Calculation of the covariant matrix elements, and cross-sections of Compton diffusion on a bound electron

Regular Article
First Online:
Received:
Accepted:
  • 21 Downloads

Abstract.

This paper completes a previous published work that calculated analytically the relativistic wavefunctions for bound electron in a Compton diffusion process. This work calculates the relativistic propagator and the Wronskian of the two associated Feynman diagrams of Compton diffusion (emission first and absorption first). Then find an explicit expression for the covariant matrix elements separated into two parts: spin-angular part and radial part. Using these explicit expressions, the effective cross-section for Compton diffusion in the most general form is obtained in terms of basic dynamical and static quantities, like electron’s and photon’s 4-momenta and atomic number. The form of the cross-section is put ready for numerical calculations.

References

  1. 1.
    Salwa Al Saleh, Eur. Phys. J. Plus 131, 146 (2016)CrossRefGoogle Scholar
  2. 2.
    S. Al Saleh-Mahrousseh, Calcul relativiste en électrodynamique quantique de la diffusion Compton sur un électron lié, Thèse, Université Blaise Pascal - Clermont-Ferrand II, 1988Google Scholar
  3. 3.
    William R. Alling, W.R. Johnson, Phys. Rev. A 139, 1050 (1965)ADSCrossRefGoogle Scholar
  4. 4.
    S.J. Brodsky, P.J. Mohr, Quantum electrodynamics in strong and supercritical fields, in Structure and Collisions of Ions and Atoms (Springer, 1978) pp. 3--67Google Scholar
  5. 5.
    G.E. Brown, D.F. Mayers, Proc. R. Soc. London Ser. A 234, 387 (1956)ADSCrossRefGoogle Scholar
  6. 6.
    G.E. Brown, G.W. Schaefer, Proc. R. Soc. London Ser. A 233, 527 (1956)ADSCrossRefGoogle Scholar
  7. 7.
    C. Fronsdal, Phys. Rev. 179, 1513 (1969)ADSCrossRefGoogle Scholar
  8. 8.
    Mihai Gavrila, Phys. Rev. A 6, 1348 (1972)ADSCrossRefGoogle Scholar
  9. 9.
    Mihai Gavrila, Phys. Rev. A 6, 1360 (1972)ADSCrossRefGoogle Scholar
  10. 10.
    H. Grotch, E. Kazes, G. Bhatt, D.A. Owen, Phys. Rev. A 27, 243 (1983)ADSCrossRefGoogle Scholar
  11. 11.
    Peter Holm, Phys. Rev. A 37, 3706 (1988)ADSCrossRefGoogle Scholar
  12. 12.
    Josef M. Jauch, Fritz Rohrlich, The Theory of Photons and Electrons: The Relativistic Quantum Field Theory of Charged Particles with Spin One-half (Springer Science & Business Media, 2012)Google Scholar
  13. 13.
    Oskar Klein, Yoshio Nishina, Z. Phys. 52, 853 (1929)ADSCrossRefGoogle Scholar
  14. 14.
    Roland Ribberfors, Phys. Rev. B 12, 3136 (1975)ADSCrossRefGoogle Scholar
  15. 15.
    Roland Ribbers, Phys. Rev. B 12, 2067 (1975)ADSCrossRefGoogle Scholar
  16. 16.
    Morris Edgar Rose, W.H. Furry, Am. J. Phys. 29, 866 (1961)ADSCrossRefGoogle Scholar
  17. 17.
    William J. Veigele, Philip T. Tracy, E. Michael Henry, Am. J. Phys. 34, 1116 (1966)ADSCrossRefGoogle Scholar
  18. 18.
    I.B. Whittingham, J. Phys. A 4, 21 (1971)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, College of ScienceKing Saud UniversityRiyadhSaudi Arabia

Personalised recommendations