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Operator Perturbation Theory for Atomic Systems in a Strong DC Electric Field

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Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 27))

Abstract

A consistent uniform quantum approach to the solution of the non-stationary state problems including the DC (Direct Current) strong-field Stark effect and also scattering problem is presented. It is based on the operator form of the perturbation theory for the Schrödinger equation. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. The zero-order Hamiltonian possessing only stationary states is determined only by its spectrum without specifying its explicit form. The method allows calculating the resonance complex energies and widths plus a complete orthogonal complementary of the scattering state functions. The calculation results of the Stark resonance energies and widths for the hydrogen and sodium atoms are presented and compared with other theoretical data.

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References

  1. Stark J (1914) Ann Phys 43:965

    Article  CAS  Google Scholar 

  2. Bethe HA, Salpeter EE (1957) Quantum mechanics of one- and two-electron atoms. Springer, Berlin

    Book  Google Scholar 

  3. Landau LD, Lifshitz EM (1977) Quantum mechanics. Pergamon, Oxford

    Google Scholar 

  4. Stebbings RF, Dunning FB (eds) (1983) Rydberg states of atoms and molecules. Cambridge University Press, Cambridge

    Google Scholar 

  5. Nayfeh MN, Clark CW (eds) (1984) Atomic excitation and recombination in external fields. NBS, Gaithersburg

    Google Scholar 

  6. Glushkov AV (2005) Atom in an electromagnetic field. KNT, Kiev, pp 1–450

    Google Scholar 

  7. Lisitsa VS (1987) Phys Usp 153:369

    Article  Google Scholar 

  8. Ivanov LN, Letokhov VS (1975) Quantum Electron 2:585

    CAS  Google Scholar 

  9. Ivanov LN, Ivanova EP (1979) At Data Nucl Data Tables 24:95

    Article  CAS  Google Scholar 

  10. Glushkov AV, Ivanov LN (1992) Phys Lett A 170:33

    Article  CAS  Google Scholar 

  11. Ivanova EP, Grant IP (1998) J Phys B, At Mol Opt Phys 31:2871

    Article  CAS  Google Scholar 

  12. Glushkov AV (2012) In: Nishikawa K, Maruani J, Brändas E, Delgado-Barrio G, Piecuch P (eds) Advances in the theory of quantum systems in chemistry and physics. Frontiers in theoretical physics and chemistry, vol 26. Springer, Berlin, pp 231–254

    Chapter  Google Scholar 

  13. Delone NB, Fedorov MV (1989) Phys Usp 158:215

    Article  CAS  Google Scholar 

  14. Siegert AJF (1939) Phys Rev 56:750

    Article  CAS  Google Scholar 

  15. Mendelson LB (1968) Phys Rev 176:90

    Article  Google Scholar 

  16. Dolgov AD, Turbiner AV (1977) Phys Lett A 77:15

    Article  Google Scholar 

  17. Alexander MH (1969) Phys Rev 178:34

    Article  CAS  Google Scholar 

  18. Rao J, Liu W, Li B (1994) Phys Rev A 50:1916

    Article  CAS  Google Scholar 

  19. Rao J, Li B (1995) Phys Rev A 51:4526

    Article  CAS  Google Scholar 

  20. Meng H-Y, Zhang Y-X, Kang S, Shi T-Y, Zhan M-S (2008) J Phys B, At Mol Opt Phys 41:155003

    Article  Google Scholar 

  21. Hehenberger M, McIntosh HV, Brändas E (1974) Phys Rev A 10:1494

    Article  CAS  Google Scholar 

  22. Hehenberger M, McIntosh HV, Brändas E (1975) Phys Rev A 12:1

    Article  Google Scholar 

  23. Brändas E, Froelich P (1977) Phys Rev A 16:2207

    Article  Google Scholar 

  24. Brändas E, Hehenberger M, McIntosh HV (1975) Int J Quant Chem 9:103

    Article  Google Scholar 

  25. Rittby M, Elander N, Brändas E (1981) Phys Rev A 24:1636

    Article  CAS  Google Scholar 

  26. Froelich P, Davidson ER, Brändas E (1983) Phys Rev A 28:2641

    Article  CAS  Google Scholar 

  27. Lipkin N, Moiseyev N, Brändas E (1989) Phys Rev A 40:549

    Article  CAS  Google Scholar 

  28. Rittby M, Elander N, Brändas E (1983) Int J Quant Chem 23:865

    Article  CAS  Google Scholar 

  29. Simon B (1979) Phys Lett A 7(1):211

    Article  Google Scholar 

  30. Nicolaides CA, Beck DR (1978) Phys Lett A 65:11

    Article  Google Scholar 

  31. Brändas E, Froelich P, Obcemea CH, Elander N, Rittby M (1982) Phys Rev A 26:3656

    Article  Google Scholar 

  32. Engdahl E, Brändas E, Rittby M, Elander N (1986) J Math Phys 27:2629

    Article  Google Scholar 

  33. Engdahl E, Brändas E, Rittby M, Elander N (1988) Phys Rev A 37:3777

    Article  CAS  Google Scholar 

  34. Brändas E, Elander N (eds) (1989) Resonances: the unifying route towards the formulation of dynamical processes—foundations and applications in nuclear, atomic and molecular physics. Lecture notes in physics, vol 325. Springer, Berlin, pp 1–564

    Book  Google Scholar 

  35. Scrinzi A, Elander N (1993) J Chem Phys 98:3866

    Article  CAS  Google Scholar 

  36. Ostrovsky VN, Elander N (2005) Phys Rev A 71:052707

    Article  Google Scholar 

  37. Sigal JM (1988) Commun Math Phys 119:287

    Article  Google Scholar 

  38. Herbst IW, Simon B (1978) Phys Rev Lett 41:67

    Article  CAS  Google Scholar 

  39. Silverstone HJ, Adams BG, Cizek J, Otto P (1979) Phys Rev Lett 43:1498

    Article  CAS  Google Scholar 

  40. Cerjan C, Hedges R, Holt C, Reinhardt WP, Scheibner K, Wendoloski JJ (1978) Int J Quant Chem 14:393

    Article  CAS  Google Scholar 

  41. Maquet A, Chu SI, Reinhardt WP (1983) Phys Rev A 27:2946

    Article  CAS  Google Scholar 

  42. Damburg RJ, Kolosov VV (1976) J Phys B, At Mol Phys 9:3149

    Article  CAS  Google Scholar 

  43. Luc-Koenig E, Bachelier A (1980) J Phys B, At Mol Phys 13:1743

    Article  CAS  Google Scholar 

  44. Reinhardt WP (1982) Int J Quant Chem 21:133

    Article  CAS  Google Scholar 

  45. Franceschini V, Grecchi V, Silverstone HJ (1985) Phys Rev A 32:1338

    Article  CAS  Google Scholar 

  46. Benassi L, Grecchi V (1980) J Phys B, At Mol Phys 13:911–924

    Article  CAS  Google Scholar 

  47. Farrelly D, Reinhardt WP (1983) J Phys B, At Mol Phys 16:2103

    Article  CAS  Google Scholar 

  48. Kolosov VV (1987) J Phys B, At Mol Phys 20:2359

    Article  CAS  Google Scholar 

  49. Filho O, Fonseca A, Nazareno H, Guimarães P (1990) Phys Rev A 42:4008

    Article  CAS  Google Scholar 

  50. Kondratovich VD, Ostrovsky VN (1984) J Phys B, At Mol Phys 17:2011

    Article  CAS  Google Scholar 

  51. Anokhin SB, Ivanov MV (1984) Opt Spectrosc 59:499

    Google Scholar 

  52. Telnov DA (1989) J Phys B, At Mol Opt Phys 22:1399–1403

    Article  Google Scholar 

  53. Ho Y-K (1983) Phys Rep 99:3

    Article  Google Scholar 

  54. Ivanov IA, Ho Y-K (2004) Phys Rev A 69:023407

    Article  Google Scholar 

  55. González-Férez R, Schweizer W (2000) In: Hernández-Laguna A, Maruani J, McWeeny R, Wilson S (eds) Quantum systems in chemistry and physics. Progress in theoretical chemistry and physics, vol 2/3. Springer, Berlin, p 17

    Chapter  Google Scholar 

  56. Glushkov AV, Ivanov LN (1992) Proc of 3rd symposium on atomic spectroscopy. Moscow, Chernogolovka

    Google Scholar 

  57. Glushkov AV, Ivanov LN (1993) J Phys B, At Mol Phys 26:L379

    Article  CAS  Google Scholar 

  58. Glushkov AV, Malinovskaya SV, Ambrosov SV, Shpinareva IM, Troitskaya OV (1997) J Tech Phys 38:215

    CAS  Google Scholar 

  59. Glushkov AV, Ambrosov SV, Ignatenko AV, Korchevsky DA (2004) Int J Quant Chem 99:936

    Article  CAS  Google Scholar 

  60. Glushkov AV, Loboda AV (2007) J Appl Spectrosc (Springer) 74:305

    Article  CAS  Google Scholar 

  61. Glushkov AV, Khetselius OYu, Loboda AV, Svinarenko AA (2008) In: Wilson S, Grout PJ, Maruani J, Delgado-Barrio G, Piecuch P (eds) Frontiers in quantum systems in chemistry and physics. Progress in theoretical chemistry and physics, vol 18. Springer, Berlin, pp 523–588

    Google Scholar 

  62. Glushkov AV, Khetselius O, Malinovskaya S (2008) Eur Phys J T 160:195

    Google Scholar 

  63. Glushkov AV, Khetselius OYu, Svinarenko AA, Prepelitsa GP (2011) In: Duarte FJ (ed) Coherence and ultrashort pulsed emission. Intech, Vienna, pp 159–186

    Google Scholar 

  64. Zimmerman ML, Littman MG, Kash MM, Kleppner D (1979) Phys Rev A 20:2251

    Article  CAS  Google Scholar 

  65. Harmin DA (1982) Phys Rev A 26:2656

    Article  CAS  Google Scholar 

  66. Popov V, Mur V, Sergeev A, Weinberg V (1990) Phys Lett A 149:418, 425

    Google Scholar 

  67. Grutter M, Zehnder O, Softley T, Merkt F (2008) J Phys B, At Mol Opt Phys 41:115001

    Article  Google Scholar 

  68. Stambulchik E, Maron Y (2008) J Phys B, At Mol Opt Phys 41:095703

    Article  Google Scholar 

  69. Dunning FB, Mestayer JJ, Reinhold CO, Yoshida S, Burgdörfer J (2009) J Phys B, At Mol Opt Phys 42:022001

    Article  Google Scholar 

  70. Bryant HC, Clark DA, Butterfield KB et al. (1983) Phys Rev A 27:2889

    Article  CAS  Google Scholar 

  71. Glushkov AV, Ambrosov S, Khetselius OYu, Loboda AV, Gurnitskaya E (2006) In: Julien J-P, Maruani J, Mayou D, Wilson S, Delgado-Barrio G (eds) Recent advances in theoretical physics and chemistry systems. Progress in theoretical chemistry and physics, vol 15. Springer, Berlin, pp 285–300

    Chapter  Google Scholar 

  72. Khetselius OYu (2012) J Phys Conf Ser 397:012012

    Article  Google Scholar 

  73. Khetselius OYu (2009) Int J Quant Chem 109:3330

    Article  CAS  Google Scholar 

  74. Khetselius O, Florko T, Svinarenko A, Tkach T (2013) Phys Scr T 153:01437

    Google Scholar 

  75. Ivanova EP, Ivanov LN, Glushkov AV, Kramida AE (1985) Phys Scr 32:512

    Article  Google Scholar 

  76. Ivanova EP, Glushkov AV (1986) J Quant Spectrosc Radiat Transf 36:127

    Article  CAS  Google Scholar 

  77. Benvenuto F, Casati G, Shepelyansky DL (1994) Z Phys B 94:481

    Article  CAS  Google Scholar 

  78. Buchleitner A, Delande D (1997) Phys Rev A 55:1585

    Article  Google Scholar 

  79. Gallagher TF, Noel M, Griffith MW (2000) Phys Rev A 62:063401

    Article  Google Scholar 

  80. Glushkov AV, Ambrosov SV (1996) J Tech Phys 37:347

    CAS  Google Scholar 

  81. Glushkov AV, Khokhlov V, Tsenenko I (2004) Nonlinear Process Geophys 11:285

    Google Scholar 

  82. Glushkov A, Khohlov V, Loboda N, Bunyakova Yu (2008) Atmos Environ 42:7284

    Article  Google Scholar 

  83. Glushkov AV, Khetselius OYu, Malinovskaya SV (2008) Mol Phys 106:1257

    Article  CAS  Google Scholar 

  84. Glushkov AV, Rusov VD, Ambrosov SV, Loboda AV (2003) In: Fazio G, Hanappe F (eds) New projects and new lines of research in nuclear physics. World Scientific, Singapore, pp 126–142

    Chapter  Google Scholar 

  85. Glushkov AV (2005) In: Grzonka D, Czyzykiewicz R, Oelert W, Rozek T, Winter P (eds) Low energy antiproton physics, vol 796. AIP, New York, pp 206–210

    Google Scholar 

  86. Glushkov AV (2007) In: Krewald S, Machner H (eds) Meson-nucleon physics and the structure of the nucleon, vol 2. IKP, Juelich. SLAC eConf C070910 (Menlo Park, CA, USA, 2007), pp 111–117

    Google Scholar 

  87. Glushkov AV, Khetselius OYu, Loboda AV, Malinovskaya SV (2007) In: Krewald S, Machner H (eds) Meson-nucleon physics and the structure of the nucleon, vol 2. IKP, Juelich. SLAC eConf C070910 (Menlo Park, CA, USA, 2007), pp 118–122

    Google Scholar 

  88. Glushkov AV, Khetselius OYu, Lovett L, Gurnitskaya EP, Dubrovskaya YuV, Loboda AV (2009) Int J Mod Phys A, Part Fields Nucl Phys 24:611

    CAS  Google Scholar 

  89. Glushkov AV, Khetselius OYu, Lovett L (2010) In: Piecuch P, Maruani J, Delgado-Barrio G, Wilson S (eds) Advances in the theory of atomic and molecular systems: dynamics, spectroscopy, clusters, and nanostructures. Progress in theoretical chemistry and physics, vol 20. Springer, Berlin, pp 125–151

    Chapter  Google Scholar 

  90. Glushkov AV, Khetselius OYu, Svinarenko AA (2012) In: Hoggan P, Brändas E, Maruani J, Delgado-Barrio G, Piecuch P (eds) Advances in the theory of quantum systems in chemistry and physics. Progress in theoretical chemistry and physics, vol 22. Springer, Berlin, pp 51–70

    Chapter  Google Scholar 

  91. Glushkov AV (2008) Relativistic quantum theory. Quantum mechanics of atomic systems Astroprint, Odessa, pp 1–704

    Google Scholar 

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Acknowledgements

The author would like to thank Prof. Jean Maruani and Prof. Matti Hotokka (the organizer of QSCP XVII-2012, Turku, Finland) for the friendly cooperation and invaluable advises.

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Authors and Affiliations

  1. Odessa State University—OSENU, L’vovskaya str., 15, Odessa-9, 65016, Ukraine

    Alexander V. Glushkov

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  1. Alexander V. Glushkov
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Correspondence to Alexander V. Glushkov .

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Editors and Affiliations

  1. Department of Physical Chemistry, Åbo Akademi University, Turku, Finland

    Matti Hotokka

  2. Uppsala University Department of Quantum Chemistry, Uppsala, Sweden

    Erkki J. Brändas

  3. Laboratoire de Chimie Physique, Paris, France

    Jean Maruani

  4. Instituto de Física Fundamental, CSIC, Madrid, Spain

    Gerardo Delgado-Barrio

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Glushkov, A.V. (2013). Operator Perturbation Theory for Atomic Systems in a Strong DC Electric Field. In: Hotokka, M., Brändas, E., Maruani, J., Delgado-Barrio, G. (eds) Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology. Progress in Theoretical Chemistry and Physics, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-01529-3_9

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