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

2 Photon Interactions

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 Beam Hardening

5 Photon Interactions

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

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 Cross Section  The units of cross section are barns 1 barn (b) = m 2 = 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 Cross Section  One can find the scattering rate by

10 Cross Section  For students working at collider accelerators

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

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 Photoelectric Effect  More detailed calculations show

15 Photon Interactions  Typical photon cross sections

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 Photoelectric Effect

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

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

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

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

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

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

25 Photoelectric Effect  Fluorescence yield Y for K shell

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

27 Cross Section

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

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

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

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