L. E. Reichl, The Transition to Chaos (Springer, New York, 1992); K. Nakamura, Quantum Chaos (Cambridge University Press, Cambridge, 1993).
47. M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989); M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990); L. E. Reichl, The Transition to Chaos (Springer, New York, 1992); K. Nakamura, Quantum Chaos (Cambridge University Press, Cambridge, 1993).
48. M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989); M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990); L. E. Reichl, The Transition to Chaos (Springer, New York, 1992); K. Nakamura, Quantum Chaos (Cambridge University Press, Cambridge, 1993).
49. K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003).
50. S. Takahashi and K. Takatsuka, Phys. Rev. A 70, 052103 (2004).
51. P. Kustaanheimo and E. Stiefel, J. Reine Angew. Math. 218, 204 (1965).
52. S. J. Aarseth and K. Zare, Celest. Mech. 10, 185 (1974).
53. L. D. Landau and E. M. Lifshitz, Mechanics (Addison-Wesley, New York, 1960).
54. H. Ushiyama and K. Takatsuka, J. Chem. Phys. 122, 224112 (2005).
55. A. Inoue-Ushiyama and K. Takatsuka, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.78.1404 78, 1404 (1997); A. Inoue-Ushiyama and K. Takatsuka, Phys. Rev. A 59, 3256 (1999).
56. A. Inoue-Ushiyama and K. Takatsuka, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.78.1404 78, 1404 (1997); A. Inoue-Ushiyama and K. Takatsuka, Phys. Rev. A 59, 3256 (1999).
57. W. H. Miller, J. Chem. Phys. 53, 3578 (1970).
58. W. H. Miller, J. Phys. Chem. A 105, 2942 (2001).
59. Y. Zhao and W. H. Miller, J. Chem. Phys. 117, 9605 (2002).
60. E. J. Heller, J. Chem. Phys. 94, 2723 (1991).
61. M. A. Sepúlveda and E. J. Heller, J. Chem. Phys. 0021-9606 10.1063/1.468227 101, 8004 (1994); M. A. Sepúlveda and F. Grossmann, Adv. Chem. Phys. 96, 191 (1996).
62. M. A. Sepúlveda and E. J. Heller, J. Chem. Phys. 0021-9606 10.1063/1.468227 101, 8004 (1994); M. A. Sepúlveda and F. Grossmann, Adv. Chem. Phys. 96, 191 (1996).
63. G. Campolieti and P. Brumer, Phys. Rev. A 1050-2947 10.1103/PhysRevA.50. 997 50, 997 (1994); D. Provost and P. Brumer, Phys. Rev. Lett. 74, 250 (1995).
64. G. Campolieti and P. Brumer, Phys. Rev. A 1050-2947 10.1103/PhysRevA.50. 997 50, 997 (1994); D. Provost and P. Brumer, Phys. Rev. Lett. 74, 250 (1995).
65. K. G. Kay, J. Chem. Phys. 0021-9606 10.1063/1.466320 100, 4377 (1994); K. G. Kay, J. Chem. Phys. 100, 4432 (1994).
66. K. G. Kay, J. Chem. Phys. 0021-9606 10.1063/1.466320 100, 4377 (1994); K. G. Kay, J. Chem. Phys. 100, 4432 (1994).
67. H. Goldstein, Classical Mechanics (Addison-Wesley, New York, 1980).
68. K. Takatsuka, Phys. Rev. E 64, 016224 (2001).
69. S. Takahashi and K. Takatsuka, Phys. Rev. A 69, 022110 (2004).
70. H. Ushiyama, Y. Arasaki, and K. Takatsuka, Chem. Phys. Lett. 346, 169 (2001).
71. T. Yanao and K. Takatsuka, J. Chem. Phys. 120, 8924 (2004).
72. M. Klein, A. Martinez, R. Seiler, and X. P. Wang, Commun. Math. Phys. 143, 607 (1992).
73. G. A. Hagedorn, Commun. Math. Phys. 116, 23 (1988).