Skip to main content
SpringerLink
Log in

Ionization of atoms in electric and magnetic fields and the imaginary time method

  • Atoms, Spectra, Radiation
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. D. Landau and E. M. Lifshitz, Quantum Mechanics. Nonrelativistic Theory, Pergamon, New York (1974).

    Google Scholar 

  2. B. M. Smirnov and M. I. Chibisov, Zh. Éksp. Teor. Fiz. 49, 841 (1965) [Sov. Phys. JETP 22, 585 (1965)].

    Google Scholar 

  3. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Zh. Éksp. Teor. Fiz. 50, 1393 (1966) [Sov. Phys. JETP 23, 924 (1966)]; Zh. Éksp. Teor. Fiz. 51, 309 (1966) [Sov. Phys. JETP 24, 207 (1966)].

    Google Scholar 

  4. A. I. Nikishov and V. I. Ritus, Zh. Éksp. Teor. Fiz. 50, 255 (1966) [Sov. Phys. JETP 23, 168 (1966)].

    Google Scholar 

  5. J. D. Bekenstein and J. B. Krieger, Phys. Rev. 188, 130 (1969).

    Article  ADS  MathSciNet  Google Scholar 

  6. T. Yamabe, A. Tachibana, and H. J. Silverstone, Phys. Rev. A 16, 877 (1977).

    Article  ADS  Google Scholar 

  7. Yu. N. Demkov and G. F. Drukarev, Zh. Éksp. Teor. Fiz. 47, 918 (1964) [Sov. Phys. JETP 20, 614 (1964)].

    Google Scholar 

  8. Yu. N. Demkov and V. N. Ostrovskii, Zero-Range Potentials and their Applications in Atomic Physics, Plenum Press, New York (1988).

    Google Scholar 

  9. V. S. Lisitsa, Usp. Fiz. Nauk 153, 379 (1987) [Sov. Phys. Usp. 30, 927 (1987)].

    MathSciNet  Google Scholar 

  10. L. P. Gor’kov and I. E. Dzyaloshinskii, Zh. Éksp. Teor. Fiz. 53, 717 (1967) [Sov. Phys. JETP 26, 449 (1967)].

    Google Scholar 

  11. B. R. Johnson, K. F. Scheibner, and D. Ferrely, Phys. Rev. Lett. 51, 2280 (1983).

    Article  ADS  Google Scholar 

  12. Yu. N. Demkov, B. S. Monozon, and V. N. Ostrovskii, Zh. Éksp. Teor. Fiz. 57, 1431 (1969) [Sov. Phys. JETP 30, 775 (1969)].

    Google Scholar 

  13. E. A. Solov’ev, Zh. Éksp. Teor. Fiz. 85, 109 (1983) [Sov. Phys. JETP 58, 63 (1983)].

    ADS  Google Scholar 

  14. N. L. Manakov, S. I. Marmo, and V. D. Ovsyanikov, Zh. Éksp. Teor. Fiz. 91, 404 (1986) [Sov. Phys. JETP 64, 236 (1986)].

    Google Scholar 

  15. V. M. Vaiberg, V. S. Popov, and A. V. Sergeev, Zh. Éksp. Teor. Fiz. 98, 847 (1990) [Sov. Phys. JETP 71, 470 (1990)].

    Google Scholar 

  16. V. S. Melezhik, Phys. Rev. A 48, 4528 (1993).

    Article  ADS  Google Scholar 

  17. R. J. Damberg and V. V. Kolosov, J. Phys. B 9, 3149 (1976); 11, 1921 (1978).

    ADS  Google Scholar 

  18. H. J. Silverstone, Phys. Rev. A 18, 1853 (1978); Phys. Rev. Lett. 43, 1498 (1979).

    Article  ADS  Google Scholar 

  19. S. P. Alliluev, V. L. Eletsky, and V. S. Popov, Phys. Lett. A 73, 103 (1979); S. P. Alliluev, V. M. Vainberg, V. L. Eletskii, and V. S. Popov, Zh. Éksp. Teor. Fiz. 82, 77 (1982) [Sov. Phys. JETP 55, 46 (1982)].

    Article  ADS  Google Scholar 

  20. V. Franceschini, V. Grecchi, and H. J. Silverstone, Phys. Rev. A 32, 1338 (1985).

    Article  ADS  Google Scholar 

  21. V. M. Vainberg, V. D. Mur, V. S. Popov et al., JETP Lett. 44, 9 (1986); JETP Lett. 46, 225 (1987); Zh. Éksp. Teor. Fiz. 93, 450 (1987) [Sov. Phys. JETP 66, 258 (1987)].

    ADS  Google Scholar 

  22. V. S. Popov, V. D. Mur, A. V. Sergeev et al., Phys. Lett. A 124, 77 (1987); 149, 418, 425 (1990).

    Article  ADS  Google Scholar 

  23. V. S. Popov, Phys. Lett. A 173, 63 (1993).

    ADS  Google Scholar 

  24. F. M. Fernandez, Phys. Rev. A 54, 1206 (1996).

    ADS  Google Scholar 

  25. M. C. Chu and H. Friedrich, Phys. Rev. A 28, 1423, 3651 (1983); 29, 675 (1984).

    ADS  Google Scholar 

  26. J. Main and G. Wunner, J. Phys. B 27, 2835 (1994).

    Article  ADS  Google Scholar 

  27. J. H. Wang and C. S. Hsue, Phys. Rev. A 52, 4508 (1995).

    ADS  Google Scholar 

  28. I. Seipp and W. Shweizer, Astron. Astrophys. 318, 990 (1997).

    ADS  Google Scholar 

  29. L. P. Kotova, A. M. Perelomov, and V. S. Popov, Zh. Éksp. Teor. Fiz. 54, 1151 (1968) [Sov. Phys. JETP 27, 616 (1968)].

    Google Scholar 

  30. G. F. Drukarev and B. S. Monozon, Zh. Éksp. Teor. Fiz. 61, 956 (1971) [Sov. Phys. JETP 34, 509 (1971)].

    Google Scholar 

  31. S. P. Andreev and V. A. Polunin, JETP Lett. 42, 190 (1985).

    ADS  Google Scholar 

  32. L. V. Keldysh, Zh. Éksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1964)].

    Google Scholar 

  33. B. A. Zon, N. L. Manakov, and L. P. Rapoport, Zh. Éksp. Teor. Fiz. 61, 968 (1971) [Sov. Phys. JETP 34, 515 (1971)]; L. P. Rapoport, B. A. Zon, and N. L. Manakov, The Theory of Many-Photon Processes in Atoms [in Russian], Atomizdat, Moscow (1978).

    Google Scholar 

  34. A. I. Nikishov and V. I. Ritus, Zh. Éksp. Teor. Fiz. 52, 223 (1967) [Sov. Phys. JETP 25, 145 (1967)].

    Google Scholar 

  35. A. M. Perelomov and V. S. Popov, Zh. Éksp. Teor. Fiz. 52, 514 (1967) [Sov. Phys. JETP 25, 336 (1967)].

    Google Scholar 

  36. V. S. Popov, V. P. Kuznetsov, and A. M. Perelomov, Zh. Éksp. Teor. Fiz. 53, 331 (1967) [Sov. Phys. JETP 26, 222 (1967)].

    Google Scholar 

  37. B. M. Karnakov, V. D. Mur, and V. S. Popov, JETP Lett. 65, 405 (1997).

    Article  ADS  Google Scholar 

  38. V. S. Popov and A. V. Sergeev, JETP Lett. 63, 417 (1996).

    Article  ADS  Google Scholar 

  39. V. S. Popov, B. M. Karnakov, and V. D. Mur, Phys. Lett. A 229, 306 (1997).

    Article  ADS  Google Scholar 

  40. A. S. Davydov, Solid State Theory [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  41. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  42. A. A. Radtsig and B. M. Smirnov, Parameters of Atoms and Atomic Ions [in Russian], É nergoatomizdat, Moscow (1968).

    Google Scholar 

  43. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).

    Google Scholar 

  44. D. R. Herschbach, J. Avery, and O. Goscinsky (eds), Dimensional Scaling in Chemical Physics, Kluwer Academic, Dordrecht (1993).

    Google Scholar 

  45. C. A. Tsipis, V. S. Popov, D. R. Herschbach, and J. S. Avery (eds), New Methods in Quantum Theory, Kluwer Academic, Dordrecht (1996).

    Google Scholar 

  46. S. P. Alliluev and V. S. Popov, Zh. Éksp. Teor. Fiz. 104, 3569 (1993) [JETP 77, 701 (1993)].

    MathSciNet  Google Scholar 

  47. V. S. Popov, V. D. Mur, and B. M. Karnakov, JETP Lett. 66, 229 (1997).

    Article  ADS  Google Scholar 

  48. S. P. Andreev, B. M. Karnakov, and V. D. Mur, JETP Lett. 37, 187 (1983); Teor. Mat. Fiz. 64, 287 (1985).

    ADS  Google Scholar 

  49. L. I. Magarill and S. K. Savvinykh, Zh. Éksp. Teor. Fiz. 60, 175 (1971) [Sov. Phys. JETP 33, 97 (1971)].

    Google Scholar 

  50. S. P. Andreev, B. M. Karnakov, V. D. Mur, and V. A. Polunin, Zh. Éksp. Teor. Fiz. 86, 866 (1984) [Sov. Phys. JETP 59, 506 (1984)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical and Experimental Physics, 117259, Moscow, Russia

    V. S. Popov

  2. Moscow Engineering Physics Institute (Technical University), 115409, Moscow, Russia

    B. M. Karnakov & V. D. Mur

Authors
  1. V. S. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. M. Karnakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. D. Mur
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Zh. Éksp. Teor. Fiz. 113, 1579–1605 (May 1998)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popov, V.S., Karnakov, B.M. & Mur, V.D. Ionization of atoms in electric and magnetic fields and the imaginary time method. J. Exp. Theor. Phys. 86, 860–874 (1998). https://doi.org/10.1134/1.558557

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.558557

Keywords

Search

Navigation