Channeling Radiation — Quantum Theory

  • J. U. Andersen
  • E. Bonderup
  • E. Laegsgaard
Part of the Topics in Current Physics book series (TCPHY, volume 38)


A general introduction to channeling and channeling radiation is followed by a derivation of a wave equation for the transverse motion of a channeled particle. Owing to the predominance of forward scattering, the deoth of penetration can be treated as a time variable in this equation, and it assumes the form of a time-dependent Schrödinger equation. It is obtained from the Klein-Gordon equation, including interaction with the radiation field. The neglect of spin simplifies the formulation considerably, and it is argued to be well justified in the description of channeling radiation. The treatment also allows a natural inclusion of interaction with the crystal degrees of freedom, which leads to instability of channeling states and line broadening of the radiation. Both thermal and electronic contributions to scattering are discussed in detail, and their influence on the frequency distribution and intensity of channeling radiation is illustrated by comparisons with exoeriment. This scattering is important for the potential applications considered in the last section.


Transverse Momentum Transverse Energy Transverse State Transverse Motion Line Energy 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 6.1
    J. Lindhard: K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34, No. 14 (1965)Google Scholar
  2. 6.2
    D.S. Gemmell: Rev. Mod. Phys. 46, 129 (1974)ADSCrossRefGoogle Scholar
  3. 6.3
    J.U. Andersen, E. Bonderup, R.H. Pantell: Ann. Rev. Nucl. Part Sci. 33, 453 (1983)ADSCrossRefGoogle Scholar
  4. 6.4
    H. Überall: Phys. Rev. 103, 1055 (1956)ADSCrossRefGoogle Scholar
  5. 6.5
    M.L. Ter-Mikaelian: High-Energy Electromagnetic Processes in Condensed Media (Wiley-Interscience, New York 1972)Google Scholar
  6. 6.6
    M.A. Kumakhov: Phys. Lett. 57A, 17 (1976)Google Scholar
  7. 6.7
    J.U. Andersen, S.K. Andersen, W.M. Augustyniak: K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 39, No. 10 (1977)Google Scholar
  8. 6.8
    M.A. Kumakhov: Phys. Status Solidi (b) 84, 41 (1977)ADSCrossRefGoogle Scholar
  9. 6.9
    M.A. Kumakhov, R. Wedell: Phys. Status Solidi (b) 84, 581 (1977)ADSCrossRefGoogle Scholar
  10. 6.10
    N.K. Zhevago: Zh. Eksp. Teor. Fiz. 75, 1389 (1978) [English trans.: Sov. Phys.-JETP 48, 701 (1978)]Google Scholar
  11. 6.11
    A.W. Saenz, H. Überall, A. Nagl : Nucl. Phys. A372, 90 (1981)ADSGoogle Scholar
  12. 6.12
    D.M. Bird, B.F. Buxton: Proc. Roy. Soc. (London), Ser. A: 379, 459 (1982)ADSCrossRefGoogle Scholar
  13. 6.13
    P. Lervig, J. Lindhard, V. Nielsen: Nucl. Phys. A96, 481 (1967)ADSGoogle Scholar
  14. 6.14
    V.A. Bazylev, N.K. Zhevago: Zh. Eksp. Teor. Fiz. 73, 1697 (1977) [English transl.: Sov. Phys.-JETP 46, 891 (1977)]Google Scholar
  15. 6.15
    G. Baym: Lectures on Quantum Mechanics (Benjamin, New York 1969)zbMATHGoogle Scholar
  16. 6.16
    J.D. Jackson: Classical Electrodynamics, 2nd edn. (Wiley, New York 1975), Chap.11zbMATHGoogle Scholar
  17. 6.17
    W. Heitler: The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford 1954)zbMATHGoogle Scholar
  18. 6.18
    J.U. Andersen, E. Bonderup, E. Laegsgaard, A.H. Sørensen: Phys. Scr. 28, 308 (1983)ADSCrossRefGoogle Scholar
  19. 6.19
    A.H. Compton, S.K. Allison: X Rays in Theory and Experiment (Van Nostrand, New York 1935)Google Scholar
  20. 6.20
    J.U. Andersen, E. Bonderup, E. Laegsgaard, B.B. Marsh, A.H. Sørensen: Nucl. Instrum. Methods 194, 209 (1982)ADSCrossRefGoogle Scholar
  21. 6.21
    R.W. Terhune, R.H. Pantell: Appl. Phys. Lett. 30, 265 (1977)ADSCrossRefGoogle Scholar
  22. 6.22
    J.U. Andersen, E. Laegsgaard: Phys. Rev. Lett. 44, 1079 (1980)ADSCrossRefGoogle Scholar
  23. 6.23
    N. Cue, E. Bonderup, B.B. Marsh, H. Bakhru, R.E. Benenson, R. Haight, K. Inglis, G.O. Williams: Phys. Lett. A80, 26 (1980)ADSGoogle Scholar
  24. 6.24
    P.A. Doyle, P.S. Turner: Acta Crystallogr., Sect. A: 24, 390 (1968)ADSCrossRefGoogle Scholar
  25. 6.25
    J.U. Andersen, E. Laegsgaard, A.H. Sørensen: Nucl. Instrum. Methods B2, 63 (1984)ADSGoogle Scholar
  26. 6.26
    J.U. Andersen, S. Datz, E. Laegsgaard, J.P.F. Sellschop, A.H. Sørensen: Phys. Rev. Lett. 49, 215 (1982)ADSCrossRefGoogle Scholar
  27. 6.27
    E. Laegsgaard, J.U. Andersen: Nucl. Instrum. Methods B2, 99 (1984)ADSGoogle Scholar
  28. 6.28
    J.U. Andersen, K.R. Eriksen, E. Laegsgaard: Phys. Scr. 24, 588 (1981)ADSCrossRefGoogle Scholar
  29. 6.29
    P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, J.M. Whelan: Electron Microscopy of Thin Crystals (Butterworth, London 1965)Google Scholar
  30. 6.30
    J.U. Andersen: Nucl . Instrum. Methods 170, 1 (1980)ADSzbMATHCrossRefGoogle Scholar
  31. 6.31
    A.H. Sørensen: Ph. D. Thesis, University of Aarhus, Denmark (1983)Google Scholar
  32. 6.32
    R.H. Pantell, M.J. Alguard: J. Appl. Phys. 50, 798 (1979)ADSCrossRefGoogle Scholar
  33. 6.33
    V.A. Bazylev, V.V. Goloviznin: Radiat. Eff. 60, 101 (1982);CrossRefGoogle Scholar
  34. 6.33
    V.A. Bazylev, V.V. Goloviznin: Zh. Eksp. Teor. Fiz. 82, 1204 (1982)Google Scholar
  35. 6.33
    V.A. Bazylev, V.V. Goloviznin: English transl.: Sov. Phys.-JETP 55, 700 (1982)Google Scholar
  36. 6.34
    K. Komaki, F. Fujimoto, A. Ootuka: Nucl. Instrum. Methods 194, 243 (1982)ADSCrossRefGoogle Scholar
  37. 6.35
    P.H. Dederichs: Solid State Phys. 27, 135 (1972)CrossRefGoogle Scholar
  38. 6.36
    H. Esbensen, J.A. Golovchenko: Nucl. Phys. A298, 382 (1978)ADSGoogle Scholar
  39. 6.37
    H. Esbensen, O. Fich, J.A. Golovchenko, K.O. Nielsen, E. Uggerhøj, C. Vraast-Thomsen, G. Charpak, S. Majewski, F. Sauli, J.P. Ponpon: Nucl. Phys. B127, 281 (1977)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • J. U. Andersen
  • E. Bonderup
  • E. Laegsgaard

There are no affiliations available

Personalised recommendations