Advertisement

Applied Magnetic Resonance

, Volume 47, Issue 11, pp 1207–1227 | Cite as

Consistent Paradigm of the Spectra Decomposition into Independent Resonance Lines

  • K. M. Salikhov
Original Paper

Abstract

The shapes of the spin resonance spectra have been analyzed theoretically in the case, when the kinetic equation for the spin density matrix is linear. Examples of the random relaxation processes which lead to the linear kinetic equations for the spin coherences have been presented in short. A consistent approach has been described for the decomposition of the multicomponent spectra into individual resonance lines based on finding independent collective modes for the evolution of quantum coherences. For the model situations with two and three transitions between the energy levels, the spectra are decomposed following this approach. The contributions of their collective evolution modes to the magnetic resonance spectra have been analyzed comprehensively. In the presence of the coherence transfer, the shapes of resonance lines corresponding to these modes can be a mixture of Lorentzian absorption and dispersion curves. The results obtained make it possible to visualize in detail transformations of the spectra as a consequence of the coherence transfer caused by random relaxation processes. This consistent approach makes it possible to describe on a common platform the transformations of spectra at any coherence transfer rate: from the very slow coherence transfer rate which leads to line broadening, then to the rate which results in the coalescence of the spectral lines and further to the very fast rate which leads to exchange narrowed spectra. It is shown that in the limit of the fast coherence transfer corresponding to the exchange narrowing effect one collective mode gives the dominant contribution to the experimental spectrum, namely, in-phase evolution of all transition coherences. The shape of the resonance corresponding to this in-phase evolution is described by the narrowed Lorentzian absorption curve.

Keywords

Electron Paramagnetic Resonance Spectrum Transverse Magnetization Spin Exchange Absorption Contribution Collective Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I am grateful to my colleagues at the Zavoisky Physical-Technical Institute of the Russian Academy of Sciences, in particular, Prof. V.F. Tarasov, Prof. V.K. Voronkova, Dr. R.T. Galeev, and M.M. Bakirov and to Prof. B.L. Bales, Prof. A.I. Kokorin for numerous discussions. I thank Dr. L.V. Mosina for language editing of the manuscript. This work was supported by the Grant for the fundamental research of the Presidium of the Russian Academy of Sciences 1.26 П.

References

  1. 1.
    K.I. Zamaraev, Yu.N. Molin, K.M. Salikhov, Spin Exchange (Nauka, Siberian Branch, Novosibirsk, 1977). (in Russian) Google Scholar
  2. 2.
    Yu.N. Molin, K.M. Salikhov, K.I. Zamaraev, Spin Exchange. Principles and Applications in Chemistry and Biology (Springer-Verlag, Berlin, 1980)Google Scholar
  3. 3.
    H.M. McConnell, J. Chem. Phys. 28, 430 (1956)ADSCrossRefGoogle Scholar
  4. 4.
    J.D. Currin, Phys. Rev. 126, 1996 (1962)ADSCrossRefGoogle Scholar
  5. 5.
    S. Ogawa, R.W. Fessenden, J. Chem. Phys. 41, 994 (1964)ADSCrossRefGoogle Scholar
  6. 6.
    R.R. Kuehne, T. Schaffhauser, A. Wokaun, R.R. Ernst, J. Magn. Reson. 35, 39 (1979)ADSGoogle Scholar
  7. 7.
    R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon Press, Oxford, 1987)Google Scholar
  8. 8.
    A. Hadson, G.R. Luckhurst, Chem. Rev. 69, 191 (1969)CrossRefGoogle Scholar
  9. 9.
    A. Abragam, Nuclear Magnetism. Principles of Nuclear Magnetism (Ch. VIII. Oxford University Press, London, 1961)Google Scholar
  10. 10.
    K.M. Salikhov, A.G. Semenov, Yu.D. Tsvetkov, Electron Spin Echo (Nauka, Siberian Branch, Novosibirsk, 1976). (in Russian) Google Scholar
  11. 11.
    R.T. Galeev, K.M. Salikhov, Khim. Fiz. 15, 48 (1996). in Russian Google Scholar
  12. 12.
    K.M. Salikhov, Appl. Magn. Reson. 38, 237 (2010)CrossRefGoogle Scholar
  13. 13.
    V.I. Smirnov, Kurs Vysshei Matematiki (Publishing House of the Literature on Physics and Mathematics, Moscow, 1958) Chapter 3, Section 27Google Scholar
  14. 14.
    K.M. Salikhov, M.M. Bakirov, R.T. Galeev, Appl. Magn. Reson. (2016). doi: 10.1007/s00723-016-0818-0 Google Scholar
  15. 15.
    B.L. Bales, D. Willett, J. Chem. Phys. 80, 2997 (1984)ADSCrossRefGoogle Scholar
  16. 16.
    B.L. Bales. in Biological Magnetic Resonance, ed. by L.J. Berliner, 8, 77 (1989)Google Scholar
  17. 17.
    B.L. Bales, M. Peric, J. Phys. Chem. B 101, 8707 (1997)CrossRefGoogle Scholar
  18. 18.
    B.L. Bales, M. Peric, J. Phys. Chem. A 106, 4846 (2002)CrossRefGoogle Scholar
  19. 19.
    M.N. Uvarov, J. Behrends, A.G. Maryasov, L.V. Kulik, Appl. Magn. Reson. 47, 781 (2016)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Zavoisky Physical-Technical InstituteRussian Academy of SciencesKazanRussia

Personalised recommendations