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972 B3102005 Xray1

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5. Fig. 1.1 Classical scattering of an unpolarized primary beam by a single free electron at the origin. 6. Fig. 1.2 Illustration of the electric field ε , produced by a…
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  • 5. Fig. 1.1 Classical scattering of an unpolarized primary beam by a single free electron at the origin.
  • 6. Fig. 1.2 Illustration of the electric field ε , produced by a charge q with acceleration a, according to classical electromagnetic theory. (1.1)
  • 7. (1.2) (1.3)
  • 8. Thomson equation Polarization factor
  • 9. Fig. 1.3 A double scattering experiment which illustrates the production of a polarized beam by scattering at 90, °and the analysis of the polarized beam by a second scattering at 90. °
  • 10. Complex variable
  • 11. Computation of complex variable |Z| 2 =Z · Z*=(a+bi) · (a-bi)=a 2 +b 2 Z 2 =Z · Z=(a+bi) · (a+bi)=a 2 -b 2 +2abi ≠ |Z| 2
  • 12. Vector addition of waves
  • 13. Fig. 1.4 Scattering of a plane parallel primary beam by several scattering centers. The lengths X n are the total distances from a wave front W in the primary beam to the point of observation P .
  • 14. (1.4) (1.5)
  • 15. E 
  • 16. (1.6)
  • 17. (1.7) (1.8)
  • 18. Fig. 1.5 Scattering by a group of electrons at positions r n .The unit vectors s o and s give the direction of the primary beam and the direction to the point of observation P . Field acting on electron n
  • 19. (1.9) (1.10) Field at P caused by electron n: For one electron charge distributed in space:
  • 20. Fig. 1.6 Relation between the s-s o vector and the vector r for an atom centered at O . Electron scattering factor:
  • 21. (1.12) (1.13) (1.14) For an atom with Z electrons, the atomic scattering factor f: …electron scattering factor
  • 22. (1.16) Accounts for the incoherent scattering intensity For an atom of atomic number Z:
  • 23. For an electron with charge distribution  :
  • 24. Then, for K-shell and L-shell electrons:
  • 25. Fig. 1.7 Values of f eL , f eK , f , and i(M) for an assumed charge distribution in neutral Li.
  • 26. Thomson equation
  • 27. Scattering by an atom
  • 28. Atomic scattering factor
  • 29. The atomic scattering factor of copper
  • 30. When incident  << all absorption edges, then f c ≈ f
  • 31. Incoherent scattering (Compton modified scattering)  Å      sin   h ν 1 e Before impact after impact e h  2  Elastic collision of photon and electron
  • 32. Effect produced by the passage of x-rays through matter
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