1. 1 Photon Interactions  When a photon beam enters matter, it undergoes an interaction at random and is removed from the beam

2. 2 Photon Interactions

3. 3  Notes  is the average distance a photon travels before interacting  is also the distance where the intensity drops by a factor of 1/e = 37% For medical applications, HVL is frequently used  Half Value Layer  Thickness needed to reduce the intensity by ½  Gives an indirect measure of the photon energies of a beam (under the conditions of a narrow- beam geometry) In shielding calculations, you will see TVL used a lot

4. 4 Beam Hardening

5. 5 Photon Interactions

6. 6  What is a cross section?  What is the relation of  to the cross section  for the physical process?

7. 7 Cross Section  Consider scattering from a hard sphere  What would you expect the cross section to be? b θ α R α α

8. 8 Cross Section  The units of cross section are barns 1 barn (b) = 10 -28 m 2 = 10 -24 cm 2 The units are area. One can think of the cross section as the effective target area for collisions. We sometimes take σ=πr 2

9. 9 Cross Section  One can find the scattering rate by

10. 10 Cross Section  For students working at collider accelerators

11. 11 Photon Interactions  In increasing order of energy the relevant photon interaction processes are Photoelectric effect Rayleigh scattering Compton scattering Photonuclear absorption Pair production

12. 12 Photon Interactions  Relative importance of the photoelectric effect, Compton scattering, and pair production versus energy and atomic number Z

13. 13 Photoelectric Effect  An approximate expression for the photoelectric effect cross section is  What’s important is that the photoelectric effect is important For high Z materials At low energies (say < 0.1 MeV)

14. 14 Photoelectric Effect  More detailed calculations show

15. 15 Photon Interactions  Typical photon cross sections

16. 16 Photoelectric Effect  The energy of the (photo)electron is  Binding energies for some of the heavier elements are shown on the next page  Recall from the Bohr model, the binding energies go as

17. 17 Photoelectric Effect

18. 18 Photoelectric Effect  The energy spectrum looks like  This is because at these photon/electron energies the electron is almost always absorbed in a short distance As are any x-rays emitted from the ionized atom

19. Photoelectric Effect and X-rays  PE proportionality to Z 5 makes diagnostic x- ray imaging possible  Photon attenuation in Air – negligible Bone – significant (Ca) Soft tissue (muscle e.g.) – similar to water Fat – less than water Lungs – weak (density)  Organs (soft tissue) can be differentiated by the use of barium (abdomen) and iodine (urography, angiography) 19

20. Photoelectric Effect and X-rays  Typical diagnostic x-ray spectrum 1 anode, 2 window, 3 additional filters 20

21. Photon Interactions  Sometimes easy to loose sight of real thickness of material involved

22. Photon Interactions  X-ray contrast depends on differing attenuation lengths

23. 23 Photoelectric Effect  Related to kerma (Kinetic Energy Released in Mass Absorption) and absorbed dose is the fraction of energy transferred to the photoelectron  As we learned in a previous lecture, removal of an inner atomic electron is followed by x-ray fluorescence and/or the ejection of Auger electrons The latter will contribute to kerma and absorbed dose

24. 24 Photoelectric Effect  Thus a better approximation of the energy transferred to the photoelectron is  We can then define e.g.

25. 25 Photoelectric Effect  Fluorescence yield Y for K shell

26. 26 Cross Section  dΩ=dA/r 2 =sinθdθdφ

27. 27 Cross Section

28. 28 Cross Section  If a particle arrives with an impact parameter between b and b+db, it will emerge with a scattering angle between θ and θ+dθ  If a particle arrives within an area of dσ, it will emerge into a solid angle dΩ

29. 29 Cross Section  From the figure on slide 7 we see  This is the relation between b and θ for hard sphere scattering

30. 30 Cross Section  We have  And the proportionality constant dσ/dΩ is called the differential cross section

31. 31 Cross Section  Then we have  And for the hard sphere example

32. 32 Cross Section  Finally  This is just as we expect  The cross section formalism developed here is the same for any type of scattering (Coulomb, nuclear, …) Except in QM, the scattering is not deterministic

33. 33 Cross Section  We have  And the proportionality constant dσ/dΩ is called the differential cross section  The total cross section σ  is just