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Ionising Radiation
There are two types of radiation; ionising and non-ionising.
Non-ionising
Directly ionising (charged particles)
Electrons, protons, α-particles…
Radiation
Ionising
Indirectly ionising (neutral particles)
Photons, neutrons…
Non-ionising Radiation
As its name implies this does not have the ability to give or remove charge from a
neutral particle and thus cannot ionise matter.
Ionising Radiation
This radiation can ionise matter in two ways:
•
•
Directly ionising radiation (charged particles) electrons, protons, α-particles
and heavy ions, or
Indirectly ionising radiation (neutral particles) photons (x-rays and γ-rays) and
neutrons.
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Directly Ionising Radiation
Directly ionising radiation deposits energy in the medium with
which it is interacting by Coulomb interaction of the charged
particle (radiation) with electrons of atoms in the matter
which is being ionised.
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Indirectly Ionising Radiation
Indirectly ionising radiation is not in the form of a charged
particle and so cannot interact directly to ionise the medium
through Coulomb interactions. It must first react with the
matter to release a charged particle which can then go on to
interact with the medium and ionise it through Coulomb
interactions.
E = hν
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Ionising Photons
There are four classifications of ionising photon radiation:
• Characteristic x-rays which result from electron transitions
from atomic shells
• Bremsstrahlung which results from electron-nucleus
Coulomb interactions
• γ-rays which result from nuclear transitions
• Annihilation quanta which result from positron-electron
annihilations (511 keV)
E = hν
E = hν
γ
e-
e+
180°
E = 511 keV
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Electron Interactions
As energetic electrons traverse matter they interact with it
through Coulomb interactions and lose energy. There are two
possible results of these interactions:
• The electron loses energy through collisions or radiative
losses
• The electron can be deflected from its original path
Energy losses are described by the stopping power
Scattering is described by scattering power
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Electron Interactions
The type of interaction of the
incident electron with a particular
atom depends on the impact
parameter b.
b>>a
Soft collision between electron and
electron. Only a small amount of the
incident electron’s kinetic energy will be
transferred to the orbital electrons.
Electron Trajectory
e-
b
Nucleus
a
Electron Cloud
b≈a
This will result in a hard collision and an appreciable amount of the
electrons kinetic energy will be given to the orbital electrons. This can
result in ionisation of the atom or excitation.
b<<a
Coulomb interaction of the electron with the nucleus. This results in x-ray
production through Bremsstrahlung and electron scattering
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Stopping Power
Energy losses by an electron moving through a medium of density ρ are
described by the total mass-energy stopping power (S/ρ)tot This is a
measure of the loss in kinetic energy Ek of the electron per unit path
length x.
S
 
ρ
  tot
dE
 1 k(MeV.cm
ρ dx
2 /g)
The total stopping power consists of two components – the collision
stopping powers (S/ρ)coll (atomic excitations and ionisations) and the
radiative stopping powers (S/ρ)rad (Bremsstrahlung production)
(S/ρ)tot = (S/ρ)coll + (S/ρ)rad
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Linear Energy Transfer (LET)
The stopping power focuses on the amount of energy lost by
an electron traversing a medium. If we focus on how much
energy the medium is gaining from the electron we can
describe a linear rate of energy absorption.
The rate of energy absorption by the material, called the
Linear Energy Transfer (LET), is defined as the average energy
locally imparted to the absorbing medium by an electron of
specified energy traversing a given distance in the medium.
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Photon Beam Attenuation
The intensity of a beam of monoenergetic photons attenuated
by an attenuator of thickness x is given by
I(x) = I(0) e-μ(hν, Z)x
where
I(0) is the intensity of the unattenuated beam, and
μ(hν, Z) is the linear attenuation coefficient which depends on
the energy of the photon hν and the atomic number Z of the
attenuator.
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Half Value Layer (HVL)
The Half Value Layer (HVL or x½) is defined as the thickness of
the attenuator that will attenuate the photon beam to 50% of
it’s original intensity
From
I(x) = I(0) e-μ(hν, Z)x
we have
½ = 1 e-μx½
-ln 2 = -μx½
x½ = (ln 2)/μ
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Linear Attenuation Coefficient μ
The linear attenuation coefficient μ is related to the mass
attenuation coefficient μm, atomic attenuation coefficient aμ
and electronic attenuation coefficient eμ as follows:
μ = ρ μm = (ρ NA aμ)/A = (ρ NA eμ Z)/A
The units of the linear, mass, atomic and electronic
attenuation coefficients are: cm-1, cm2/g, cm2/atom and
cm2/electron.
This implies that the thickness given in (–μx) must be quoted in
units of: cm, g/cm2, atoms/cm2 and electrons/cm2 respectively
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The Photoelectric Effect
In the photoelectric effect the photon interacts with an orbital
electron and disappears, while the electron is ejected from
the atom thus ionising it. The energy of the photoelectron is
given by
Ek = hν – EB
Where Ek is the kinetic energy of the ejected electron, hν the
energy of the photon and EB the binding energy of the
electron.
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The Photoelectric Effect
The mass attenuation coefficient for the photoelectric effect
is proportional to (Z/hν)3
Mass attenuation coefficient (cm2/g)
The plot of hν versus mass attenuation shows some sharp discontinuities
where hν equals the binding energy of particular electronic shells. These
discontinuities, called absorption edges, are caused because for a
particular shell, the electrons cannot undergo the photoelectric effect
without energy hν greater than or equal to the binding energy of that shell.
L edges
1000
100
10
K edge
1
0.1
0.01
0.01
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0.1
1
Photon energy (MeV)
10
Compton Effect
The Compton effect represents a
photon scattering off an atom and
ejecting an orbital electron from
that atom. As hν>>EB the electron
can be treated as free and
stationary when compared to the
photon.
Recoil electron
Incident photon
θ
The energy of the photon dictates
the average angle of deflection. For
θ = 0, φ = π/2 (no change in photon
direction) and for θ = π, φ = 0 (back
scattering of the photon).
Incident
The following is a table of average
scattering and recoil values
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φ
Scattered photon
Photon Energy
(MeV)
Scattered
Photon Energy
(MeV)
Recoil Electron
Energy (MeV)
0.1
0.085
0.015
1
0.560
0.440
10
3.1
6.9
100
20
80
Pair Production
In pair production, a photon in the nuclear Coulomb field of an
atom converts to an electron-positron pair.
e+
E = hν
There is a minimum activation energy for
this conversion of hν ≥ 2mec2 = 1.02 MeV
Any photonic energy above this minimum
threshold is shared equally by the
electron-positron pair as kinetic energy
If the pair production occurs in the field of an orbital electron
then three particles are created and this process is called triplet
production. An electron-positron pair are created and an orbital
electron. The minimum energy for this activation is 4mec2 and
all particles share this energy.
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180°
e-
Mass attenuation coefficient (cm2/g)
Photonic Attenuation
1000
1000
L edges
Photoelectric Effect
mass attenuation coefficient
100
10
K edge
1
Combined
mass attenuation
coefficient
0.1
0.01
100
10
1
0.1
Compton Effect
mass attenuation coefficient
0.01
0.1
0.01
1
10
Pair Production
mass attenuation
coefficient
100
Photon energy (MeV)
The above graph shows the individual and combined mass
attenuation effects upon photons at varying photon energies.
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Atomic Number Z
Photonic Attenuation
Photoelectric
Effect
Dominant
Pair
Production
Dominant
Compton
Effect
Dominant
Photon Energy (MeV)
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