2. X-rays The electric field E(r,t) is given as a cosine function.

3. X-rays In formal derivations the vector potential A is used. The electric field E(r,t) is directly related to the vector potential A(r,t).

4. Interaction of x-rays with matter 1 The photon moves towards the atom

5. Interaction of x-rays with matter 1 The photon meets an electron and is annihilated

6. Interaction of x-rays with matter 1 The electron gains the energy of the photon and is turned into a blue electron.

7. Interaction of x-rays with matter 1 The blue electron (feeling lonely) leaves the atom and scatters of neighbors (cf. EXAFS) or escapes from the sample (cf. XPS)

8. Interaction of x-rays with matter 1 The probability of photon annihilation determines the intensity of the transmitted photon beam I0I0 I EkEk

9. Interaction of x-rays with matter 2 The photon moves towards the atom

10. Interaction of x-rays with matter 2 The photon meets an electron and is scattered

11. Interaction of x-rays with matter 2 The photon leaves the atom under a different angle. (Interference between scattering events yields XRD)

12. I ( ,k,q) I’ (  ’,k’,q’) I” (E k,k”,  ) Energy  Spectroscopy Direction  Structure Polarization  Magnetism Interaction of x-rays with matter

13. H INT(1) describes the interaction of the vector field A on the momentum operator p of an electron, or in other words the electric field E acting on the electron moments. The momentum operator p is given as the electron charge q times the displacement operator r. Interaction of x-rays with matter

14. Interaction of x-rays with matter 1 The photon meets the electron and is annihilated A p=qr

15. H INT(1) describes the interaction of the vector field A on the momentum operator p of an electron, or in other words the electric field E acting on the electron moments. The momentum operator p is given as the electron charge q times the displacement operator r. Interaction of x-rays with matter

16. H INT(2) describes the second order interaction of the vector field A. This gives rise to the elastic scattering of the x-rays by the electrons. This is the basis for x-ray diffraction (XRD) and small angle x-ray scattering (SAXS) Interaction of x-rays with matter

17. XAFS studies photoelectric absorption Elastic scattering (Thompson) Inelastic scattering (Compton) Mn

18. Excitation of core electrons to empty states. Fermi Golden Rule Spectrum given by the Fermi Golden Rule X-ray absorption and X-ray photoemission

19. I (  FIXED ) X-ray absorption and X-ray photoemission

21. X-ray emission: core hole decay Basis for X-ray Fluorescence (XRF) and Energy Dispersive X-ray analysis (EDX)

22. Interaction of x-rays with matter Photoelectric effect: (annihilation of photon) XAS, XPS XES, XRF, EDX X-ray scattering: (photon-in photon-out) XRD, SAXS

23. Interaction of x-rays with matter X-ray scattering: - with H int(2) - with H int(1) via a (virtual) intermediate state = Resonant X-ray scattering

24. Interaction of x-rays with matter 3 The photon moves towards the atom

25. Interaction of x-rays with matter 3 The photon meets an electron and is annihilated

26. Interaction of x-rays with matter 3 The electron gains the energy of the photon and is turned into a virtual blue electron.

27. Interaction of x-rays with matter 3 The virtual blue electron loses a photon with exactly the same energy as gained

28. Interaction of x-rays with matter 3 The photon leaves the atom

29. Resonant X-ray scattering Combination of XAS and XES [only H int(1) ] - RXES - Resonant Inelastic X-ray Scattering (RIXS) (also called Resonant X-ray Raman Spectroscopy) Combination of H int(1) and H int(2) - Resonant XRD (also called: anomalous) - Multi-wavelength anomalous Diffraction (MAD) - Resonant SAXS (ASAXS) - TEDDI