Issues

 / 

2015

 / 

January

  

Reviews of topical problems


Current progress in developing the nonlinear ionization theory of atoms and ions

 a,  a,  a,  b
a National Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
b Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

This paper reviews the status ofthe theory ofionization ofatoms and ions by intense laser radiation (Keldysh's theory). It discusses the applicability ofthe theory, its relation to the Landau—Dykhne method and its application tothe ionization ofatoms byultrashort nonmonochromatic laser pulses ofarbitrary shape. The semiclassical Imaginary Time Method is applied to describe electron sub-barrier motion using classical equations ofmotion with imaginary time t → it for anelectron inthe field ofanelectromagnetic wave. The paper discusses tunneling interference of transition amplitudes, a phenomenon generating fast oscillations inthe momentum distribution ofphotoelectrons. A nonperturbative account of the Coulomb interaction between the outgoing electron and the atomic residual causes significant changes in the photoelectron momentum distribution and in the level ionization rates, the latter usually increasing by orders of magnitude both for tunneling and multiphoton ionization. The effect of a static magnetic field onthe ionization rate and the magnetic cumulation process isexamined. The theory ofrelativistic tunneling isdiscussed, relativistic and spin corrections tothe ionization rate are calculated, and the applicability limits of the nonrelativistic Keldysh theory are determined. Finally, the application ofthe Fock method to the covariant description ofnonlinear ionization inthe relativistic regime isdiscussed.

Fulltext pdf (970 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0185.201501b.0003
Keywords: tunnel and multiphoton ionization, relativistic ionization, intense laser radiation, superstring magnetic field, Keldysh theory, imaginary time method
PACS: 03.65.Sq, 32.80.Fb, 32.80.Rm, 32.80.Wr, 34.80.Qb (all)
DOI: 10.3367/UFNe.0185.201501b.0003
URL: https://ufn.ru/en/articles/2015/1/b/
000352305900001
2-s2.0-84927132159
2015PhyU...58....3K
Citation: Karnakov B M, Mur V D, Popruzhenko S V, Popov V S "Current progress in developing the nonlinear ionization theory of atoms and ions" Phys. Usp. 58 3–32 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 11th, July 2014, revised: 4th, October 2014, 15th, July 2014

Îðèãèíàë: Êàðíàêîâ Á Ì, Ìóð Â Ä, Ïîïðóæåíêî Ñ Â, Ïîïîâ Â Ñ «Ñîâðåìåííîå ðàçâèòèå òåîðèè íåëèíåéíîé èîíèçàöèè àòîìîâ è èîíîâ» ÓÔÍ 185 3–34 (2015); DOI: 10.3367/UFNr.0185.201501b.0003

References (177) ↓ Cited by (63) Similar articles (20)

  1. Keldysh L V Zh. Eksp. Teor. Fiz. 47 1945 (1964); Keldysh L V Sov. Phys. JETP 20 1307 (1965)
  2. Nikishov A I, Ritus V I Zh. Eksp. Teor. Fiz. 50 255 (1966); Nikishov A I, Ritus V I Sov. Phys. JETP 23 168 (1966)
  3. Perelomov A M, Popov V S, Terent’ev M V Zh. Eksp. Teor. Fiz. 50 1393 (1966); Perelomov A M, Popov V S, Terent’ev M V Sov. Phys. JETP 23 924 (1966)
  4. Perelomov A M, Popov V S, Terent’ev M V Zh. Eksp. Teor. Fiz. 51 309 (1966); Perelomov A M, Popov V S, Terent’ev M V Sov. Phys. JETP 24 207 (1967)
  5. Popov V S, Kuznetsov V P, Perelomov A M Zh. Eksp. Teor. Fiz. 53 331 (1967); Popov V S, Kuznetsov V P, Perelomov A M Sov. Phys. JETP 26 222 (1968)
  6. Nikishov A I, Ritus V I Zh. Eksp. Teor. Fiz. 52 223 (1967); Nikishov A I, Ritus V I Sov. Phys. JETP 25 145 (1967)
  7. Perelomov A M, Popov V S Zh. Eksp. Teor. Fiz. 52 514 (1967); Perelomov A M, Popov V S Sov. Phys. JETP 25 336 (1967)
  8. Popruzhenko S V, Mur V D, Popov V S, Bauer D Phys. Rev. Lett. 101 193003 (2008)
  9. Popruzhenko S V, Mur V D, Popov V S, Bauer D Zh. Eksp. Teor. Fiz. 135 1092 (2009); Popruzhenko S V, Mur V D, Popov V S, Bauer D JETP 108 947 (2009)
  10. Karnakov B M, Mur V D, Popov V S, Popruzhenko S V Pis’ma ZhETF 93 256 (2011); Karnakov B M, Mur V D, Popov V S, Popruzhenko S V JETP Lett. 93 238 (2011)
  11. Faisal F H M J. Phys. B At. Mol. Phys. 6 L89 (1973)
  12. Reiss H R Phys. Rev. A 22 1786 (1980)
  13. Delone N B, Krainov V P Nelineinaya Ionizatsiya Atomov Lazernym Izlucheniem (M.: Fizmatlit, 2001)
  14. Becker W et al. Adv. At. Mol. Opt. Phys. 48 35 (2002)
  15. Popov V S Usp. Fiz. Nauk 174 921 (2004); Popov V S Phys. Usp. 47 855 (2004)
  16. Becker A, Faisal F H M J. Phys. B At. Mol. Opt. Phys. 38 R1 (2005)
  17. Milošević D B et al. J. Phys. B At. Mol. Opt. Phys. 39 R203 (2006)
  18. Popruzhenko S V J. Phys. B At. Mol. Opt. Phys. 47 204001 (2014)
  19. Agostini P, DiMauro L F Rep. Prog. Phys. 67 813 (2004)
  20. Mourou G A, Tajima T, Bulanov S V Rev. Mod. Phys. 78 309 (2006)
  21. Shchelev M Ya Usp. Fiz. Nauk 182 649 (2012); Schelev M Ya Phys. Usp. 55 607 (2012)
  22. Agostini P, DiMauro L F Adv. At. Mol. Opt. Phys. 61 117 (2012)
  23. Krausz F, Ivanov M Rev. Mod. Phys. 81 163 (2009)
  24. Andruszkow J et al. Phys. Rev. Lett. 85 3825 (2000)
  25. Shintake T et al. Nature Photon. 2 555 (2008)
  26. Emma P et al. Nature Photon. 4 641 (2010)
  27. Young L et al. Nature 466 56 (2010)
  28. Ionin A A Usp. Fiz. Nauk 182 773 (2012); Ionin A A Phys. Usp. 55 721 (2012)
  29. Free-electron laser FLASH, http://flash.desy.de
  30. Yanovsky V et al. Opt. Express 16 2109 (2008)
  31. http://www.extreme-light-infrastructure.eu
  32. XCELS, http://www.xcels.iapras.ru
  33. IZEST Project, http://www.izest.polytechnique.edu
  34. Dunne G V Eur. Phys. J. Special Topics 223 1055 (2014)
  35. Sauter F Z. Phys. 69 742 (1931); Sauter F Z. Phys. 73 547 (1932)
  36. Heisenberg W, Euler H Z. Phys. 98 714 (1936)
  37. Schwinger J Phys. Rev. 82 664 (1951)
  38. Di Piazza A et al. Rev. Mod. Phys. 84 1177 (2012)
  39. Narozhny N B, Fedotov A M Eur. Phys. J. Special Topics 223 1083 (2014)
  40. Paulus G G et al. Nature 414 182 (2001)
  41. Karnakov B M, Mur V D, Popov V S Pis’ma ZhETF 88 495 (2008); Karnakov B M, Mur V D, Popov V S JETP Lett. 88 423 (2008)
  42. Karnakov B M, Mur V D, Popov V S, Popruzhenko S V Phys. Lett. A 374 386 (2009)
  43. Alekseev A I Sbornik Zadach Po Klassicheskoi Elektrodinamike (M.: Nauka, 1977), zadacha 409
  44. Fuji T, Nomura Y Appl. Sci. 3 122 (2013)
  45. Wolkow D M Z. Phys. 94 250 (1935)
  46. Volkov D M Zh. Eksp. Teor. Fiz. 7 1286 (1937)
  47. Berestetskii V B, Lifshits E M, Pitaevskii L P Kvantovaya Elektrodinamika (M.: Nauka, 1989); Berestetskii V B, Lifshitz E M, Pitaevskii L P Quantum Electrodynamics (Oxford: Pergamon Press, 1982)
  48. Landau L D, Lifshits E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya (M.: Nauka, 1989); Landau L D, Lifshitz E M Quantum Mechanics: Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
  49. Rastunkov V S, Krainov V P J. Phys. B At. Mol. Opt. Phys. 40 2277 (2007)
  50. Krainov V P, Sofronov V S Phys. Rev. A 77 063418 (2008)
  51. Dykhne A M Zh. Eksp. Teor. Fiz. 41 1324 (1961); Dykhne A M Sov. Phys. JETP 14 941 (1962)
  52. Dykhne A M, Yudin G L Usp. Fiz. Nauk 125 377 (1978); Dykhne A M, Yudin G L Sov. Phys. Usp. 21 549 (1978)
  53. Landau L D, Lifshits E M Mekhanika (M.: Nauka, 1988); Landau L D, Lifshitz E M Mechanics (Oxford: Pergamon Press, 1976)
  54. Goldstein H Classical Mechanics (Cambridge, Mass.: Addison-Wesley Press, 1950); Goldstein G Klassicheskaya Mekhanika (M.: Gostekhizdat, 1957)
  55. Popov V S Yad. Fiz. 68 717 (2005); Popov V S Phys. Atom. Nucl. 68 686 (2005)
  56. Popov V S, Mur V D, Karnakov B M Pis’ma ZhETF 66 213 (1997); Popov V S, Mur V D, Karnakov B M JETP Lett. 66 229 (1997)
  57. Popov V S, Karnakov B M, Mur V D Pis’ma ZhETF 79 320 (2004); Popov V S, Karnakov B M, Mur V D JETP Lett. 79 262 (2004)
  58. Popov V S, Karnakov B M, Mur V D, Pozdnyakov S G Zh. Eksp. Teor. Fiz. 129 871 (2006); Popov V S, Karnakov B M, Mur V D, Pozdnyakov S G JETP 102 760 (2006); Popov V S, Karnakov B M, Mur V D, Pozdnyakov S G Preprint ¹22-05 (M.: ITEF, 2005)
  59. Popov V S Laser Phys. 10 1033 (2000)
  60. Popov V S Pis’ma ZhETF 73 3 (2001); Popov V S JETP Lett. 73 1 (2001)
  61. Popov V S Zh. Eksp. Teor. Fiz. 120 315 (2001); Popov V S JETP 93 278 (2001)
  62. Migdal A B Kachestvennye Metody v Kvantovoi Teorii (M.: Nauka, 1975), Gl. 1; Migdal A B Qualitative Methods In Quantum Theory (Reading, Mass.: W.A. Benjamin, 1977)
  63. Keldysh L Multiphoton ionization by a very short pulse, chastnoe soobshchenie
  64. Lindner F et al. Phys. Rev. Lett. 95 040401 (2005)
  65. Gopal R et al. Phys. Rev. Lett. 103 053001 (2009)
  66. Demkov Yu N, Drukarev G F Zh. Eksp. Teor. Fiz. 47 918 (1964); Demkov Yu N, Drukarev G F Sov. Phys. JETP 20 614 (1965)
  67. Paulus G G et al. Phys. Rev. Lett. 91 253004 (2003)
  68. Reichle R, Helm H, Kiyan I Yu Phys. Rev. Lett. 87 243001 (2001); Reichle R, Helm H, Kiyan I Yu Phys. Rev. A 68 063404 (2003)
  69. Kiyan I Yu, Helm H Phys. Rev. Lett. 90 183001 (2003)
  70. Bergues B et al. Phys. Rev. Lett. 95 263002 (2005)
  71. Bergues B et al. Phys. Rev. A 75 063415 (2007)
  72. Gazibegović-Busuladžić A, Milošević D B, Becker W Opt. Commun. 275 116 (2007)
  73. Gazibegović-Busuladžić A et al. Phys. Rev. Lett. 104 103004 (2010)
  74. Manakov N L et al. J. Phys. B At. Mol. Opt. Phys. 36 R49 (2003)
  75. Frolov M V et al. Phys. Rev. Lett. 91 053003 (2003)
  76. Bauer D, Milošević D B, Becker W Phys. Rev. A 72 023415 (2005)
  77. Korneev Ph A et al. New J. Phys. 14 055019 (2012)
  78. Chin S L et al. Phys. Rev. Lett. 61 153 (1988)
  79. Ammosov M V, Delone N B, Krainov V P Zh. Eksp. Teor. Fiz. 91 2008 (1986); Ammosov M V, Delone N B, Krainov V P Sov. Phys. JETP 64 11918 (1986)
  80. Delone N B, Krainov V P Usp. Fiz. Nauk 168 531 (1998); Delone N B, Krainov V P Phys. Usp. 41 469 (1998)
  81. Popov V S Usp. Fiz. Nauk 169 819 (1999); Popov V S Phys. Usp. 42 733 (1999)
  82. Goreslavski S P, Paulus G G, Popruzhenko S V, Shvetsov-Shilovskii N I Phys. Rev. Lett. 93 233002 (2004)
  83. Popov V S, Mur V D, Popruzhenko S V Pis’ma ZhETF 85 275 (2007); Popov V S, Mur V D, Popruzhenko S V JETP Lett. 85 223 (2007)
  84. Popruzhenko S V, Paulus G G, Bauer D Phys. Rev. A 77 053409 (2008)
  85. Popruzhenko S V, Bauer D J. Mod. Opt. 55 2573 (2008)
  86. Smirnova O, Spanner M, Ivanov M Phys. Rev. A 77 033407 (2008)
  87. Torlina L, Smirnova O Phys. Rev. A 86 043408 (2012)
  88. Potvliege R M Comp. Phys. Commun. 114 42 (1998)
  89. Bauer D, Koval P Comp. Phys. Commun. 174 396 (2006)
  90. Bashkansky M, Bucksbaum P H, Schumacher D W Phys. Rev. Lett. 60 2458 (1988)
  91. Paulus G G et al. Phys. Rev. Lett. 84 3791 (2000)
  92. Yan T-M, Popruzhenko S V, Vrakking M J J, Bauer D Phys. Rev. Lett. 105 253002 (2010)
  93. Sorokin A A et al. Phys. Rev. Lett. 99 213002 (2007)
  94. Torlina L et al. arXiv:1402.5620
  95. Torlina L et al. J. Phys. B At. Mol. Opt. Phys. 47 204021 (2014)
  96. Torlina L et al. Phys. Rev. A 86 043409 (2012)
  97. Huismans Y et al. Science 331 61 (2011)
  98. Marchenko T et al. Phys. Rev. A 84 053427 (2011)
  99. Castañeda Cortés H M, Popruzhenko S V, Bauer D, Pálffy A New J. Phys. 13 063007 (2011)
  100. Fedotov A M et al. Phys. Rev. Lett. 105 080402 (2010)
  101. Schenk M, Küger M, Hommelhoff P Phys. Rev. Lett. 105 257601 (2010)
  102. Popov V S, Karnakov B M, Mur V D Phys. Lett. A 229 306 (1997)
  103. Popov V S, Karnakov B M, Mur V D Zh. Eksp. Teor. Fiz. 113 1579 (1998); Popov V S, Karnakov B M, Mur V D JETP 86 860 (1998)
  104. Popov V S, Sergeev A V Pis’ma ZhETF 63 398 (1996); Popov V S, Sergeev A V JETP Lett. 63 417 (1996)
  105. Karnakov B M, Mur V D, Popov V S Pis’ma ZhETF 65 391 (1997); Karnakov B M, Mur V D, Popov V S JETP Lett. 65 405 (1997)
  106. Popov V S, Karnakov B M, Mur V D Zh. Eksp. Teor. Fiz. 115 1642 (1999); Popov V S, Karnakov B M, Mur V D JETP 88 902 (1999)
  107. Davydov A S Teoriya Tverdogo Tela (M.: Nauka, 1976)
  108. Sakharov A D Dokl. Akad. Nauk SSSR 165 65 (1965); Sakharov A D Sov. Phys. Dokl. 10 1045 (1966)
  109. Sakharov A D Usp. Fiz. Nauk 88 725 (1966); Sakharov A D Sov. Phys. Usp. 9 294 (1966)
  110. Sakharov A D Nauchnye Trudy (M.: OTF FIAN. Tsentrkom, 1995)
  111. Pavlovskii A I Sakharov A D. Nauchnye Trudy (M.: OTF FIAN. Tsentrkom, 1995) p. 85
  112. Terent’ev M V Istoriya Efira (M.: FAZIS, 1982)
  113. Dirak P A M Priroda (3) 68 (1972)
  114. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982); Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  115. Sarri G et al. Phys. Rev. Lett. 109 205002 (2012)
  116. Wagner U et al. Phys. Rev. E 70 026401 (2004)
  117. Popov V S, Karnakov B M Usp. Fiz. Nauk 184 273 (2014); Popov V S, Karnakov B M Phys. Usp. 57 257 (2014)
  118. Popov V S, Mur V D, Karnakov B M Pis’ma ZhETF 66 213 (1997); Popov V S, Mur V D, Karnakov B M JETP Lett. 66 229 (1997)
  119. Popov V S, Mur V D, Karnakov B M Phys. Lett. A 250 20 (1998)
  120. Mur V D, Karnakov B M, Popov V S Zh. Eksp. Teor. Fiz. 114 798 (1998); Mur V D, Karnakov B M, Popov V S JETP 87 433 (1998)
  121. Karnakov B M, Mur V D, Popov V S Yad. Fiz. 62 1444 (1999); Karnakov B M, Mur V D, Popov V S Phys. Atom. Nucl. 62 1363 (1999)
  122. Karnakov B M, Mur V D, Popov V S Zh. Eksp. Teor. Fiz. 132 331 (2007); Karnakov B M, Mur V D, Popov V S JETP 105 292 (2007)
  123. Fok V A Izv. AN SSSR (4 - 5) 551 (1937); Fock V A Phys. Z. Sowjetunion 12 404 (1937)
  124. Fok V A Raboty Po Kvantovoi Teorii Polya (L.: Izd-vo Leningr. un-ta, 1957) p. 141
  125. Popov V S Diss. ... dokt. fiz.-mat. nauk (M.: ITEF, 1974) p. 219
  126. Klein O Z. Phys. 37 895 (1926)
  127. Fock V Z. Phys. 38 242 (1926); Fock V Z. Phys. 39 226 (1926)
  128. Gordon W Z. Phys. 40 117 (1926)
  129. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 51 1492 (1966); Zel’dovich Ya B Sov. Phys. JETP 24 1006 (1967); Zel’dovich Ya B Usp. Fiz. Nauk 110 139 (1973); Zel’dovich Ya B Sov. Phys. Usp. 16 427 (1973)
  130. Ritus V I Zh. Eksp. Teor. Fiz. 51 1544 (1966); Ritus V I Sov. Phys. JETP 24 1041 (1967)
  131. Manakov N L, Rapoport L P Zh. Eksp. Teor. Fiz. 69 842 (1975); Manakov N L, Rapoport L P Sov. Phys. JETP 42 430 (1975)
  132. Berson I J J. Phys. B At. Mol. Opt. Phys. 8 3078 (1975)
  133. Manakov N L, Ovsiannikov V D, Rapoport L P Phys. Rep. 141 320 (1986)
  134. Okun’ L B Usp. Fiz. Nauk 180 871 (2010); Okun L B Phys. Usp. 53 835 (2010)
  135. Mur V D, Popov V S Teor. Mat. Fiz. 27 204 (1976); Mur V D, Popov V S Theor. Math. Phys. 27 429 (1976)
  136. Popov V S, Eletskii V L, Mur V D Zh. Eksp. Teor. Fiz. 71 856 (1976); Popov V S, Eletskii V L, Mur V D Sov. Phys. JETP 44 451 (1976)
  137. Karnakov B M, Mur V D, Popov V S Laser Phys. 15 1556 (2005)
  138. Dirac P A M The Principles Of Quantum Mechanics (Oxford: Clarendon Press, 1958); Dirak P Printsipy Kvantovoi Mekhaniki (M.: Nauka, 1979) p. 71
  139. Wightman A S Introduction To Some Aspects Of Relativistic Dynamics Of Quantized Fields (Princeton: Princeton Univ. Press, 1964)
  140. Zel’dovich Ya B, Popov V S Usp. Fiz. Nauk 105 403 (1971); Zeldovich Ya B, Popov V S Sov. Phys. Usp. 14 673 (1972)
  141. Richtmyer R D Principles Of Advanced Mathematical Physics (New York: Springer-Verlag, 1978); Rikhtmaier R Printsipy Sovremennoi Matematicheskoi Fiziki (M.: Mir, 1982), Gl. 5
  142. Voronov B L, Gitman D M, Tyutin I V Teor. Mat. Fiz. 150 41 (2007); Voronov B L, Gitman D M, Tyutin I V Theor. Math. Phys. 150 34 (2007)
  143. Pomeranchuk I Ya, Smorodinsky Ya A J. Phys. USSR 9 97 (1945)
  144. Zommerfel’d A Puti Poznaniya v Fizike (M.: Nauka, 1973) p. 191
  145. Gershtein S S, Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 57 654 (1969); Gershtein S S, Zel’dovich Ya B Sov. Phys. JETP 30 358 (1970)
  146. Zel’dovich Ya B i dr. Usp. Fiz. Nauk 105 780 (1971); Zel’dovich Ya B et al. Sov. Phys. Usp. 14 811 (1972)
  147. Brodsky S Comm. At. Mol. Phys. 4 109 (1973)
  148. Okun L B Comm. Nucl. Part. Phys. 6 25 (1974)
  149. Bandrauk A Molecules In Laser Fields (New York: Dekker, 1994)
  150. Posthumus J H Rep. Prog. Phys. 67 623 (2004)
  151. Stapelfeldt H, Seideman T Rev. Mod. Phys. 75 543 (2003)
  152. Becker W et al. Phys. Rev. A 76 033403 (2007)
  153. Busuladžić M, Milošević D B Phys. Rev. A 82 015401 (2010)
  154. Borzunov S V et al. Phys. Rev. A 88 033410 (2013)
  155. Gertsvolf M et al. Phys. Rev. Lett. 101 243001 (2008)
  156. Rajeev P P et al. Phys. Rev. Lett. 102 083001 (2009)
  157. Ghimire S et al. J. Phys. B At. Mol. Opt. Phys. 47 204030 (2014)
  158. Eckle P et al. Science 322 1525 (2008)
  159. Eckle P et al. Nature Phys. 4 565 (2008)
  160. Pfeiffer A N et al. Nature Phys. 8 76 (2011)
  161. Pfeiffer A N et al. Phys. Rev. Lett. 109 083002 (2012)
  162. Pfeiffer A N et al. Chem. Phys. 414 84 (2013)
  163. McDonald C R et al. Phys. Rev. Lett. 111 090405 (2013)
  164. Kheifets A S, Ivanov I A Phys. Rev. Lett. 105 233002 (2010)
  165. Dahlström J M, L’Huillier A, Maquet A J. Phys.. B At. Mol. Opt. Phys 45 183001 (2012)
  166. Nubbemeyer T et al. Phys. Rev. Lett. 101 233001 (2008)
  167. Blaga C I et al. Nature Phys. 5 335 (2009)
  168. Quan W et al. Phys. Rev. Lett. 103 093001 (2009)
  169. Wu C Y et al. Phys. Rev. Lett. 109 043001 (2012)
  170. Dura J, Camus N, Thai A Sci. Rep. 3 2675 (2013)
  171. Faisal F H M Nature Phys. 5 319 (2009)
  172. Liu C, Hatsagortsyan K Z Phys. Rev. Lett. 105 113003 (2010)
  173. Kästner A, Saalmann U, Rost J M Phys. Rev. Lett. 108 033201 (2012)
  174. Becker W et al. J. Phys. B At. Mol. Opt. Phys. 47 204022 (2014)
  175. Dimitrovski D et al. Phys. Rev. Lett. 113 103005 (2014)
  176. "Special issue on 50 years of optical tunneling" J. Phys. B At. Mol. Opt. Phys. 47 (20) (2014)
  177. Baz’ A I, Zel’dovich Ya B, Perelomov A M Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike (M.: Nauka, 1969), Gl. IX; Baz’A I, Zel’dovich Ya B, Perelomov A M Scattering, Reactions And Decay In Nonrelativistic Quantum Mechanics (Jerusalem: Israel Program for Scientific Translations, 1971)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions