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Physics of Radiotherapy
Lecture II: Interaction of Ionizing Radiation With Matter
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Charge Particle Interaction
Energetic charged particles interact with matter by electrical forces and lose kinetic energy via:
• Excitation
• Ionization
• Radiative losses (Bremsstrahlung Production)
~ 70% of charged particle energy deposition leads to non-ionizing excitation
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Specific Ionization
• Number of primary and secondary ion pairs produced per unit length of charged particle’s path is called specific ionization
• Expressed in ion pairs (IP)/mm
Increases with electrical charge of particle (more for alpha as compare to electron)
Decreases with incident particle velocity
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Linear Energy Transfer (Stopping
Power of The Medium)
Amount of energy deposited per unit path length (eV/cm) is called the linear energy transfer (LET) and is also known as stopping power of the medium
LET of a charged particle is proportional to the square of the charge and inversely proportional to its kinetic energy
High LET radiations (alpha particles, protons, etc.) are more damaging to tissue than low LET radiations (electrons, gamma and x-rays)
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Electron Interaction
As an energetic electron traverses matter, it undergoes• Coulomb interactions with absorber atoms,
i.e., with: Atomic orbital electrons
Atomic nuclei
Through these collisions the electrons may:• Lose their kinetic energy (collision and
radiation loss).
• Change direction of motion (scattering).
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Energy losses are described by stopping power (LET).
Scattering is described by angular scattering power.
Collision between the incident electron and an absorber atom may be:• Elastic
• Inelastic
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In elastic collision the incident electron is deflected from its original path but no energy loss occurs.
In an inelastic collision with orbital electron the incident electron is deflected from its original path and loses part of its kinetic energy (collisional loss).
In an inelastic collision with nucleus the incident electron is deflected from its original path and loses part of its kinetic energy in the form of bremsstrahlung (radiative loss)
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The energy loss by incident electron through inelastic collisions is described by the total linear stopping power Stot which represents the kinetic energy EK loss by the electron per unit path length x:
Stot =dEK/dx MeV/cm
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Mass Stopping Power
Total mass stopping power is defined as the linear stopping power divided by the density of the absorbing medium.
It has two parts, collisional and radiative
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Electrons traversing an absorber lose their kinetic energy through ionization collisionsand radiation collisions.
The rate of energy loss per gram and per cm2 is called the mass stopping power and it is a sum of two components:• Mass collision stopping power• Mass radiation stopping power
The rate of energy loss for a therapy electron beam in water and water-like tissues, averaged over the electron’s range, is about 2 MeV/cm.
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Photon Interactions
Probability• “chance” of event happening
can be mathematically expressed
example:
The probability of a woman experiencing breast cancer in her lifetime is 1:9
• x-ray interactions are chance events
relative predictions can be made • energy of the photons
• type of matter the x rays are passing through
cannot predict how one photon will interact
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Photon Interactions
Probability of photon interaction depends on
• Energy of Incident Photon
• The type of traversing matter
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Photon Interactions
Transmitted through matter (unchanged)
Change direction with no energy loss
1.Classical Scattering (Coherent Scattering)
Change direction and lose energy
2.Compton Scattering
Deposit all energy in the matter
3.Photoelectric Effect
4.Pair Production
5.Photodisintegration
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Classical Scattering
(Coherent or Elastic) Occurs at low energy (< 10 keV)
Atom first excited by photon
Then releases (radiates) photon of same keV &
New photon travels in different direction from original photon but usually forward (small scatter angle)
Coherent Scattering is further classified as Rayleigh Scattering
• If interaction occurs with whole atom
Thompson Scattering
• If interaction occurs with shell e-
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Photoelectric Effect (Complete
absorption)
The orbital electron is ejected from the atom with kinetic energy
EK=hν-EB
• where EB is the binding energy of the orbital electron.
The ejected orbital electron is called a photoelectron.
When the photon energy hν exceeds the K-shell binding energy EB of the absorber atom, the photoelectric effect is most likely to occur with a K-shell electron in comparison with higher shell electrons.
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Photoelectric Effect
Electrons in higher energy shells cascade down to fill energy void of inner shell
Characteristic radiation
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Photoelectric interaction probability• inversely proportional to cube of photon
energy low energy event
• proportional to cube of atomic number
P.E ~ Z3/E3
More likely with inner (higher) shells• tightly bound electrons
Interaction much more likely for• low energy photons
• high atomic number elements
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Photon Energy Threshold
• binding energy of orbital electron
binding energy depends on
• atomic number
higher for increasing atomic number
• shell
lower for higher (outer) shells
most likely to occur when photon energy & electron binding energy are nearly the same
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Photoelectric interactions decrease with increasing photon energy BUT• When photon energies just reaches binding
energy of next (inner) shell, photoelectric interaction now possible with that shell
shell offers new candidate target electrons
Causes step increases in interaction probability as photon energy exceeds shell binding energies
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Photon Energy
InteractionProbability
K-shell interactions
possible
L-shell interactions
possible
L-shell binding energy
K-shell binding energy
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Compton Scattering
Source of virtually all scattered radiation
Process
• incident photon (relatively high energy) interacts with free (loosely bound) electron
• some energy transferred to recoil electron
electron liberated from atom (ionization)
• emerging photon has
less energy than incident
new directionElectron out(recoil electron)
Photon inPhoton out
-
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What is a “free” electron?
• low binding energy
outer shells for high Z materials
all shells for low Z materials
Electron out(recoil electron)
Photon in Photon out
-
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Incident photon energy split between electron & emerging photon
Fraction of energy carried by emerging photon depends on
• incident photon energy
• angle of deflection
similar principle tobilliard ball collision
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higher incident energy = less photon deflection
high energy (1MeV) photons primarily scatter forward
diagnostic energy photons scatter fairly uniformly
• forward & backward
at diagnostic energy photons lose very little energy during Compton Scattering
At therapy energy level, photons lose most of energy through Compton scattering
• higher deflection = less energy retained
Electron out(recoil electron)
Photon in Photon out
deflectionangle
-
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' 1 cose
h
m c
λ’ is wavelength of scattered photon and λis the wavelength of incident photon
max
2
1 2eE hf
(Ee)Max is maximum energy transfer torecoil electron and α=hf/mec
2 (rest massenergy of electron
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Interaction Probability is
• independent of atomic number (except for hydrogen)
• Proportional to electron density (electrons/gram)
• fairly equal for all elements except hydrogen (~ double)
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Interaction Probability
• decreases with increasing photon energy
decrease much less pronounced than for photoelectric effect
Photon Energy
InteractionProbability Compton
Photoelectric
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Pair Production (Complete absorption)
Exist at high photon energy
• Ei > 1.022 MeV
(e- rest mass energy = .511 MeV)
Photon interacts with nuclear force field
• uses 1.022 MeV to produce pair of electron like particles
e+ (positron) & e- (negatron)
Photon ceases to exist
E = 1.022 MeV + Ee+KE + Ee-KE
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Photon Interaction Probabilities
Photoelectric Pair Production
COMPTON
Z
10
100
Energy (MeV)
0.01 0.1 1.0 10 100
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Linear Attenuation Coefficient
The most important parameter used for characterization of x-ray or gamma ray penetration into absorbing media is the linear attenuation coefficient μ
The linear attenuation coefficient depends upon:• Energy of the photon beam• Atomic number Z of the absorber
The linear attenuation coefficient may be described as the probability per unit path length that a photon will have an interaction with the absorber
This interaction may be any one of the interactions discussed so for (PE,CS PP etc.)
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For collimated beam of mono-energetic photons, the intensity of photon beam after passing through thickness x of some homogenous medium is
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Several thicknesses of special interest are defined as parameters for mono-energetic photon beam characterization in narrow beam geometry:• Half-value layer (HVL1 or x1/2)
Absorber thickness that attenuates the original intensity to 50%.
• Mean free path (MFP ) Absorber thickness which attenuates the beam
intensity to 1/e = 36.8%.
• Tenth-value layer (TVL or x1/10) Absorber thickness which attenuates the beam
intensity to 10%.
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In medical physics photon interactions fall into four groups:• Interactions of major importance
Photoelectric effect Compton scattering by free electron Pair production (including triplet production)
• Interactions of moderate importance Rayleigh scattering Thomson scattering by free electron
• Interactions of minor importance Photonuclear reactions
• Negligible interactions Thomson and Compton scattering by the nucleus
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For a given hν and Z:
• Linear attenuation coefficient μ is sum of all interaction probabilities, mostly
μ = PE Cross-section + Scattering Cross-section + PP Cross-section