RSS feeds
ÐóññêèéEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2004

 / 

September

←  →

Reviews of topical problems


Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory)


Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

The theoretical description of the nonlinear photoionization of atoms and ions exposed to high-intensity laser radiation is underlain by the Keldysh theory proposed in 1964. The paper reviews this theory and its further development. The discussion is concerned with the energy and angular photoelectron distributions for the cases of linearly, circularly, and elliptically polarized laser radiation, with the ionization rate of atomic states exposed to a monochromatic electromagnetic wave and to ultrashort laser pulses of various shape, and with momentum and angular photoelectron spectra in these cases. The limiting cases of tunnel (γ " 1) and multiphoton (γ " 1) ionization are discussed, where c is the adiabaticity parameter, or the Keldysh parameter. The probability of above-barrier ionization is calculated for hydrogen atoms in a low-frequency laser field. The effect of a strong magnetic field on the ionization probability is discussed. The process of Lorentz ionization occurring in the motion of atoms and ions in a constant magnetic field is considered. The properties of an exactly solvable model-the ionization of an s-level bound by zero-range forces in the field of a circularly polarized electromagnetic wave-are described. In connection with this example, the Zel’dovich regularization method in the theory of quasistationary states is discussed. Results of the Keldysh theory are compared with experiment. A brief discussion is made of the relativistic ionization theory applicable when the binding energy of the atomic level is comparable with the electron rest mass (multiply charged ions) and the sub-barrier electron motion can no longer be considered to be nonrelativistic. A similar process of electron-positron pair production from a vacuum by the field of high-power optical or X-ray lasers (the Schwinger effect) is considered. The calculations invoke the method of imaginary time, which provides a convenient and physically clear way of calculating the probability of particle tunneling through time-varying barriers. Discussed in the Appendices are the properties of the asymptotic coefficients of the atomic wave function, the expansions for the Keldysh function, and the so-called ’ADK theory’.

Fulltext pdf (625 KB)
Fulltext is also available at DOI: 10.1070/PU2004v047n09ABEH001812
PACS: 12.20.Ds, 32.80.−t, 42.50.Hz (all)
DOI: 10.1070/PU2004v047n09ABEH001812
URL: https://ufn.ru/en/articles/2004/9/a/
000226203600001
2004PhyU...47..855P
Citation: Popov V S "Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory)" Phys. Usp. 47 855–885 (2004)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ïîïîâ Â Ñ «Òóííåëüíàÿ è ìíîãîôîòîííàÿ èîíèçàöèÿ àòîìîâ è èîíîâ â ñèëüíîì ëàçåðíîì ïîëå (òåîðèÿ Êåëäûøà)» ÓÔÍ 174 921–951 (2004); DOI: 10.3367/UFNr.0174.200409a.0921

References (157) ↓ Cited by (473) Similar articles (20)

  1. Keldysh L V Zh. Eksp. Teor. Fiz. 47 1945 (1964) [Sov. Phys. JETP 20 1307 (1965)]
  2. Volkov D M Z. Phys. 94 250 (1935); Zh. Eksp. Teor. Fiz. 7 1286 (1937)
  3. Berestetskii V B, Lifshitz E M, Pitaevskii L P Relyativistskaya Kvantovaya Teoriya (Relativistic Quantum Theory) Pt. 1 (Moscow: Nauka, 1968) [Translated into English (Oxford: Pergamon Press, 1971)]
  4. Nikishov A I, Ritus V I Zh. Eksp. Teor. Fiz. 50 255 (1966) [Sov. Phys. JETP 23 162 (1966)]
  5. Perelomov A M, Popov V S, Terent’ev M V Zh. Eksp. Teor. Fiz. 50 1393; 51 309 (1966) [Sov. Phys. JETP 23 924 (1966); 24 207 (1967)]
  6. Perelomov A M, Popov V S Zh. Eksp. Teor. Fiz. 52 514 (1967) [Sov. Phys. JETP 25 482 (1967)]
  7. Nikishov A I, Ritus V I Zh. Eksp. Teor. Fiz. 52 223 (1967) [Sov. Phys. JETP 25 145 (1967)]
  8. Popov V S, Kuznetsov V P, Perelomov A M Zh. Eksp. Teor. Fiz. 53 331 (1967) [Sov. Phys. JETP 26 240 (1968)]; Preprint No. 517 (Moscow: Institute of Theoretical and Experimental Physics of the USSR Academy of Sciences, 1967)
  9. Nikishov A I Tr. Fiz. Inst. Akad. Nauk SSSR 111 152 (1979)
  10. Kotova L P, Perelomov A M, Popov V S Zh. Eksp. Teor. Fiz. 54 1151 (1968) [Sov. Phys. JETP 27 616 (1968)]
  11. Hartree D R Proc. Cambr. Philos. Soc. 24 89 (1927)
  12. Bates D R, Damgaard A Philos. Trans. R. Soc. London 242 101 (1949)
  13. Hartree D R The Calculation of Atomic Structures (New York: J. Wiley, 1957)
  14. Radzig A A, Smirnov B M Parametry Atomov i Atomnykh Ionov (Moscow: Energoatomizdat, 1986) [Translated into English (earlier edition) as Reference Data on Atoms, Molecules, and Ions (Berlin: Springer-Verlag, 1985)]
  15. Sobelman I I Vvedenie v Teoriyu Atomnykh Spektrov (Moscow: Nauka, 1977) [Translated into English as Atomic Spectra and Radiative Transitions (Berlin: Springer-Verlag, 1979)]
  16. Landau L D, Lifshitz E M Kvantovaya Mekhanika: Nerelyativist„skaya Teoriya (Quantum Mechanics: Non-Relativistic Theory, Moscow: Fizmatlit, 2001) [Translated into English (Oxford: Pergamon Press, 1977)]
  17. Rapoport L P, Zon B A, Manakov N L Teoriya Mnogofotonnykh Protsessov v Atomakh (Theory of Multiphoton Processes in Atoms, Moscow: Atomizdat, 1978)
  18. Seaton M J Mon. Not. R. Astron. Soc. 118 504 (1958); Rep. Prog. Phys. 46 167 (1983)
  19. Mur V D, Karnakov B M, Popov V S Dokl. Ross. Akad. Nauk 365 329 (1999) [Dokl. Phys. 44 156 (1999)]; Zh. Eksp. Teor. Fiz. 115 521 (1999) [JETP 88 286 (1999)]
  20. Abramowitz M, Stegun I A (Eds) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover Publ., 1965) [Translated into Russian (Moscow: Nauka, 1979)]
  21. Popov V S Pis’ma Zh. Eksp. Teor. Fiz. 70 493 (1999) [JETP Lett. 70 502 (1999)]; Zh. Eksp. Teor. Fiz. 118 56 (2000) [JETP 91 48 (2000)]; Laser Phys. 10 1033 (2000)
  22. Voronov G S et al. Pis’ma Zh. Eksp. Teor. Fiz. 2 377 (1965) [JETP Lett. 2 237 (1965)]; Voronov G S, Delone N B Zh. Eksp. Teor. Fiz. 50 78 (1966) [Sov. Phys. JETP 23 54 (1966)]; Voronov G S, Delone G A, Delone N B Zh. Eksp. Teor. Fiz. 51 1660 (1966) [Sov. Phys. JETP 24 1122 (1967)]
  23. Faisal F H M J. Phys. B: At. Mol. Phys. 6 L89 (1973)
  24. Reiss H R Phys. Rev. A 22 1786 (1980); 42 1476 (1990); Prog. Quantum Electron. 16 (1) 1 (1992)
  25. Reiss H R J. Opt. Soc. Am. B 7 574 (1990)
  26. Brabec T, Krausz F Rev. Mod. Phys. 72 545 (2000)
  27. Delone N B, Krainov V P Multiphoton Processes in Atoms (Berlin: Springer-Verlag, 1994; 2nd ed. — Berlin: Springer, 2000)
  28. Fock V A Z. Phys. 98 145 (1935)
  29. Bargmann V Z. Phys. 99 576 (1935)
  30. Bander M, Itzykson C Rev. Mod. Phys. 38 330, 346 (1966)
  31. Perelomov A M, Popov V S Zh. Eksp. Teor. Fiz. 50 179 (1966) [Sov. Phys. JETP 23 118 (1966)]
  32. Popov V S "O ’skrytoi’ simmetrii atoma vodoroda" ("On the ’hidden’ symmetry of the hydrogen atom), in Fizika Vysokikh Energii i Teoriya Elementarnykh Chastits (High-Energy Physics and Theory of Elementary Particles, Ed. V P Shelest, Kiev: Naukova Dumka, 1967) p. 702
  33. Smirnov B M, Chibisov M I Zh. Eksp. Teor. Fiz. 49 841 (1965) [Sov. Phys. JETP 22 585 (1966)]
  34. Demkov Yu N, Drukarev G F Zh. Eksp. Teor. Fiz. 47 918 (1964) [Sov. Phys. JETP 20 614 (1965)]
  35. Gribakin G F, Kuchiev M Yu Phys. Rev. A 55 3760 (1997)
  36. Goreslavskii S P, Shvetsov-Shilovskii N I, Shcherbachev O V, in Nauchnaya Sessiya MIFI-2004, Moskva, 26 – 30 Yanvarya 2004 g. (Scientific Session of the Moscow Engineering Physics Institute-2004, Moscow, 26 – 30 January 2004) Vol. 5 (Moscow: MIFI, 2004) p. 158; Zh. Eksp. Teor. Fiz. 127 (1, 2005)
  37. Goreslavskii S P, Popruzhenko S V Zh. Eksp. Teor. Fiz. 110 1200 (1996) [JETP 83 661 (1996)]
  38. Goreslavskii S P, Popruzhenko S V Laser Phys. 6 780 (1996); Goreslavsky S P, Popruzhenko S V Laser Phys. 7 700 (1997)
  39. Mur V D, Popruzhenko S V, Popov V S Zh. Eksp. Teor. Fiz. 119 893 (2001) [JETP 92 777 (2001)]
  40. Krainov V P J. Phys. B: At. Mol. Opt. Phys. 32 1607 (1999)
  41. Paulus G G et al. Phys. Rev. Lett. 80 484 (1998)
  42. Becker W et al. Laser Phys. 8 56 (1998)
  43. Paulus G G et al. Phys. Rev. Lett. 84 3791 (2000)
  44. Corkum P B, Burnett N H, Brunel F Phys. Rev. Lett. 62 1259 (1989)
  45. Pont M, Shakeshaft R, Potvliege R M Phys. Rev. A 42 6969 (1990); Pont M et al. Phys. Rev. A 45 8235 (1992)
  46. Dykhne A M Zh. Eksp. Teor. Fiz. 38 570 (1960); 41 1324 (1961) [Sov. Phys. JETP 11 411 (1960); 14 941 (1962)]
  47. Delone N B, Krainov V P Atom v Sil’nom Svetovom Pole (Atom in a Strong Light Field) 2nd ed. (Moscow: Energoatomizdat, 1984) [Translated into English: Atoms in Strong Light Fields (Berlin: Springer-Verlag, 1985)]
  48. Delone N B, Krainov V P J. Opt. Soc. Am. B 8 1207 (1991)
  49. Krainov V P J. Opt. Soc. Am. B 14 425 (1997)
  50. Krainov V P, Ristic V M Zh. Eksp. Teor. Fiz. 101 1479 (1992) [Sov. Phys. JETP 74 789 (1992)]
  51. Delone N B, Krainov V P Usp. Fiz. Nauk 168 531 (1998) [Phys. Usp. 41 469 (1998)]
  52. Popov V S Usp. Fiz. Nauk 169 819 (1999) [Phys. Usp. 42 733 (1998)]
  53. Bashkansky M, Bucksbaum P H, Schumacher D W Phys. Rev. Lett. 60 2458 (1988)
  54. Basile S, Trombetta F, Ferrante G Phys. Rev. Lett. 61 2435 (1988)
  55. Shvetsov-Shilovskii N I, Goreslavskii S P, Popruzhenko S V, in Nauchnaya Sessiya MIFI-2004, Moskva, 26 – 30 Yanvarya 2004 g. (Scientific Session of the Moscow Institute of Engineering Physics-2004, Moscow, 26 – 30 January 2004) Vol. 5 (Moscow: MIFI, 2004) p. 208; Phys. Rev. Lett. 93 233002 (2004)
  56. Hehenberger M, McIntosh H V, Brändas E Phys. Rev. A 10 1494 (1974)
  57. Yamabe T, Tachibana A, Silverstone H J Phys. Rev. A 16 877 (1977)
  58. Benassi L, Grecchi V J. Phys. B: At. Mol. Phys. 13 911 (1980)
  59. Franceschini V, Grecchi V, Silverstone H J Phys. Rev. A 32 1338 (1985)
  60. Vainberg V M et al. Pis’ma Zh. Eksp. Teor. Fiz. 44 9 (1986) [JETP Lett. 44 9 (1986)]; Zh. Eksp. Teor. Fiz. 93 450 (1987) [Sov. Phys. JETP 66 258 (1987)]
  61. Popov V S et al. Phys. Lett. A 124 77 (1987); 149 418 (1990); Popov V S, Mur V D, Sergeev A V Phys. Lett. A 193 159 (1994)
  62. Fernández F M Phys. Rev. A 54 1206 (1996)
  63. Barenblatt G I, Zel’dovich Ya B Usp. Mat. Nauk 26 115 (1971) [Russ. Math. Surv. 26 45 (1972)]
  64. Zel’dovich Ya B, Sokolov D D Usp. Fiz. Nauk 146 493 (1985) [Sov. Phys. Usp. 28 608 (1985)]
  65. Benassi L et al. Phys. Rev. Lett. 42 704, 1430 (1979)
  66. Popov V S Phys. Lett. A 173 63 (1993)
  67. Yaffe L G Rev. Mod. Phys. 54 407 (1982)
  68. Doren D J, Herschbach D R Phys. Rev. A 34 2654 (1986)
  69. Tsipis C A et al. (Eds) New Methods in Quantum Theory (Dordrecht: Kluwer Acad., 1996)
  70. Keldysh L "Multiphoton ionization by a very short laser pulse" (private commun.)
  71. Popov V S Laser Phys. 10 1033 (2000); Pis’ma Zh. Eksp. Teor. Fiz. 73 3 (2001) [JETP Lett. 73 1 (2001)]; Zh. Eksp. Teor. Fiz. 120 315 (2001) [JETP 93 278 (2001)]
  72. Popov V S, Karnakov B M, Mur V D Phys. Lett. A 229 306 (1997); Zh. Eksp. Teor. Fiz. 113 1579 (1998) [JETP 86 860 (1998)]
  73. Baz’ A I, Zel’dovich Ya B, Perelomov A M Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike (Scattering, Reactions and Decays in Nonrelativistic Quantum Mechanics) 2nd ed. (Moscow: Nauka, 1971) [Translated into English 1st ed. (Jerusalem: Israel Program for Scientific Translations, 1969)]
  74. Popov V S Zh. Eksp. Teor. Fiz. 61 1334 (1971); 63 1586 (1972) [Sov. Phys. JETP 34 709 (1972); 36 840 (1973)]
  75. Landau L D Phys. Z. Sowjetunion 1 88; 2 46 (1932); Sobranie Trudov (Collected Works) Vol. 1 (Moscow: Nauka, 1969) pp. 71, 81
  76. Lifshitz E M Zh. Eksp. Teor. Fiz. 8 930 (1938)
  77. Nikitin E E, Pitaevskii L P Usp. Phys. Nauk 163 (9) 101 (1993) [Phys. Usp. 36 851 (1993)]
  78. Landau L D, Lifshitz E M Mekhanika (Mechanics, Moscow: Fizmatlit, 2001) [Translated into English (Oxford: Pergamon Press, 1976)]
  79. Gaponov A V, Miller M A Zh. Eksp. Teor. Fiz. 34 242 (1958) [Sov. Phys. JETP 7 168 (1958)]
  80. Muller H G, Tip A, van der Wiel M J J. Phys. B: At. Mol. Phys. 16 L679 (1983)
  81. Goreslavsky S P, Narozhny N B, Yakovlev V P J. Opt. Soc. Am. B 6 1752 (1989)
  82. Popov V S, Sergeev A V Pis’ma Zh. Eksp. Teor. Fiz. 63 398 (1996) [JETP Lett. 63 417 (1996)]
  83. Drukarev G F, Monozon B S Zh. Eksp. Teor. Fiz. 61 956 (1971) [Sov. Phys. JETP 34 509 (1972)]
  84. Dyson F J Phys. Rev. 85 631 (1952)
  85. Kazakov D I, Shirkov D V Fortschr. Phys. 28 465 (1980)
  86. Itzykson C, Zuber J-B Quantum Field Theory (New York: McGraw-Hill Intern. Book Co., 1980) [Translated into Russian: Vol. 2 (Moscow: Mir, 1984) Ch. 9]
  87. Kazakov D I, Popov V S Zh. Eksp. Teor. Fiz. 122 675 (2002) [JETP 95 581 (2002)]
  88. Popov V S, Sergeev A V Zh. Eksp. Teor. Fiz. 113 2047 (1998) [JETP 86 1122 (1998)]
  89. Popov V S, Sergeev A V, Shcheblykin A V Zh. Eksp. Teor. Fiz. 102 1453 (1992) [Sov. Phys. JETP 75 787 (1992)]; Popov V S, Sergeev A V Zh. Eksp. Teor. Fiz. 105 568 (1994) [JETP 78 303 (1994)]
  90. Popov V S, Sergeev A V Phys. Lett. A 172 193 (1993); 193 165 (1994)
  91. López-Cabrera M et al. Phys. Rev. Lett. 68 1992 (1992)
  92. Kais S, Herschbach D R J. Chem. Phys. 98 3990 (1993)
  93. Karnakov B M, Mur V D, Popov V S Pis’ma Zh. Eksp. Teor. Fiz. 65 391 (1997) [JETP Lett. 65 405 (1997)]; Popov V S, Karnakov B M, Mur V D Zh. Eksp. Teor. Fiz. 115 1642 (1999) [JETP 88 902 (1999)]
  94. Sakharov A D et al. Dokl. Akad. Nauk SSSR 196 65 (1965)
  95. Sakharov A D Usp. Fiz. Nauk 88 725 (1966) [Sov. Phys. Usp. 9 294 (1966)]
  96. Pavlovskii A I, in Akademik A.D. Sakharov. Nauchnye Trudy (Academician A.D. Sakharov. Scientific Works, Eds B L Al’tshuler et al., Moscow: Tsentrkom OTF FIAN, 1995) p. 85
  97. Fabrika S N, Balyavin G G, Preprint No. 129 (Nizhnii Arkhyz: Special Astrophysical Observatory of the Russian Academy of Sciences, 1998)
  98. Nikishov A I Zh. Eksp. Teor. Fiz. 60 1614 (1971) [Sov. Phys. JETP 33 873 (1971)]; Tr. Fiz. Inst. Akad. Nauk SSSR 113 211 (1979)
  99. Manakov N L et al. J. Phys. B: At. Mol. Opt. Phys. 33 R141 (2000)
  100. Bunkin F V, Prokhorov A M Zh. Eksp. Teor. Fiz. 46 1090 (1964) [Sov. Phys. JETP 19 739 (1964)]
  101. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 51 1492 (1966) [Sov. Phys. JETP 24 1006 (1967)]; Usp. Fiz. Nauk 110 139 (1973) [Sov. Phys. Usp. 16 427 (1973)]
  102. Ritus V I Zh. Eksp. Teor. Fiz. 51 1544 (1966) [Sov. Phys. JETP 24 1041 (1967)]
  103. Manakov N L, Rapoport L P Zh. Eksp. Teor. Fiz. 69 842 (1975) [Sov. Phys. JETP 42 430 (1976)]; Manakov N L, Ovsiannikov V D, Rapoport L P Phys. Rep. 141 319 (1986)
  104. Berson I J J. Phys. B: At. Mol. Phys. 8 3078 (1975)
  105. Mur V D et al. Pis’ma Zh. Eksp. Teor. Fiz. 75 294 (2002) [JETP Lett. 75 249 (2002)]; Yad. Fiz. 66 2014 (2003) [Phys. At. Nucl. 66 1964 (2003)]
  106. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 39 776 (1960) [Sov. Phys. JETP 12 542 (1961)]
  107. Andreev S P, Karnakov B M, Mur V D Pis’ma Zh. Eksp. Teor. Fiz. 37 155 (1983) [JETP Lett. 37 187 (1983)]; Andreev S P et al. Zh. Eksp. Teor. Fiz. 86 866 (1984) [Sov. Phys. JETP 59 506 (1984)]
  108. Mur V D et al. Phys. Lett. A 316 226 (2003)
  109. Manakov N L et al. Pis’ma Zh. Eksp. Teor. Fiz. 72 426 (2000) [JETP Lett. 72 294 (2000)]
  110. Borca B et al. Phys. Rev. Lett. 88 193001 (2002); Manakov N L et al. J. Phys. B: At. Mol. Opt. Phys. 36 R49 (2003)
  111. Xiong W, Chin S L Zh. Eksp. Teor. Fiz. 99 481 (1991) [Sov. Phys. JETP 72 268 (1991)]
  112. Fittinghoff D N et al. Phys. Rev. Lett. 69 2642 (1992)
  113. Moshammer R et al. Phys. Rev. Lett. 84 447 (2000)
  114. Mohideen U et al. Phys. Rev. Lett. 71 509 (1993)
  115. Ammosov M V, Delone N B, Krainov V P Zh. Eksp. Teor. Fiz. 91 2008 (1986) [Sov. Phys. JETP 64 1191 (1986)]
  116. Tajima T, Mourou G Phys. Rev. ST Accel. Beams 5 031301 (2002)
  117. Sauter F Z. Phys. 69 742; 73 547 (1931)
  118. Heisenberg W, Euler H Z. Phys. 98 714 (1936)
  119. Schwinger J Phys. Rev. 82 664 (1951)
  120. Akhiezer A I, Berestetskii V B Kvantovaya Elektrodinamika (Quantum Electrodynamics, Moscow: Nauka, 1981) [Translated into English from the 2nd Russian ed. (New York: Interscience Publ., 1965)]
  121. Marinov M S, Popov V S Yad. Fiz. 15 1271 (1972); Fortschr. Phys. 25 373 (1977)
  122. Bargmann V, Michel L, Telegdi V L Phys. Rev. Lett. 2 435 (1959)
  123. Breit G Nature 122 649 (1928)
  124. Perelomov A M, Popov V S Yad. Fiz. 14 661 (1971)
  125. Popov V S Yad. Fiz. 12 429 (1970); 14 458 (1971); 64 421 (2001) [Phys. At. Nucl. 64 367 (2001)]
  126. Zel’dovich Ya B, Popov V S Usp. Fiz. Nauk 105 403 (1971) [Sov. Phys. Usp. 14 673 (1972)]
  127. Schiff L I Quantum Mechanics 2nd ed. (New York: McGraw-Hill, 1955) [Translated into Russian (Moscow: IL, 1957)]
  128. Popov V S, Karnakov B M, Mur V D Pis’ma Zh. Eksp. Teor. Fiz. 79 320 (2004) [JETP Lett. 79 262 (2004)]
  129. Popov V S, Mur V D, Karnakov B M Pis’ma Zh. Eksp. Teor. Fiz. 66 213 (1997) [JETP Lett. 66 229 (1997)]; Phys. Lett. A 250 20 (1998)
  130. Mur V D, Karnakov B M, Popov V S Zh. Eksp. Teor. Fiz. 114 798 (1998) [JETP 87 433 (1998)]
  131. Karnakov B M, Mur V D, Popov V S Yad. Fiz. 62 1444 (1999) [Phys. At. Nucl. 62 1363 (1999)]
  132. Milosevic N, Krainov V P, Brabec T Phys. Rev. Lett. 89 193001 (2002)
  133. Milosevic N, Krainov V P, Brabec T J. Phys. B: At. Mol. Opt. Phys. 35 3515 (2002)
  134. Karnakov B M, Mur V D, Popov V S, quant-ph/0405158
  135. Brezin E, Itzykson C Phys. Rev. D 2 1191 (1970)
  136. Popov V S Pis’ma Zh. Eksp. Teor. Fiz. 13 261 (1971) [JETP Lett. 13 185 (1971)]; Zh. Eksp. Teor. Fiz. 61 1334 (1971) [Sov. Phys. JETP 34 709 (1972)]
  137. Popov V S Pis’ma Zh. Eksp. Teor. Fiz. 18 453 (1973) [JETP Lett. 18 255 (1973)]; Yad. Fiz. 19 155 (1974)
  138. Narozhnyi N B, Nikishov A I Zh. Eksp. Teor. Fiz. 65 862 (1973) [Sov. Phys. JETP 38 427 (1974)]
  139. Mostepanenko V M, Frolov V M Yad. Fiz. 19 885 (1974)
  140. Popov V S Pis’ma Zh. Eksp. Teor. Fiz. 74 151 (2001) [JETP Lett. 74 133 (2001)]; Zh. Eksp. Teor. Fiz. 121 1235 (2002) [JETP 94 1057 (2002)]
  141. Nikishov A I Nucl. Phys. B 21 346 (1970); Narozhnyi N B, Nikishov A I Yad. Fiz. 11 1072 (1970) [Sov. J. Nucl. Phys. 11 596 (1970)]
  142. Alkofer R et al. Phys. Rev. Lett. 87 193902 (2001)
  143. Ringwald A Phys. Lett. B 510 107 (2001)
  144. Popov V S Phys. Lett. A 298 83 (2002)
  145. Bulanov S S et al. Phys. Lett. A (2004, in press)
  146. Narozhny N B, Fofanov M S Zh. Eksp. Teor. Fiz. 117 867 (2000) [JETP 90 753 (2000)]; Phys. Lett. A 295 87 (2002)
  147. Oppenheimer J R Phys. Rev. 31 66 (1928)
  148. Yamabe T, Tachibana A, Silverstone H J Phys. Rev. A 16 877 (1977)
  149. Landau L D, Lifshitz E M Kvantovaya Mekhanika (Quantum Mechanics) 2nd ed. (Moscow: Fizmatlit, 1963) p. 327 [Translated into English (Oxford: Pergamon Press, 1965)]
  150. Reichle R, Helm H, Kiyan I Yu Phys. Rev. Lett. 87 243001 (2001)
  151. Kiyan I Yu, Helm H Phys. Rev. Lett. 90 183001 (2003)
  152. Agostini P et al. Phys. Rev. Lett. 42 1127 (1979)
  153. JST Intern. Symp. on Control of Molecules in Intense Laser Fields, Tokyo, Japan, Sept. 9 – 10, 2002, Program and Abstracts (Tokyo, 2002)
  154. Goldberger M L, Watson K M Collision Theory (New York: Wiley, 1964) [Translated into Russian (Moscow: Mir, 1967)]
  155. Curtis A R Coulomb Wave Functions (Cambridge: Univ. Press, 1964)
  156. Krainov V P, Xiong W, Chin S L Laser Phys. 2 467 (1992)
  157. Delone N B, Krainov V P Nelineinaya Ionizatsiya Atomov Lazernym Izlucheniem (Nonlinear Atom Ionization by Laser Radiation, Moscow: Fizmatlit, 2001)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions