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Discrete semiclassical methods in the theory of Rydberg atoms in external fields

P. A. Braun

P. A. Braun

  • Department of Theoretical Physics, Institute of Physics, St. Petersburg University, St. Petersburg 198 904, Russia

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Rev. Mod. Phys. 65, 115 – Published 1 January, 1993

DOI: https://doi.org/10.1103/RevModPhys.65.115

Abstract

The properties of the WKB method in the discrete representation are reviewed. The method provides the eigenvalues and the eigenvectors of the three-term recursion relations or, which is the same thing, the tridiagonal band matrices. Applications of the method to the splitting of the Rydberg atom levels in the external electric and magnetic fields are considered. Analytical treatment is given to the problem of the oscillator strength distribution in the quadratic Zeeman and the Stark-Zeeman spectra. In the case of the nonhydrogenic Rydberg atoms, the effect of the core on the pattern of the splitting is studied. Certain alternative applications of the discrete WKB method are considered in brief (the quasienergy spectra of nonlinear oscillators in resonant fields, rotational molecular spectra, calculation of infinite continued fractions).

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References (169)

  1. Adamov, M. N., V. K. Kagan, and T. K. Rebane, 1964, Vestnik Leningradskogo Universiteta 10, 31
  2. Alhassid, Y., E. A. Hinds, and D. Meschede, 1987, Phys. Rev. Lett. 59, 1545
  3. Arnold, V. I., 1974, Mathematical Methods of Classical Mechanics (Nauka, 1974). In Russian
  4. Baldacchini, G., S. Marchatti, and V. Montelatici, 1982, J. Mol. Spectrosc. 91, 80
  5. Barton, G., 1987, Proc. R. Soc. London Ser. A 410, 175
  6. Barton, G., 1988, Phys. Scr. 21, 11
  7. Barton, G.Bassani, G. F., M. Inguscio, and T. W. Hänsch, 1989, Eds., The Hydrogen Atom (Springer, Berlin)
  8. Baz, A. I., Ya. B. Zel'dovich, and A. M. Perelomov, 1971, Scattering, Reactions, and Decays in Nonrelativistic Quantum Mechanics (Nauka, Moscow). In Russian
  9. Belov, A. A., A. P. Kazantsev, D. V. Khveschenko, and V. L. Pokrovsky, 1985, J. Phys. B 18, 4683
  10. Belov, A. A., Yu. E. Lozovik, and V. L. Pokrovsky, 1989, Zh. Eksp. Teor. Fiz. 96, 552 [Sov. Phys.—JETP 69, 312 (1989)]
  11. Bender, C. W., G. S. Guralnik, and M. Silverstone, 1979, Phys. Rev. D 20, 2583
  12. Beterov, I. M., and P. B. Lerner, 1989, Usp. Fiz. Nauk 159, 665 [Sov. Phys. Usp. 32, 1084 (1989)]
  13. Bethe, H. A., and E. E. Salpeter, 1957, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin)
  14. Bivona, S., W. Schweizer, P. F. O'Mahony, and K. T. Taylor, 1988, J. Phys. B 21, L617
  15. Bogomolny, E. B., 1989, Zh. Eksp. Teor. Fiz. 96, 487 [Sov. Phys. JETP 69, 275 (1989)]
  16. Born, M., 1960, Mechanics of the Atom (Ungar, New York)
  17. Braun, P. A., 1978, Teor. Mat. Fizika 37, 355 [Sov. Phys. Theor. Math. Phys. 37, 1070 (1978)]
  18. Braun, P. A., 1979, Teor. Mat. Fizika 41, 336 [Sov. Phys. Theor. Math. Phys. 41, 1060 (1979)]
  19. Braun, P. A., 1981, in Problems of the Quantum Theory of Atoms and Molecules, edited by I. V. Abarenkov, No. 2 (Leningrad University), p. 110
  20. Braun, P. A., 1983a, Zh. Eksp. Teor. Fiz. 84, 850 [Sov. Phys. JETP 57, 492 (1983)]
  21. Braun, P. A., 1983b, J. Phys. B 16, 4323
  22. Braun, P. A., 1984, doctoral thesis (Leningrad University)
  23. Braun, P. A., 1985, J. Phys. B 18, 4183
  24. Braun, P. A., 1986, Opt. Spectrosk. 61, 253 [Opt. Spectrosc. (USSR) 61, 164 (1986)]
  25. Braun, P. A., 1989a, Opt. Spectrosk. 66, 57 [Opt. Spectrosc. (USSR) 66, 32 (1989)]
  26. Braun, P. A., 1989b, Zh. Eksp. Teor. Fiz. 96, 1650 [Sov. Phys. JETP 69, 934 (1989)]
  27. Braun, P. A., 1990a, Opt. Spectrosk. 69, 252
  28. Braun, P. A., 1990b, Opt. Spectrosk. 69, 1208
  29. Braun, P. A., 1990c, J. Phys. B 23, 3083
  30. Braun, P. A., 1991a, J. Phys. B 24, 399
  31. Braun, P. A., 1991b, J. Phys. B 24, 2313
  32. Braun, P. A., and A. A. Kiselev, 1983, Introduction to Theory of Molecular Spectra (Leningrad University, Leningrad), in Russian
  33. Braun, P. A., and G. P. Miroshnichenko, 1980, Opt. Spectrosk. 48, 1081
  34. Braun, P. A., V. N. Ostrovsky, and N. V. Prudov, 1990, Phys. Rev. A 42, 6537
  35. Braun, P. A., and M. V. Senyushkin, 1991, Zh. Eksp. Teor. Fiz. 100, 1461
  36. Braun, P. A., A. M. Shirokov, and Yu. F. Smirnov, 1985, Mol. Phys. 56, 573
  37. Braun, P. A., A. M. Shirokov, and Yu. F. Smirnov, 1987, Izv. Akad. Nauk SSSR, Ser. Fiz. 51, 176 [Bull. Acad. Sci. USSR, Phys. Ser. 51, 162 (1987)]
  38. Braun, P. A., and E. A. Solov'ev, 1984, Zh. Eksp. Teor. Fiz. 86, 68 [Sov. Phys. JETP 59, 38 (1984)]
  39. Brussard, P., and J. H. Tolhoek, 1957, Physica 23, 955
  40. Bruyev, A. S., 1986, Zh. Eksp. Teor. Fiz. 90, 35 [Sov. Phys. JETP 63, 20 (1986)]
  41. Cacciani, P., S. Liberman, E. Luc-Koenig, J. Pinard, and C. Thomas, 1989, Phys. Rev. A 40, 3026
  42. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1986a, Phys. Rev. Lett. 56, 1124
  43. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1986b, Phys. Rev. Lett. 56, 1467
  44. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1986c, J. Phys. B 19, L519
  45. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1988a, J. Phys. B 21, 3473
  46. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1988b, J. Phys. B 21, 3499
  47. Cacciani, P., E. Luc-Koenig, J. Pinard, C. Thomas, and S. Liberman, 1988c, J. Phys. B 21, 3523
  48. Carruthers, P., and M. M. Nieto, 1968, Rev. Mod. Phys. 40, 411
  49. Chardonnet, C., D. Delande, and J. C. Gay, 1989, Phys. Rev. A 39, 1066
  50. Clark, Ch. W. 1981, Phys. Rev. A 24, 605
  51. Clark, Ch. W., and K. T. Taylor, 1980, J. Phys. B 13, L737
  52. Clark, Ch. W., and K. T. Taylor, 1982, J. Phys. B 15, 1175
  53. Colwell, S. M., N. C. Handy, and W. H. Miller, 1978, J. Chem. Phys. 68, 745
  54. Delande, D., and J. C. Gay, 1981a, Phys. Lett. A 82, 393
  55. Delande, D., and J. C. Gay, 1981b, Phys. Lett. A 82, 399
  56. Delande, D., and J. C. Gay, 1984, J. Phys. B 17, L335
  57. Delande, D., and J. C. Gay, 1987, Phys. Rev. Lett. 59, 1809
  58. Delande, D., and J. C. Gay, 1991, Phys. Rev. Lett. 66, 3237
  59. Delos, J. B., and M. L. Du, 1988, IEEE J. Quantum Electron. 24, 1445
  60. Delos, J. B., S. K. Knudson, and D. W. Noid, 1983a, Phys. Rev. Lett. 50, 579
  61. Delos, J. B., S. K. Knudson, and D. W. Noid, 1983b, Phys. Rev. A 28, 7
  62. Delos, J. B., R. L. Waterland, and M. L. Du, 1988, Phys. Rev. A 37, 1185
  63. Demkov, Yu. N., B. S. Monozon, and V. N. Ostrovsky, 1969, Zh. Eksp. Teor. Fiz. 57, 1431 [Sov. Phys. JETP 30, 775 (1970)]
  64. Du, M. L., and J. B. Delos, 1988, Phys. Rev. A 38, 1896
  65. Edmonds, A. R., 1960, Angular Momentum in Quantum Mechanics (Princeton University, Princeton)
  66. Epstein, P. S., 1926, Phys. Rev. 28, 695
  67. Fabre, C., Y. Kaluzny, R. Calabrese, Liang Jun, P. Goy, and S. Haroche, 1984, J. Phys. B 17, 3217
  68. Fano, U., F. Robicheaux, and A. R. P. Rau, 1988, Phys. Rev. A 37, 3655
  69. Fauth, M., H. Walther, and E. Werner, 1987, Z. Phys. D 7, 293
  70. Fedorov, M. V., 1977, Zh. Eksp. Teor. Fiz. 73, 134
  71. Fox, K., H. W. Galbraith, B. J. Krohn, and J. D. Kouck, 1977, Phys. Rev. A 15, 1363
  72. Friedrich, H., and D. Wintgen, 1989, Phys. Rep. 183, 37
  73. Ganesan, K., and M. Lakshmanan, 1990, Phys. Rev. A 42, 3940
  74. Gay, J. C., 1985, in Photophysics and Photochemistry in the Vacuum Ultraviolet, edited by S. P. McGlynn, G. L. Findley, and R. H. Huebner (Reidel, Dordrecht), p. 631
  75. Gay, J. C., 1986, in Atoms in Unusual Situations, edited by J. P. Briand (Plenum, New York), p. 107
  76. Gay, J. C., 1988, in Spectrum of Atomic Hydrogen, edited by G. W. Series (World Scientific, Singapore), p. 367
  77. Gay, J. C., and D. Delande, 1983, Comments At. Mol. Phys. 13, 275
  78. Gay, J. C., D. Delande, and F. Biraben, 1980, J. Phys. B 13, L729
  79. Gay, J. C., D. Delande, F. Biraben, and F. Penent, 1983, J. Phys. B 16, L693
  80. Gay, J. C., D. Delande, and A. Bommier, 1988, in Proceedings of 11th International Conference on Atomic Physics, edited by C. Fabre and D. Delande (École Normale Supérieure, Paris). Book of Abstracts, VIII-51
  81. Gilmore, R., and D. H. Feng, 1978, Nucl. Phys. A 301, 189
  82. Grozdanov, T. P., and M. J. Raković, 1988, J. Phys. B 21, 4087
  83. Grozdanov, T. P., and E. A. Solov'ev, 1984, J. Phys. B 17, 555
  84. Grozdanov, T. P., and H. S. Taylor, 1986, J. Phys. B 19, 4075
  85. Harmin, D. A., 1984, Phys. Rev. A 30, 2413
  86. Haroche, S., 1986, in Atoms in Unusual Situations, edited by J. P. Briand (Plenum, New York), p. 77
  87. Harter, W. G., and C. W. Patterson, 1977, J. Chem. Phys. 66, 4872
  88. Hasegawa, H., and S. Adachi, 1988, J. Phys. Soc. Jpn. 57, 80
  89. Hasegawa, H., A. Harada, and Y. Okazaki, 1984, J. Phys. A 17, L883
  90. Hasegawa, H., M. Robnik, and G. Wunner, 1989, Prog. Theor. Phys. Suppl. 98, 198
  91. Herrick, D., 1982, Phys. Rev. A 26, 323
  92. Hinds, E. A., 1990, Adv. At. Mol. Opt. Phys. 28, 235
  93. Holle, A., B. Hager, and K. H. Welge, 1985, in Proceedings of II European Conference on Atomic and Molecular Physics, edited by A. E. de Vries and M. J. van der Wiel (Europ. Phys. Soc., Amsterdam), Book of Abstracts, p. 6
  94. Holle, A., J. Main, G. Wiebusch, H. Rottke, and K. H. Welge, 1988, Phys. Rev. Lett. 61, 161
  95. Jenkins, F. A., and E. Segre, 1939, Phys. Rev. 55, 52
  96. Jones, W. B., and W. J. Thron, 1980, Continued Fractions: Analytic Theory and Applications (Addison-Wesley, Reading)
  97. Kazantsev, A. P., and V. L. Pokrovsky, 1983a, Pis'ma Zh. Eksp. Teor. Fiz. 37, 471
  98. Kazantsev, A. P., and V. L. Pokrovsky, 1983b, Zh. Eksp. Teor. Fiz. 85, 1917
  99. Kazantsev, A. P., and V. L. Pokrovsky, 1983c, J. Phys. B 16, L601
  100. Kazantsev, A. P., V. L. Pokrovsky, and J. Bergou, 1983, Phys. Rev. A 28, 3659
  101. Komarov, I. V., T. P. Grozdanov, and R. R. Janev, 1980, J. Phys. B 13, L573
  102. Komarov, I. V., L. I. Ponomarev, and S. Yu. Slavyanov, 1976, The Spheroidal and Coulomb Spheroidal Functions (Nauka, Moscow). In Russian
  103. König, A., J. Neukammer, K. Vietzke, M. Kohl, H. J. Grabka, H. Hieronymus, and H. Rinneberg, 1988, Phys. Rev. A 38, 547
  104. Korevaar, E. G., and M. G. Littman, 1983, J. Phys. B 16, L437
  105. Kravchenko, V. A., and A. S. Prostnev, 1973, Dok. Akad. Nauk SSSR 211, 75
  106. Landau, L. D., and E. M. Lifshitz, 1989, Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow). In Russian
  107. Landau, L. D., and E. M. Lifshitz, 1988, Mechanics (Nauka, Moscow). In Russian
  108. Langer, R. E., 1937, Phys. Rev. 51, 669
  109. Lee, M. H., J. Hong, and J. Florencio, Jr., 1987, Phys. Scr. T19, 498
  110. Leopold, J. G., and D. Richards, 1989, J. Phys. B 22, 1931
  111. Lindgard, A., and S. E. Nielsen, 1977, At. Data Nucl. Data 19, 533
  112. Lipkin, H. J., N. Meshkov, and A. J. Glick, 1965, Nucl. Phys. 62, 188
  113. Lisitsa, V. S., 1987, Usp. Fiz. Nauk 153, 379 [Sov. Phys. Usp. 30, 927 (1987)]
  114. Makarov, V. P., and M. V. Fedorov, 1976, Zh. Eksp. Teor. Fiz. 70, 1185
  115. Maslov, V. P., 1973, The Operator Methods (Nauka, Moscow). In Russian
  116. Maslov, V. P., and M. V. Fedoryuk, 1981, Quasiclassical Approximation for the Equations of Quantum Mechanics (Reidel, Dordrecht)
  117. Mur, V. D., and V. S. Popov, 1988, Zh. Eksp. Teor. Fiz. 94, 125 [Sov. Phys.—JETP 67, 2027 (1988)]
  118. Mur, V. D.V. S. PopovNayfeh, M. H., and C. W. Clark, 1985, Eds., Atomic Excitation and Recombination in External Fields (Gordon and Breach, New York)
  119. Nikitin, S. I., and V. N. Ostrovsky, 1982, J. Phys. B 15, 1609
  120. O'Mahony, P. F., 1988, in Fundamental Processes of Atomic Dynamics, edited by J. S. Briggs, H. Kleinpoppen, and H. O. Lutz (Plenum, New York), p. 197
  121. O'Mahony, P. F., and K. T. Taylor, 1986a, Phys. Rev. Lett. 57, 2931
  122. O'Mahony, P. F., and K. T. Taylor, 1986b, J. Phys. B 19, L65
  123. Ostrovsky, V. N., and D. A. Telnov, 1987, J. Phys. B 20, 2397
  124. Pauli, W., 1926, Z. Phys. 36, 336
  125. Penent, F., D. Delande, F. Biraben, and J. C. Gay, 1984, Opt. Commun. 49, 184
  126. Penent, F., D. Delande, and J. C. Gay, 1988, Phys. Rev. A 37, 4707
  127. Ponzano, C., and T. Regge, 1968, in Spectroscopic and Group Theoretical Methods in Physics, edited by F. Bloch, S. G. Cohen, A. De-Shalit, S. Sambursky, and I. Talmi (Wiley, New York), p. 53
  128. Raithel, G., M. Fauth, and H. Walther, 1991, Phys. Rev. A 44, 1898
  129. Rath, O., and D. Richards, 1988, J. Phys. B 21, 555
  130. Rau, A. R. P., 1989, Phys. Rev. Lett. 63, 244
  131. Rau, A. R. P., 1990, Rep. Prog. Phys. 53, 181
  132. Rau, A. R. P., and Lijun Zhang, 1990, Phys. Rev. A 42, 6342
  133. Rau, A. R. P., and Q. Molina, 1989, J. Phys. B 22, 189
  134. Reinhardt, W. P., 1983, J. Phys. B 16, L635
  135. Richards, D., 1983, J. Phys. B 16, 749
  136. Richter, K., D. Wintgen, and J. S. Briggs, 1987, J. Phys. B 20, L627
  137. Rinneberg, H., J. Neukammer, A. König, H. Hieronymus, M. Kohl, and G. Jönsson, 1986, in Proceedings of Oji International Seminar on Highly Excited States of Atoms and Molecules, edited by S. S. Kano and M. Matsuzawa (Fuji-Yoshida, Japan), p. 7
  138. Rinneberg, H., J. Neukammer, A. König, K. Vietzke, H. Hieronymus, M. Kohl, H. J. Grabka, and G. J. Jönsson, 1987, Hyperfine Interact. 38, 515
  139. Robnik, M., 1981, J. Phys. A 14, 3195
  140. Robnik, M., 1982, J. Phys. (Paris) Colloq. 43, c2-45
  141. Sazonov, V. N., 1978, Teor. Nat. Fizika 35, 361 [Sov. Phys. Theor. Math. Phys. 35, 514 (1978)]
  142. Schiff, L. I., and H. Snyder, 1939, Phys. Rev. 55, 59
  143. Schulten, K., and R. G. Gordon, 1975, J. Math. Phys. 16, 1970
  144. Sokoloff, J. B., 1985, Phys. Rep. 126, 189
  145. Solov'ev, E. A., 1981, Pis'ma Zh. Eksp. Teor. Fiz. 34, 278 [JETP Lett. 34, 265 (1981)]
  146. Solov'ev, E. A., 1982, Zh. Eksp. Teor. Fiz. 82, 1762 [Sov. Phys. JETP 55, 1017 (1982)]
  147. Solov'ev, E. A., 1983, Zh. Eksp. Teor. Fiz. 85, 109 [Sov. Phys. JETP 58, 63 (1983)]
  148. Sumetsky, M. Yu., 1982, Zh. Eksp. Teor. Fiz. 83, 1661 [Sov. Phys. JETP 56, 959 (1983)]
  149. Sumetsky, M. Yu.Taylor, K. T., C. W. Clark, and M. H. Nayfeh, 1988, Eds., Atomic Spectra and Collisions in External Fields (Plenum, New York)
  150. Uzer, T., 1990, Phys. Rev. A 42, 5787
  151. van der Veldt, T., G. J. Kuik, and W. Hogervorst, 1990, in Proceedings of 22nd European Group on Atomic Spectroscopy, edited by K. Bethge (European Physical Society, Uppsala), Book of Abstracts, p. 529
  152. van der Veldt, T., W. Vassen, and W. Hogervorst, 1992, J. Phys. B 25, 3295
  153. Vasil'eva, A. B., and V. F. Butuzov, 1978, Singularly Perturbed Equations in the Critical Cases (Moscow University, Moscow). In Russian
  154. Wall, H. S., 1983, Analytic Theory of Continued Fractions (Chelsea, New York)
  155. Watanabe, S., 1989, Phys. Rev. A 39, 417
  156. Waterland, R. L., J. B. Delos, and M. L. Du, 1987, Phys. Rev. A 35, 5064
  157. Watson, J. K. G., 1967, J. Chem. Phys., 46, 1935
  158. Watson, J. K. G., 1977, in Vibrational Spectra and Structure, edited by J. R. Durig (Elsevier, Amsterdam), Vol. 6, p. 1
  159. Wiebusch, G., J. Main, K. Krüger, H. Rottke, A. Holle, and K. H. Welge, 1989, Phys. Rev. Lett. 62, 2821
  160. Windholz, L., 1990, Z. Phys. D 15, 87
  161. Wintgen, D., and H. Friedrich, 1986a, J. Phys. B 19, 991
  162. Wintgen, D., and H. Friedrich, 1986b, J. Phys. B 19, 1261
  163. Wintgen, D., and H. Friedrich, 1987, Phys. Rev. A 36, 131
  164. Wintgen, D., A. Holle, G. Wiebusch, J. Main, H. Friedrich, and K. H. Welge, 1986, J. Phys. B 19, L557
  165. Wunner, G., 1986, J. Phys. B 19, 1623
  166. Zeller, G., R. Niemeier, W. Schweizer, and G. Wunner, 1989, in Proceedings of the III European Conference on Atomic and Molecular Physica (Bordeaux), Book of Abstracts, p. 223
  167. Ziman, J. M., 1964, Principles of the Theory of Solids (Cambridge University, Cambridge)
  168. Zimmerman, M. L., M. M. Kash, and D. Kleppner, 1980, Phys. Rev. Lett. 45, 1092
  169. Zimmerman, M. L., M. G. Littman, M. M. Kash, and D. Kleppner, 1980, Phys. Rev. A 20, 2251

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Rev. Mod. Phys. 65, 115– Published 1 January, 1993

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