1. Interactions of Ionizing Radiation

2. Attenuation Collimated beam:
Absorber
Collimator
Beam
Intensity I0 x
Collimated beam:
dI = –N dx N = atomic density  = cross section
Integrating gives: I = I0 exp(-N x)
= I0 exp(- x)
 linear attenuation coefficient – depends on density 
 m =  / mass-attenuation coefficient

3. Coefficients Linear attenuation coefficient (, cm-1)
Depend on the energy of the photons
the nature of the material
Mass attenuation coefficient (/, cm2/g)
Independent of density of material
Depend on the atomic composition

4. Interactions of photons with matter
Photo disintegration (>10 MeV)
Coherent scattering (coh)
Photoelectric effect ()
Compton effect (c)
Pair production ()

5. They have very different dependencies on photon energy Eγ and atomic number Z of the absorbing medium.

6. Coherent scattering Classical scattering or Rayleigh scattering  K L M
Classical scattering or Rayleigh scattering
No energy is changed into electronic motion
No energy is absorbed in the medium
The only effect is the scattering of the photon at small angles.
In high Z materials and with photons of low energy

7. Photoelectric effect (1)
A photon interacts with an atom and ejects one of the orbital electrons.
h-EB

8. KEpe = Eγ - Ф Ф = electron binding energy
Photoelectric effect
Incident photon E
Photo-electron E - 
Complete conversion of Eγ into releasing an atomic electron
- usually from an inner atomic shell
Occurs near an atom to conserve energy and momentum
The photoelectron is ejected with kinetic energy
KEpe = Eγ - Ф Ф = electron binding energy

9. Secondary effects
Vacancy is filled by an electron from a higher shell
Leading to:
Secondary photon (X-ray fluorescence) or
Electron emission (Auger electron)
There may be a cascade of secondary emission
Depositing all the energy in the medium contributes to a full-energy peak in the spectrum

10. Photoelectric effect (2)
15 keV
L absorption edge
/  Z3/E3
The angular distribution of electrons depends on the photon energy.
88 keV
K absorption edge

11. Compton scattering Recoil electron Incident photon
Scattered photon h’
Compton scattering

12. Compton electron
Compton effect (1) K L M h  
h’
Free electron
The photon interacts with an atomic electron as though it were a “free” electron.
The law of conservation of energy
The law of conservation of momentum
…………(1)
………(2)
…...…………(3)

13. Compton effect (2)  = h0/m0c2 = h0/0.511 E h0 h’ By (1), (2), (3)
Free electron  
h’
By (1), (2), (3)
 = h0/m0c2 = h0/0.511

14. KE(electron) = always < E incident photon
Maximum when h’ = min ( = 180o)  Compton edge
Minimum (zero) when h’= max
at  = 0o

15. Compton Scattering scattered electron (Ese) incident photon (Eip)
loosely bound
electron (Eie)
scattered
electron (Ese)
incident
photon (Eip)  
scattered
photon (Esp)

16. Compton Scattering Ese = mc2 Eie = moc2 Eip = hc ip E*sp = hc sp hc 
Ese = mc2
Eie = moc2
Eip = hc
ip
E*sp = hc
sp hc
ip
+ moc2 =
sp
+ mc2
Conservation of Energy:

17. Compton Scattering Pse = mv Pie = 0 Pip = h ip P*sp = h sp 
P*sp = h
sp
Conservation
of Momentum: h
ip =
sp
cos + mv cos
horizontal
vertical
0 = h
sp
sin + mv sin

18. Special cases of Compton effect
The radiation scattered at right angles (=90°) is independent of incident energy and has a maximum value of MeV.
The radiation scattered backwards is independent of incident energy and has a maximum energy of MeV.

19. Dependence of Compton effect on energy
As the photon energy increase, the photoelectric effect decreases rapidly and Compton effect becomes more and more important.
The Compton effect also decreases with increasing photon energy.

20. Dependence of Compton effect on Z
Independent of Z
Dependence only on the number of electrons per gram
electrons/g

21. Pair production  KE(pair) = E - 2mc2 - deposited in medium
h’= 511 keV
Positron
h’= 511 keV 
Incident photon E
Electron
KE(pair) = E - 2mc2
- deposited in medium
Pair production can only occur near a heavy body (atom)
Positron (anti-electron) slows down then attracts and annihilates with an electron.
Two (511 keV) photons are created – emitted back-to-back

22. The photon interacts with the electromagnetic field of an atomic nucleus.
The threshold energy is 1.02 MeV.
The total kinetic energy for the electron-positron pair is (h-1.02) MeV - deposited in medium

23. Relative importance of -ray interactions