Skip to main content
Log in

Siegert state approach to quantum defect theory

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R-matrix but rather by the equation 1 − RnnLn = 0, relating R-matrix element Rnn to decay channel logarithmic derivative Ln. Extension of Siegert state equation to multichannel system results in the replacement of channel R- matrix element Rnn by its reduced counterpart Rnn. One proves the Siegert state is a pole, (1 − RnnLn)−1, of multichannel collision matrix. The Siegert equation 1 − RnnLn = 0, (n – Rydberg channel), implies basic results of Quantum Defect Theory as Seaton’s theorem, complex quantum defect, channel resonances and threshold continuity of averaged multichannel collision matrix elements.

Graphical abstract

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

Access this article

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. A.J.F. Siegert, Phys. Rev. 56, 750 (1939)

    Article  ADS  Google Scholar 

  2. A.M. Perelomov, Ya.B. Zel’dovich, Quantum Mechanics; Selected Topics (World Scientific, Singapore, 1998)

  3. V.I. Kukulin, V.M. Krasnopolsky, J. Horacek, Theory of Resonances: Principles and Applications (Kluwer Academic Publishers, Prague, 1989)

  4. E. Hernandez, A. Jauregui, A. Mondragon, Phys. Rev. A 67, 022721 (2003)

    Article  ADS  Google Scholar 

  5. N. Michel, W. Nazarewicz, M. Ploszajczak, T. Vertse, J. Phys. G 36, 013101 (2009)

    Article  ADS  Google Scholar 

  6. A.M. Lane, D. Robson, Phys. Rev. 151, 774 (1966)

    Article  ADS  Google Scholar 

  7. D. Robson, A.M. Lane, Phys. Rev. 161, 982 (1967)

    Article  ADS  Google Scholar 

  8. C. Bloch, Nucl. Phys. 4, 503 (1957)

    Article  Google Scholar 

  9. A.M. Lane, R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958)

    Article  ADS  MathSciNet  Google Scholar 

  10. D. Robson, in Nuclear spectroscopy and reactions, edited by J. Cerny (Academic Press, New York, 1975)

  11. D. Robson, in Isospin in nuclear physics, edited by D.H. Wilkinson (North-Holland Publ. Comp., Amsterdam, 1969)

  12. S.N. Abramovich, B.Ya Guzhovskii, L.M. Lazarev, Fizika Elem. Chastitsy i Atomnogo Yadra 23, 305 (1992)

    Google Scholar 

  13. A.M. Lane, J. Phys. B 19, 253 (1986)

    Article  ADS  Google Scholar 

  14. A.I. Baz, I.B. Zeldovich, A.M. Perelomov, Rasseianie, Reaktsii i Raspady v Nereliativistskoi Kvantovoi Mekhanike (Nauka, Moskva, 1971)

  15. A.I. Baz, I.B. Zeldovich, A.M. Perelomov, Scattering, reactions and decay in nonrelativistic quantum mechanics (Israel Program for Scientific Translations, Jerusalem, English version of first edition, 1966)

  16. L.D. Landau, E.M. Lifshitz, Mecanique Quantique (Mir, Moscou, 1980)

  17. C. Hategan, R.A. Ionescu, J. Phys. B 28, L681 (1995)

    Article  ADS  Google Scholar 

  18. M.J. Seaton, Rep. Progr. Phys. 46, 167 (1983)

    Article  ADS  Google Scholar 

  19. P.G. Burke, R-Matrix Theory of Atomic Collisions (Springer, Berlin, 2011)

  20. I.I. Sobelman, L.A. Vainshtein, E.A. Yukov, Excitation of Atoms and Broadening of Spectral Lines (Springer, Berlin, 1981)

  21. U. Fano, Comm. At. Mol. Phys. 10, 223 (1981)

    Google Scholar 

  22. U. Fano, A.R.P. Rau, Atomic Collisions and Spectra (Academic, Orlando, 1986)

  23. C.H. Greene, A.R.P. Rau, U. Fano, Phys. Rev. 26, 2441 (1982)

    Article  ADS  Google Scholar 

  24. M. Aymar, C.H. Greene, E. Luc-Koenig, Rev. Mod. Phys. 68, 1015 (1996)

    Article  ADS  Google Scholar 

  25. C.H. Greene, Ch Jungen, Adv. At. Mol. Phys. 21, 51 (1985)

    Article  ADS  Google Scholar 

  26. G.F. Drukarev, Stolknovenyia Elektronov s Atomami i Molekulami (Nauka, Moskva, 1978)

  27. G.F. Drukarev, Collisions of Electrons with Atoms and Molecules (Plenum Press, New York, 1987)

  28. V. Kokoouline, C.H. Greene, Phys. Rev. A 68, 012703 (2003)

    Article  ADS  Google Scholar 

  29. O.I. Tolstikhin, V.N. Ostrovsky, H. Nakamura, Phys. Rev. Lett. 79, 2026 (1997)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Remus Amilcar Ionescu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hategan, C., Ionescu, R.A. & Wolter, H.H. Siegert state approach to quantum defect theory. Eur. Phys. J. D 74, 71 (2020). https://doi.org/10.1140/epjd/e2020-100563-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2020-100563-2

Keywords

Navigation