4. Attenuation
Attenuation – When photons are
“attenuated” they are removed from the
beam.
This can be due to absorption or scatter
Linear Attenuation Coefficient = μ
Fraction of incident beam removed per unit
path-length
Units: 1/cm
5. Measurement of Linear Attenuation Coefficient -
“Narrow Beam”
Narrow beam of mono-energetic photons directed toward absorbing
slab of thickness x.
Small detector of size d placed at distance R >> d behind slab
directly in beam line.
No
x
( ) e
N
x
o
x
N
µ
−
=
Only photons that transverse slab without interacting are detected.
Nx
Khan,
Figure 5.1
7. Mass Attenuation Coefficient
Linear attenuation coefficient often expressed as the ratio
of µ to the density, ρ = mass attenuation coefficient
g
g
cm
g
cm cm
cm
cm
2
3
3
1
1
=
=
ρ
µ
Know these
units!
8. Half Value Layer
HVL = Thickness of material that reduces the beam
intensity to 50% of initial value.
For monoenergetic beam HVL1 = HVL2.
Take Ln of both sides
( )
2
1
⇒
=
−
e
I
HVL
o
I µ
( )
2
1
Ln
HVL =
− µ
µ
2
Ln
HVL = Important
relationship!
9. Half Value Layer
Polychromatic Beams
After a polychromatic beam
traverses the first HVL, it is
hardened.
low energy photons
preferentially absorbed.
Beam has higher effective
energy after passing
through first HVL.
More penetrating
HVL2>HVL1
Note: Monochromatic beams
HVL1=HVL2
Khan, Figure 5.3
10. Tenth Value Layer - TVL
TVL = Thickness of absorber to reduce beam
intensity to one tenth of original intensity
TVL = (3.32)HVL (important relationship for board exams)
Most shielding calculations and materials are
specified in TVLs
µ
10
Ln
TVL =
13. 1. Photoelectric Effect
Photon interacts with a tightly bound orbital electron
(K,L,M) and transfers ALL of its energy to the electron.
The electron is ejected from the atom with Kinetic
Energy TP.E.
L
+ K M
e-
E
T B
E
P
h −
= ν
.
.
e
14. Photoelectric Effect Cross-sections
i.e. probability of an interaction
Probability
Lower Energy P.E more likely
P.E interactions are less likely at higher energy
Higher Atomic Number: P.E. more likely
E
z
PE 3
3
α
µ
15. Photoelectric effect
How is the interaction probability manipulated to
achieve good contrast in diagnostic imaging?
Use low Energy Radiation in imaging, so
majority of interactions are photoelectric.
Radiation is preferentially absorbed in high Z
material (bone) achieve good contrast
between Bone and soft tissue
E
z
PE 3
3
α
µ
16. Photoelectric Effect
K and L edges
A photon with E<B.E.L does
not have enough energy to
eject L shell electron Low
probability of L shell P.E
interaction Dip in curve
When E= B.E.L very high
probability of L shell P.E
interaction Spike in curve
As energy increases E> B.E.L
probability of L shell P.E
decreases Dip in curve
When E= B.E.K very high
probability of K shell P.E
interaction Spike in curve
K-
edge
L-edge
Note: do not see K and
L edge for H20, occurs
at much lower energies
Khan, Figure 5.6
17. Photoelectric Effect Results
The fast moving photoelectron may participate in
1000s of interactions until it dissipates all of its
energy.
Other Results
• Characteristic X-rays
• Auger Electrons
Khan,
Figure 5.5
18. +
K
L
M
Characteristic X-Ray Production
Example (K-shell vacancy)
2. L shell e- fills vacancy
excess energy: E=Eb(K)
– Eb(L)
1. Incident photon ejects
K shell electron.
e
e
e
3. A photon with an energy equal
the difference in the binding
energies is released.
e
19. Aujer Electrons
When an electron displaces inner shell electron
an outer shell electron fills the vacancy and
rather than giving up the excess energy as
characteristic X-Ray, the excess energy is
given to a different outer shell electron, which
is ejected.
20. +
K
L
M
Aujer Electron Production
Example (K-shell vacancy)
2. L shell e- fills vacancy
excess energy: E=Eb(K)
– Eb(L)
1. Incident photon ejects
k shell electron
e
e
e
3. Excess Energy given to
M shell e-, (auger e-),
which is ejected with
T=Eb(K) – Eb(L) - Eb(m)
e
e
e
21. 1b. Coherent Scatter (Low Energy)
Coherent scatter occurs when the interacting
photon does not have enough energy to
liberate the electron.
Energy photon < binding energy of electron
Photon energy is re-emitted by excited
electron. The only change is a change of
direction (scatter) of the photon, hence
'unmodified' scatter.
Coherent scattering is not a major interaction
process encountered in at the energies normally
used in radiotherapy
22. 2. The Compton Effect (E>100 KeV)
A photon with energy, E=hv, incident on unbound stationary
“FREE” electron (for purposes of easier calculation).
The electron is scattered at an angle θ with energy T and the
scattered photon with E=hν’ departs at angle f with energy, hv’.
( )
φ
ν
ν
ν
cos
1
1
'
2
−
+
=
c
mo
h
h
h
'
ν
ν h
h
T −
=
Khan, Figure 5.1
23. The incident photon can never transfer ALL of
it’s energy to the electron, but it can transfer
most of its energy.
The minimum energy of the scattered photon
(max energy of scattered electron) occurs
when ϕ=180o (backscattered photon).
Compton Effect
MeV
MeV
m
h c 255
.
0
2
511
.
0
2
1
'
2
0 =
=
=
ν
( )
φ
ν
ν
ν
cos
1
1
'
2
−
+
=
c
mo
h
h
h
24. The direction of scattered photon depends on
the incident photon energy
Higher Energy is “forward” scattered
Compton Effect
( )
φ
ν
ν
ν
cos
1
1
'
2
−
+
=
c
mo
h
h
h
25. Compton Probability of an
Interaction
Compton effect is independent of Z
Compton effect does depend on e- density
Let’s consider these statements in more
detail…..
26. Compton Probability of an
Interaction
Because the Compton interaction involves essentially
free electrons in the absorbing material, it is
independent of atomic number Z.
It follows that the Compton mass attenuation coefficient
(σ/r) is independent of Z and depends only on the
number of electrons per gram.
Although the number of electrons per gram of elements
decreases slowly but systemically with atomic number,
most materials except hydrogen can be considered as
having approximately the same number of electrons per
gram.
27. Electrons per Gram
Density
(g/cm3)
Zeff
Electrons per
gram1023 (e-/g)
Fat 0.916 5.92 3.48
Muscle 1.00 7.42 3.36
Water 1.00 7.42 3.34
Air 0.001293 7.64 3.01
Bone 1.85 13.8 3.0
• most materials
except hydrogen
have approx. the
same number of
electrons per
gram.
W
A
A
Z
N
28. Compton Scatter Interactions
If the energy of the beam is in the region where the Compton effect is
the most common mode of interaction (i.e. megavoltage therapy
beams) get same attenuation in any material of equal density
thickness (density (ρ) times thicknes (x)).
For example, in the case of a beam that interacts by Compton
effect, the attenuation per g/cm2 for bone is nearly the same as that
for soft tissue.
However, 1 cm of bone will attenuate more than 1 cm of soft tissue,
because bone has a higher electron density.
Electron density = number of electrons per cubic centimeter = density times
the number of electrons per gram.
( )
cm
cm
g
cm
g
x 2
3
=
×
=
ρ
29. Electron Density
Density
(g/cm3)
Zeff
Electron per gram
1023 (e-/g)
Electron density
1023 (e/cm3)
Fat 0.916 5.92 3.48 3.19
Muscle 1.00 7.42 3.36 3.36
Water 1.00 7.42 3.34 3.34
Air 0.001293 7.64 3.01 0.0039
Bone 1.85 13.8 3.0 5.55
( )
ρ
W
A
A
Z
N
( )
( )
65
.
1
36
.
3
55
.
5
=
=
muscle
e
bone
e
ρ
ρ
• attenuation
produced by 1
cm of bone will
be equivalent to
that produced by
1.65 cm of soft
tissue.
Example
per cm of absorber
30. 3. Pair Production
Absorption process in which photon disappears
and gives rise to an electron/positron pair.
occurs in the coulomb
force field of the near
nucleus
Nucleus
e+
e-
Two photons created at
annihilation, each with 0.511
MeV and separated by 180o
e-
Positron only exists for an
instant, combines with
free e-
MeV
h 02
.
1
>
ν
31. Pair Production: Threshold Energy
The incident photon must have sufficient energy to
“create” a positron and an and electron (need rest mass
of each, 0.511 MeV), any extra energy is kinetic energy
for the positron and electron (hν = 2mc2 + KE+ + KE-).
Energy Threshold = 1.022MeV
32. Pair Production Kinematics
The incident photon must have sufficient Energy
Average KE of positron/electron
Average angle of departure of positron/electron
T
T
c
mo
h
−
+
+
+
=
2
2
ν
T
c
mo
2
=
θ
Units are in radians
to convert to degree multiply by 360o/2p
2
022
.
1 MeV
h
T
−
=
ν
33. Pair Production X-Sections
Probability of an interaction
Because the pair production results from an interaction with the
electromagnetic field of the nucleus, the probability of this
process increases rapidly with atomic number.
The attenuation coefficient for
pair production varies with:
Z2 per atom,
For a given material, above the
threshold energy, the
probability of interaction
increases as Ln(E).
Khan, Figure 5.11
34. Probability of Interaction
Three photon interactions dominate at the
energies we use in radiotherapy
Energy
Increases
Z Increases
Photoelectric Effect ↓ ( ⁄
1
𝐸𝐸3) ↑ (Z3)
Compton Scatter ↓ ( ⁄
1
𝐸𝐸) No change
Pair Production ↑ (E > 1.02 MeV) ↑ Z
36. Photon Interactions
Which of the following is FALSE? A photon can
undergo a _________ followed by a
_________ interaction.
1. Compton, Pair Production
2. Compton, another Compton
3. Compton, photoelectric
4. Photoelectric, Compton
37. Photon Interactions
Which of the following is FALSE? A photon can
undergo a _________ followed by a
_________ interaction.
1. Compton, Pair Production
2. Compton, another Compton
3. Compton, photoelectric
4. Photoelectric, Compton
KEY: So long as incident photon has sufficient energy
following first interaction, can undergo another interaction
No photon remains after
photoelectric interaction!
38. Photoelectric Effect
Which of the following statements regarding
Photoelectric Interactions is FALSE?
1. They are mainly responsible for differential attenuation
in radiographs
2. The incident photon is absorbed
3. Bound electrons are involved
4. The probability increases rapidly with increasing energy
39. Photoelectric Effect
Which of the following statements regarding
Photoelectric Interactions is FALSE?
1. They are mainly responsible for differential attenuation
in radiographs
2. The incident photon is absorbed
3. Bound electrons are involved
4. The probability increases rapidly with increasing energy
decreasing
40. Photoelectric Effect
Two materials are irradiated by the same energy
photons. Material A has an atomic number of 14
and B has an atomic number of 7. The
photoelectric interaction cross-section (probability)
of A is _____ times that of B?
41. Photoelectric Effect
Two materials are irradiated by the same energy
photons. Material A has an atomic number of 14
and B has an atomic number of 7. The
photoelectric interaction cross-section (probability)
of A is _____ times that of B?
( )
( )
B
A
B
A
8
,
7
14
3
3
=
=
E
Z
PE 3
3
α
µ
Using above equation,
set up a ratio and solve
(energy cancels out).
42. Photoelectric Effect
A photon detected following a photoelectric
interaction is most likely to be:
1. The scattered incident photon
2. A gamma ray
3. An annihilation photon
4. Crenkov Radiation
5. A characteristic X-Ray
43. Photoelectric Effect
A photon detected following a photoelectric
interaction is most likely to be:
1. The scattered incident photon
2. A gamma ray
3. An annihilation photon
4. Crenkov Radiation
5. A characteristic X-Ray
44. Trivia:
Cherenkov Radiation
Cherenkov radiation is EM
radiationemitted when a charged
particle (such as an electron) passes
through an insulator at a constant
speed greater than the speed of light
in that medium.
It is named after Russian scientist
Pavel Cherenkov, the 1958 Nobel
Prize winner who was the first to
characterize it rigorously.
The characteristic blue glow of
nuclear reactors is due to
Cherenkov radiation.
http://en.wikipedia.org/wiki/Cherenkov_radiation
45. What is the overall effect of “Photon
Beam”?
Photoelectric, Compton Scatter & Pair
Production
46. “Total” Attenuation Coefficient
Mass attenuation coefficient for photons of a
given, relevant energy in a given material
composed of the individual contributions from
the physical processes that can remove photons
from the narrow beam.
PP
CS
PE
+
+
=
ρ
µ
ρ
µ
ρ
µ
ρ
µ
47. Some important Energies: 26 keV, 150 keV, and 24 MeV
Photon Interactions in Water
as a function of energy
PE most likely
at Low E
All
Compton
1:1
Compton:PP
1:1
PE:Compton
PE most likely at
very High E
Nomenclature: T = Photoelectric, s = Compton, P = Pair Production
48. Photon Interactions (m/r)
Two materials: H20 and Pb Photoelectric effect
Higher for Pb than H20.
Pair Production
Higher for Pb than H20.
Compton effect
Similar for both materials.
PE
Compton
Pair Production
Khan, figure 5.12
51. Electron Interactions
As electrons travel through a medium they
interact with atoms through a variety of
processes due to COULOMB interactions.
Directly ionizing
Through these collisions the electron may
Lose kinetic energy (collision and radiative loss)
Change direction (scatter)
52. Electron Interactions
Collisional Interactions:
Incident electron interacts
with atomic electrons in the
absorbing medium
Radiative Interactions:
Incident electron interacts
with atomic nuclei in the
absorbing medium.
Two Types of Electron Interactions
e-
e-
53. e-
b
a
a=radius
of atom
e- passes atom at
some distance, b
Electron Interactions
Distance of electron
from atom in relation to
size of the atom will
determine the type of
e- interaction
Three Possibilities
1. b>>a
2. b=a
3. b<<a
Collision
Interactions
Radiative
Interactions
55. Collision Interactions
Soft Collision (b>>a)
Soft Collision: when an e- (primary e-) passes an atom at a
considerable distance, the e-’s coulomb force affects the
atom as a whole.
Result excite and sometimes ionize valence electrons.
Energy of transition Transfer a small amount of energy
(few eV) to atom of abs medium.
Probability Very Likely, Most numerous type of collision
interaction.
Net Effect accounts for about ½ of total energy
transferred to absorbing medium from collision
interactions.
56. Collision Interactions
Hard Collision (b=a)
Hard Collision (knock-on) b=a, incident e- (primary e-)
interacts with atomic e-.
Result d-Ray = atomic electron ejected with
considerable kinetic energy (deposits its energy along
separate track from 1o e-).
Energy of transition considerable amount of energy
to atom of abs medium.
Probability Less Likely.
Net effect accounts for about ½ of total energy
transferred to absorbing medium from coulomb
interactions.
57. Radiative Interaction b<<a
e- passes in close proximity to nucleus and
interacts with coulomb force of nucleus.
Two types of radiative interactions possible:
1. Elastic Interaction – No Energy change
2. Inelastic – Bremsstrahlung photons produced
58. Elastic Radiative Interaction
e- is scattered with NO change in energy No
energy Transferred to absorbing Medium.
Probability increases with Z2, (Z = atomic number
of medium).
Thin High Z foil can be used to elastically scatter
electrons (e.g. scattering foil).
Note: foil must be thin or too much Bremsstrahlung
production.
Accounts for 97 – 98% of radiative interactions
59. Inelastic Radiative Interaction
e- interacts with coulomb field of nucleus:
Bremsstrahlung Radiation
Energy carried away via photon emission
Accounts for 2 - 3% of radiative interactions
(for electrons).
61. Why do we care about neutrons?
Neutrons in Radiation Therapy
Neutron Therapy (very few centers exist)
Contamination Neutrons in X-Ray Therapy
Contamination Neutrons in Proton Therapy
Neutron Shielding
62. Neutron Interactions with Tissue
Neutrons are indirectly ionizing
Neutrons interact by setting charged particles in motion
i.e. give rise to densely ionizing (high LET) particles:
recoil protons, a-particles, and heavier nuclear
fragments.
These particles then deposit dose in tissue.
The type of interaction and the amount of dose
deposited in the body is strongly dependent on
neutron energy.
63. t
o
total
e
I
I Σ
−
=
Exponential Attenuation
similar concept to photon attenuation
Neutrons are removed
exponentially from a
collimated neutron beam
by absorbing material.
Io I
where
N = number of absorber atoms
per cm3 (atomic density)
s = the microscopic cross
section for the absorber,
cm2
t = the absorber thickness, cm
stotalN
64. Classification of Neutrons by Energy
The classification of neutrons by energy is somewhat dependent on the
reference text. Some sources may include an epithermal category while
others only include fast and slow (thermal).
Category Energy Range
Fast > 500 keV
Intermediate 10 keV – 500 keV
Epithermal 0.5 eV – 10 keV
Thermal < 0.5 eV
65. Fast Neutron Interactions in Tissue
Higher energy neutrons result in the release of
charged particles, spallation products, from
nuclear disintegrations, [(n, D), (n,T), (n,alpha),
etc].
These charged particles then deliver dose to
tissue.
Examples of (n,alpha)
Oxygen
Carbon
66. Fast Neutron Interactions with
Oxygen and Carbon
Recoil alpha-particles
A neutron interacts with a Carbon
atom (6 protons and 6 neutrons),
resulting in three a-particles.
(Hall, Fig 1.10)
A neutron interacts with an Oxygen
atom (8 protons and 8 neutrons) ,
resulting in four a-particles.
(Hall, Fig 1.10)
67. Intermediate Neutron Interactions in Tissue
Interact primarily with Hydrogen in Soft Tissue
For intermediate energy neutrons, the interaction
between neutrons and hydrogen nuclei is the dominant
process of energy transfer in soft tissues.
1.Hydrogen is the most abundant
atom in tissue.
2.A proton and a neutron have
similar mass, 938 MeV/cm2
versus 940 MeV/cm2.
3.Hydrogen has a large collision
cross-section for neutrons.
3 Reasons
Hall, Figure 1.9
68. Thermal Neutron Interactions in Tissue
The major component of dose from thermal neutrons
is a consequence of the 14N(n,p) into 14C + 0.62 MeV
photon
Dominant energy transfer mechanism in thermal and
epithermal region in body
Another thermal neutron interaction of some
consequence is the 1H(n,γ) into 2H + 2.2 MeV photon
2.2 MeV to gamma (non-local absorption)
Small amount of energy to deuterium recoil (local absorption)
*This 2.2 MeV photon interaction is important in shielding high energy accelerators*
69. References
The Physics of Radiation Therapy 3rd
edition, Faiz Khan, Ch 5
Herman Cember. Introduction to Health
Physics 3rd Ed. (1996)
Eric J. Hall. Radiobiology for the Radiologist
5th Ed. (2000)
Frank H. Attix. Introduction to Radiological
Physics and Radiation Dosimetry. (1986)
