Radiation Interactions
Robert Metzger, Ph.D.
Interactions with Matter
Charged particles lose energy as they interact
with the orbital electrons in matter by excitation
and ionization, and/or radiative losses.
Excitation occurs when& the incident particle
bumps an electron to a higher orbital in the
absorbing medium.
Ionization occurs when the transferred energy
exceeds the binding energy of the electron and it
is ejected. The ejected electron may then also
produce further ionizations.
Specific Ionization
The number of ion pairs produced per unit
path length is the specific ionization.
Alpha particles can produce as many as
7,000 IP/mm. Electrons produce 50-100
IP/cm in air.
LET is the product of the specific ionization
and the average energy deposited per IP
[IP/cm x eV/IP].
About 70% of electron energy loss leads to
non-ionizing excitation.
Charged Particle Tracks
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e- follow tortuous paths through matter as the result of multiple
Coulombic scattering processes
An α2+, due to it’s higher mass follows a more linear trajectory
Path length = actual distance the particle travels in matter
Range = effective linear penetration depth of the particle in matter
Range ≤ path length
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p.34.
Bremsstrahlung
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Deceleration of an e- around a
nucleus causes it to emit
Electromagnetic radiation or
bremsstrahlung (G.): ‘breaking
radiation’
Probability of bremsstrahlung
emission  Z2 Ratio of e- energy
loss due to bremsstrahlung vs.
excitation and ionization =
KE[MeV]∙Z/820
Thus, for an 100 keV e- and
tungsten (Z=74) ≈ 1%
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p.35.
Electromagnetic
Radiation Interactions
Raleigh Scattering: Photon is scattered with no
energy loss. Uncommon at diagnostic energies.
Compton Scattering:Photon strikes outer
electron and ejects it, resulting in energy loss of
photon and change of direction.
Photoelectric Effect: Photon is totally absorbed
by K or L shell electron which is ejected.
Pair Production: High energy photon interaction.
Rayleigh Scattering
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Excitation of the total
complement of atomic
electrons occurs as a result of
interaction with the incident
photon
No ionization takes place
No loss of E
<5% of interactions at
diagnostic energies.
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p. 37.
Compton Scattering
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Dominant interaction of x-rays with
soft tissue in the diagnostic range
and beyond (approx. 30 keV 30MeV)
Occurs between the photon and a
“free” e- (outer shell e- considered
free when Eg >> binding energy,
Eb of the e- )
Encounter results in ionization of
the atom and probabilistic
distribution of the incident photon
E to that of the scattered photon
and the ejected e
A probabilistic distribution
determines the angle of deflection
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p. 38.
Compton Scattering
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Compton interaction probability is dependent on the total
no. of e- in the absorber vol. (e-/cm3 = e-/gm · density)
With the exception of 1H, e-/gm is fairly constant for
organic materials (Z/A 0.5), thus the probability of
Compton interaction proportional to material density ()
Conservation of energy and momentum yield the
following equations:
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Eo = Esc + Ee-
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Esc =
E0
E0
1+
1- cosθ 
2 
m ec
, where mec2 = 511 keV
Compton Scattering
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As incident E0  both photon
and e- scattered in more
forward direction
At a given  fraction of E
transferred to the scattered
photon decreases with  E0
For high energy photons most
of the energy is transferred to
the electron
At diagnostic energies most
energy to the scattered photon
Max E to e- at  of 180o; max
E scattered photon is 511 keV
at  of 90o
c.f. Bushberg, et al. The Essential Physics of Medical Imaging,
2nd ed., p. 39.
Photoelectric Effect
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All E transferred to e- (ejected photoelectron) as kinetic energy (Ee) less the
binding energy: Ee = E0 – Eb
Empty shell immediately filled with e- from outer orbitals resulting in the
emission of characteristic x-rays (Eg = differences in Eb of orbitals), for
example, Iodine: EK = 34 keV, EL = 5 keV, EM = 0.6 keV
c.f. Bushberg, et al.
The Essential Physics
of Medical Imaging,
2nd ed., p. 41.
Photoelectric Effect
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Eb  Z2
Photoe and cation; characteristic x-rays and/or Auger e
Probability of photoe- absorption  Z3/E3 (Z = atomic no.)
Explains why contrast  as higher energy x-rays are used in the
imaging process
Due to the absorption of the incident x-ray without scatter,
maximum subject contrast arises with a photoe- effect
interaction
Increased probability of photoe- absorption just above the Eb of
the inner shells cause discontinuities in the attenuation profiles
(e.g., K-edge)
Photoelectric Effect
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1 st ed., p. 26.
Photoelectric Effect
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Edges become significant factors for higher Z materials
as the Eb are in the diagnostic energy range:
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Contrast agents – barium (Ba, Z=56) and iodine (I, Z=53)
Rare earth materials used for intensifying screens – lanthanum
(La, Z=57) and gadolinium (Gd, Z=64)
Computed radiography (CR) and digital radiography (DR)
acquisition – europium (Eu, Z=63) and cesium (Cs, Z=55)
Increased absorption probabilities improve subject contrast and
quantum detective efficiency
At photon E << 50 keV, the photoelectric effect plays an
important role in imaging soft tissue, amplifying small
differences in tissues of slightly different Z, thus
improving subject contrast (e.g., in mammography)
Pair Production
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Conversion of mass to E occurs upon the interaction of a high E
photon (> 1.02 MeV; rest mass of e- = 511 keV) in the vicinity of a
heavy nucleus
Creates a negatron (β-) - positron (β+) pair
The β+ annihilates with an e- to create two 511 keV photons
separated at an  of 180o
c.f. Bushberg, et al. The
Essential Physics of
Medical Imaging, 2nd ed.,
p. 44.
Radiation Interactions
A
B
WHICH IS
HIGH kVp CHEST
RADIOGRAPH AND
WHICH IS LOW kVp
CHEST
RADIOGRAPH ?
Compton vs Photoelectric
A
B
WHICH IS
LOW kVp BONE
RADIOGRAPH
AND WHICH IS
HIGH kVp BONE
RADIOGRAPH ?
Linear Attenuation Coef
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Cross section is a measure of the probability (‘apparent
area’) of interaction: (E) measured in barns (10-24 cm2)
Interaction probability can also be expressed in terms of
the thickness of the material – linear attenuation
coefficient: (E) [cm-1] = Z [e- /atom] · Navg [atoms/mole] ·
1/A [moles/gm] ·  [gm/cm3] · (E) [cm2/e-]
(E)  as E , e.g., for soft tissue
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(30 keV) = 0.35 cm-1 and (100 keV) = 0.16 cm-1
(E) = fractional number of photons removed
(attenuated) from the beam by absorption or scattering
Multiply by 100% to get % removed from the beam/cm
Attenuation Coefficient
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An exponential relationship between the incident
radiation intensity (I0) and the transmitted intensity (I)
with respect to thickness:
I(E) = I0(E) e-(E)·x
total(E) = PE(E) + CS(E) + RS(E) + PP(E)
At low x-ray E: PE(E) dominates and (E)  Z3/E3
At high x-ray E: CS(E) dominates and (E)  
Only at very-high E (> 1MeV) does PP(E) contribute
The value of (E) is dependent on the phase state:
water vapor << ice < water
Attenuation Coefficient
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p. 46.
Mass Attenuation Coef
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Mass attenuation coefficient m(E) [cm2/g] –
normalization for : m(E) = (E)/Independent of
phase state () and represents the fractional number
of photons attenuated per gram of material
- (E)··x
I(E) = I0(E) e m
Represent “thickness” as g/cm2 - the effective
thickness of 1 cm2 of material weighing a specified
amount (·x)
Half Value Layer
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Thickness of material required to reduce the intensity of
the incident beam by ½
½ = e-(E)·HVL or HVL = 0.693/(E)
Units of HVL expressed in mm Al for a Dx x-ray beam
For a monoenergetic incident photon beam (i.e., that
from a synchrotron), the HVL is easily calculated
Remember for any function where dN/dx  N which
upon integrating provides an exponential function (e.g.,
I(E) = I0(E) ∙ e±k·w ), the doubling (or halving) dimension w
is given by 69.3%/k% (e.g., 3.5% CD doubles in 20 yr)
For each HVL, I  by ½: 5 HVL  I/I0 = 100%/32 = 3.1%
Mean Free Path
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Mean free path (avg. path length of x-ray) = 1/ = HVL/0.693
Beam hardening
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The Bremsstrahlung process produces a wide spectrum of energies,
resulting in a polyenergetic (polychromatic) x-ray beam
As lower E photons have a greater attenuation coefficient, they are
preferentially removed from the beam
Thus the mean energy of the resulting beam is shifted to higher E
c.f. Bushberg, et al. The
Essential Physics of
Medical Imaging, 1st
ed., p. 281.
Effective Energy
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The effective (avg.) E of an x-ray beam is ⅓ to ½ the peak value
(kVp) and gives rise to an eff, the (E) that would be measured if
the x-ray beam were monoenergetic at the effective E
Homogeneity coefficient = 1st HVL/2nd HVL
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A summary description of the x-ray beam polychromaticity
HVL1 < HVL2 < … HVLn; so the homogeneity coefficient < 1
c.f. Bushberg, et al. The Essential Physics of Medical
Imaging, 2nd ed., p. 45.
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 43.
Shielding
I = BI0 e-x
I is the Intensity in shielded area
I0 is the unattenuated intensity
B is the buildup factor
 is the attenuation coefficient
X is the shield thickness
Shielding
The buildup factor is the ratio of scattered
photons that scatter back into the beam.
Since the photoelectric effect dominates at
diagnostic x-ray energies, the buildup factor
is 1.0.
Therefore lead aprons work well in diagnostic
x-ray, but not in Nuclear Medicine (140 keV
gammas)
Buildup must be considered for PET.