3.

0 INTERACTION OF RADIATION WITH MATTER

This chapter introduces the concepts and principles that govern the of interactions x- and γ-ray
photon with matter and the energetic electrons set into motion. It considers the fate of these
electrons as they subsequently transfer and distribute their kinetic energy in the material they
travel through. These electrons transfer their kinetic energy to the surrounding medium by
interacting with surrounding atoms through excitation, ionization, and radiative emissions. The
photon interactions to be discussed in this chapter include Rayleigh and Compton scattering and
photoelectric absorption. The metrics commonly used to describe the change in intensity and
quality of x- and γ-rays by attenuation as they travel through medium (matter) are also discussed.
Energy deposited from radiation per unit mass is the definition of the quantity Absorbed Dose.
The definitions of many “dose” terms, their intended applications, and related concepts are also
discussed below.

3.1 PARTICLE INTERACTIONS

Particles of ionizing radiation include charged particles, such as alpha particles (α+2), protons
(p+), beta particles (β–), positrons (β+), and energetic extranuclear electrons (e –), and uncharged
particles, such as neutrons. The behavior of heavy charged particles (e.g., alpha particles and
protons) is different from that of lighter charged particles such as electrons and positrons.

3.1.1 Excitation, Ionization, and Radiative Losses

Energetic charged particles interact with matter by electrical (i.e., coulombic) forces and lose
kinetic energy via excitation, ionization, and radiative losses. Excitation and ionization occur
when charged particles lose energy by interacting with orbital electrons in the medium. These
interactional, or collisional, losses occur due to the coulombic forces exerted on charged particles
when they pass in proximity to the electric field generated by the atom’s electrons and protons.
Excitation is the transfer of some of the incident particles’ energy to electrons in the absorbing
material, promoting them to a different orbital with a higher energy level. The main difference
between orbitals and energy levels is that orbitals show the most probable pathway of an electron
that is in motion around the nucleus whereas energy levels show the relative locations of orbitals
according to the amount of energy they possess. In excitation, the energy transferred to an
electron does not exceed its binding energy. Following excitation, the electron will return to a

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lower energy level, with the emission of the excitation energy in the form of electromagnetic
radiation or Auger electrons. This process is referred to as de-excitation (Fig. A). If the
transferred energy exceeds the binding energy of the electron, ionization occurs, whereby the
electron is ejected from the atom (Fig. B). The result of ionization is an ion pair consisting of the
ejected electron and the positively charged atom. Sometimes, the ejected electrons possess
sufficient energy to produce further ionizations called secondary ionization. These electrons are
called delta rays.

FIG. A. Excitation (left) and de-excitation (right) with the subsequent release of
electromagnetic radiation. FIG. B. Ionization and the production of delta rays.

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In soft tissue, approximately 70% of the interaction photons with electrons occurs via ionization.
However, as electron energy decreases the probability of energy loss via excitation increases. For
a very low energy electron (˜40 eV) the probabilities of excitation and ionization are equal and
with further reductions in electron energy, the probability of ionization rapidly diminishes
becoming zero (in tissue) below the first ionization state of liquid water at approximately 11.2
eV. So, while the smallest binding energies for electrons in carbon, nitrogen, and oxygen are less
than 10 eV, the average energy deposited per ion pair produced in air (mostly nitrogen and
oxygen) and soft tissue (mostly hydrogen, carbon, and oxygen) is approximately 34 and 22 eV,
respectively. The energy difference is the result of the excitation process. Medical imaging with
x-rays and γ-rays results in the production of energetic electrons by mechanisms discussed later
in this chapter. Each of these energetic electrons will result in an abundance of secondary
electrons as it deposits its energy in tissue. For example, a 10 keV electron will result in the
production of over 450 secondary electrons, most with energies between 10 and 70 eV.

3.1.2 Specific Ionization

The average number of primary and secondary ion pairs produced per unit length of a charged
particle’s path is called the specific ionization, expressed in ion pairs (IP)/mm. Specific
ionization increases with the square of the electrical charge (Q) of the particle and decreases with

the square of the incident particle velocity (v); thus, specific ionization . A larger
charge produces a greater coulombic field; as the particle loses kinetic energy, it slows down,
allowing the coulombic field to interact at a given location for a longer period of time. The
kinetic energies of alpha particles emitted by naturally occurring radionuclides extend from a
minimum of about 4.05 MeV (Th-232) to a maximum of about 10.53 MeV (Po-212). The ranges
of alpha particles in matter are quite limited and, for the alpha particle energies mentioned above,
their ranges in air are 2.49 and 11.6 cm, respectively. In tissue, the alpha particle range is reduced
to less than the diameters of a dozen or so cells (˜30 to 130 µm). The specific ionization of an
alpha particle can be as high as approximately 7,000 IP/mm in air and about 10 million IP/mm in
soft tissue. The specific ionization as a function of the particle’s path is shown for a 7.69-MeV
alpha particle from 214Po in air in the figure below. As the alpha particle slows, the specific
ionization increases to a maximum (called the Bragg peak), beyond which it decreases rapidly as

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the alpha particle acquires electrons and becomes electrically neutral, thus losing its capacity for
further ionization. The large Bragg peak associated with heavy charged particles produced by
specialized accelerators is used at some medical facilities to provide treatment in lieu of surgical
excision or conventional radiation therapy. For example, there are about 30 proton centers
currently in the United States, with many more around the world as well as at least 8 carbon ion
therapy centers. By adjusting the kinetic energy of heavy charged particles, a large radiation dose
can be delivered at a particular depth and over a fairly narrow range of tissue containing a lesion.
On either side of the Bragg peak, the dose to tissue is substantially lower. Compared to heavy
charged particles, the specific ionization of electrons is much lower (in the range of 5 to 10
IP/mm of air).

A figure showing the specific ionization (ion pairs/mm) in air of a 7.69-MeV alpha
particle from 214Po as a function of distance from the end of its range. The rapid increase in
specific ionization reaches a maximum (Bragg peak) and then drops off sharply as the
particle kinetic energy is exhausted and the charged particle is neutralized.

3.1.3 Charged Particle Tracks

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Another important distinction between heavy charged particles and electrons is their paths in
matter. Electrons follow tortuous paths in matter as the result of multiple scattering events caused
by coulombic deflections (repulsion and/or attraction). The sparse tortuous ionization track of an
electron is illustrated in Figure A below. On the other hand, the larger mass of a heavy charged
particle results in a dense and usually linear ionization track (Fig. B) below. The path length of a
particle is defined as the distance the particle travels. The range of a particle is defined as the
depth of penetration of the particle in matter. As illustrated in Figure 3, the path length of the
electron almost always exceeds its range, whereas the typically straight ionization track of a
heavy charged particle results in the path length and range being nearly equal.

3.1.4 Linear Energy Transfer

While specific ionization reflects all energy losses that occur before an ion pair is produced, the
linear energy transfer (LET) is a measure of the average amount of energy deposited locally
(near the incident particle track) in the absorber per unit path length. LET is often expressed in
units of keV or eV per µm. The LET of a charged particle is proportional to the square of the
charge and inversely proportional to the particle’s kinetic energy (i.e., LET Q2/Ek). The LET
of a particular type of radiation describes the local energy deposition density, which can have a
substantial impact on the biologic consequences of radiation exposure. In general, for a given
absorbed dose, the dense ionization tracks of “high LET” radiations (alpha particles, protons,
etc.) deposit their energy over a much shorter range and are much more damaging to cells than
the sparse ionization pattern associated with “low LET” radiations. Low LET radiation includes
energetic electrons (e.g., β– and β+) and ionizing electromagnetic radiation (γ- and x-rays, whose
interactions set electrons into motion).

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 FIGURE A. Electron scattering results in the path length of the electron being greater
than its range. B. Heavily charged particles, like alpha particles, produce a dense, nearly
linear ionization track, resulting in the path and range being essentially equal.

3.1.5 Scattering

Scattering refers to an interaction that deflects a particle or photon from its original trajectory. A
scattering event in which the total kinetic energy of the colliding particles is unchanged is
called elastic. Billiard ball collisions, for example, are elastic (disregarding frictional losses).
When scattering occurs with a loss of kinetic energy (i.e., the total kinetic energy of the scattered
particles is less than that of the particles before the interaction), the interaction is said to
be inelastic. For example, the process of ionization can be considered an elastic interaction if the
binding energy of the electron is negligible compared to the kinetic energy of the incident
electron (i.e., the kinetic energy of the ejected electron is equal to the kinetic energy lost by the
incident electron). If the binding energy that must be overcome to ionize the atom is not
insignificant compared to the kinetic energy of the incident electron (i.e., the kinetic energy of
the ejected electron is less than the kinetic energy lost by the incident electron), the process is
said to be inelastic.

3.1.6 Radiative Interactions—Bremsstrahlung

While most electron interactions with the atomic nuclei are elastic, electrons can undergo
inelastic interactions in which the path of the electron is deflected by the positively charged

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nucleus, with a loss of kinetic energy. This energy is instantaneously emitted as electromagnetic
radiation (i.e., x-rays). Energy is conserved, as the energy of the radiation is equal to the kinetic
energy lost by the electron.

The radiation emission accompanying electron deceleration is called bremsstrahlung, a German

word meaning “braking radiation” (Fig 3.1.6). The deceleration of the high-speed electrons in an
x-ray tube produces the bremsstrahlung x-rays used in diagnostic imaging.

Total bremsstrahlung emission per atom is proportional to Z2, and inversely proportional to the
square of the mass of the incident particle, that is, Z2/m2, where Z is the atomic number of the
absorber. Due to the strong influence of the particle’s mass, bremsstrahlung production by
heavier charged particles such as protons and alpha particles will be less than one-millionth of
that produced by electrons.

The energy of a bremsstrahlung x-ray photon can be any value up to and including the entire
kinetic energy of the deflected electron. Thus, when many electrons undergo bremsstrahlung
interactions, the result is a continuous spectrum of x-ray energies. This radiative energy loss is
responsible for the majority of the x-rays produced by x-ray tubes.

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 FIGURE 3.1.6 Radiative energy loss via bremsstrahlung (braking radiation).

3.2 Neutron Interactions

Unlike protons and electrons, neutrons, being uncharged particles, cannot cause excitation and
ionization via coulombic interactions with orbital electrons. They can, however, interact with
atomic nuclei, sometimes liberating charged particles or nuclear fragments that can directly cause
excitation and ionization (Fig. 3-5). Neutrons often interact with atomic nuclei of light elements
(e.g., H, C, O) by scattering in “billiard ball”-like collisions, producing recoil nuclei that lose
their energy via excitation and ionization. In tissue, energetic neutrons interact primarily with the
hydrogen in water, producing recoil protons (hydrogen nuclei). Neutrons may also be captured
by atomic nuclei. Neutron capture results in a large energy release (typically 2 to 7 MeV) due to
the large binding energy of the neutron. In some cases, one or more neutrons are reemitted; in
other cases, the neutron is retained, converting the atom into a different isotope. For example, the
capture of a neutron by a hydrogen atom ( 1H) results in deuterium (2H) and the emission of a
2.22-MeV γ-ray, reflecting the increase in the binding energy of the nucleus:

1
H + 1n → 2H + γ γ-ray energy (Eγ) = 2.22 MeV.

Some nuclides produced by neutron absorption are stable, and others are radioactive (i.e.,
unstable). As discussed in Chapter 2, neutron absorption in some very heavy nuclides such
as 235U can cause nuclear fission, producing very energetic fission fragments, neutrons, and γ-
rays. Neutron interactions important to the production of radiopharmaceuticals are described in
greater detail in Chapter 16.

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 FIGURE 3-5 Schematic example of collisional energy loss. An uncharged particle
(neutron) interacts with the atomic nucleus of an atom resulting in the ejection of a proton.
This interaction results in the transformation of the atom into a new element with an atomic
number (Z) reduced by 1.

3.2 X-RAY AND GAMMA (γ)-RAY INTERACTIONS

When traversing matter, photons will penetrate without interaction, scatter, or be absorbed. There
are four major types of interactions of x-ray and γ-ray photons with matter, the first three of
which play a role in diagnostic radiology and nuclear medicine: (1) Rayleigh scattering, (2)
Compton scattering, (3) photoelectric absorption, and (4) pair production.

3.2.1 Rayleigh Scattering

In Rayleigh scattering, the incident photon interacts with and excites the total atom, as opposed
to individual electrons as in Compton scattering or the photoelectric effect (discussed later). This
interaction occurs mainly with very low energy x-rays, such as those used in mammography (15
to 30 keV). During the Rayleigh scattering event, the electric field of the incident photon’s
electromagnetic wave expends energy, causing all of the electrons in the scattering atom to
oscillate in phase. The atom’s electron cloud immediately radiates this energy, emitting a photon
of the same energy but in a slightly different direction (Fig. 3-6). In this interaction, electrons are

9
not ejected, and thus, ionization does not occur. In general, the average scattering angle decreases
as the x-ray energy increases. In medical imaging, detection of the scattered x-ray will have a
deleterious effect on image quality. However, this type of interaction has a low probability of
occurrence in the diagnostic energy range. In soft tissue, Rayleigh scattering accounts for less
than 5% of x-ray interactions above 70 keV and at most only accounts for about 10% of
interactions at 30 keV. Rayleigh interactions are also referred to as “coherent” or “classical”
scattering.

3.2.2 Compton Scattering

Compton scattering (also called inelastic or nonclassical scattering) is the predominant

interaction of x-ray and γ-ray photons in the diagnostic energy range with soft tissue. In fact,
Compton scattering not only predominates in the diagnostic energy range above 26 keV in soft
tissue but also continues to predominate well beyond diagnostic energies to approximately 30
MeV. This interaction is most likely to occur between photons and outer (“valence”)-shell
electrons (Fig. 3-7). The electron is ejected from the atom, and the scattered photon is emitted
with some reduction in energy relative to the incident photon. As with all types of interactions,
both energy and momentum must be conserved. Thus, the energy of the incident photon (Eo) is
equal to the sum of the energy of the scattered photon (Esc) and the kinetic energy of the ejected
electron (Ee-), as shown in Equation 3-1. The binding energy of the electron that was ejected is
comparatively small and can be ignored.

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 FIGURE 3-6 Rayleigh scattering. The diagram shows that the incident photon λ1,
interacts with an atom and the scattered photon λ2 is being emitted with the same
wavelength and energy. Rayleigh scattered photons are typically emitted in the forward
direction fairly close to the trajectory of the incident photon. K, L, and M are electron shells.

Compton scattering results in the ionization of the atom and a division of the incident photon’s
energy between the scattered photon and the ejected electron. The ejected electron will lose its
kinetic energy via excitation and ionization of atoms in the surrounding material. The Compton
scattered photon may traverse the medium without interaction or may undergo subsequent
interactions such as Compton scattering, photoelectric absorption (to be discussed shortly), or
Rayleigh scattering.

The energy of the scattered photon can be calculated from the energy of the incident photon and
the angle (with respect to the incident trajectory) of the scattered photon:

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where Esc = the energy of the scattered photon, Eo = the incident photon energy, and θ = the angle
of the scattered photon.

As the incident photon energy increases, both scattered photons and electrons are scattered more
toward the forward direction (Fig. 3-8). In x-ray transmission imaging, these photons are much
more likely to be detected by the image receptor. In addition, for a given scattering angle, the
fraction of energy transferred to the scattered photon decreases with increasing incident photon
energy. Thus, for higher energy incident photons, the majority of the energy is transferred to the
scattered electron. For example, for a 60° scattering angle, the scattered photon energy (Esc) is
90% of the incident photon energy (Eo) at 100 keV but only 17% at 5 MeV. When Compton
scattering occurs at the lower x-ray energies used in diagnostic imaging (15 to 150 keV), the
majority of the incident photon energy is transferred to the scattered photon. For example,
following the Compton interaction of an 80-keV photon, the minimum energy of the scattered
photon is 61 keV. Thus, even with maximal energy loss, the scattered photons have relatively
high energies and tissue penetrability. In x-ray transmission imaging and nuclear emission
imaging, the detection of scattered photons by the image receptors results in a degradation of
image contrast and an increase in random noise.

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 FIGURE 3-7 Compton scattering. The diagram shows the incident photon with
energy Eo, interacting with a valence-shell electron that results in the ejection of the
Compton electron (Ee) and the simultaneous emission of a Compton scattered
photon Esc emerging at an angle θ relative to the trajectory of the incident photon. K, L,
and M are electron shells.

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 FIGURE 3-8 Graph illustrates relative Compton scatter probability as a function of
scattering angle for 20-, 80-, and 140-keV photons in tissue. Each curve is normalized to
100%. (Courtesy of John M. Boone, PhD, Department of Radiology, School of Medicine,
University of California, Davis.)

The laws of conservation of energy and momentum place limits on both scattering angle and
energy transfer. For example, the maximal energy transfer to the Compton electron (and thus, the
maximum reduction in photon energy) occurs with a 180° photon scatter (backscatter). In fact,
the maximal energy of the scattered photon is limited to 511 keV at 90° scattering and 255 keV
for a 180° scattering event. These limits on scattered photon energy hold even for extremely
high-energy photons (e.g., therapeutic energy range). The scattering angle of the ejected electron
cannot exceed 90°, whereas that of the scattered photon can be any value including a 180°
backscatter. In contrast to the scattered photon, the energy of the ejected electron is usually
absorbed near the scattering site.
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The incident photon energy must be substantially greater than the electron’s binding energy
before a Compton interaction is likely to take place. Thus, the relative probability of a Compton
interaction increases, compared to Rayleigh scattering or photoelectric absorption, as the incident
photon energy increases. The probability of Compton interaction also depends on the electron
density (number of electrons/g × density). Except for hydrogen, the total number of electrons/g is
fairly constant in tissue; thus, the probability of Compton scattering per unit mass is nearly
independent of Z, and the probability of Compton scattering per unit volume is approximately
proportional to the density of the material. Compared to other elements, the absence of neutrons
in the hydrogen atom results in an approximate doubling of electron density. Thus, hydrogenous
materials have a higher probability of Compton scattering than anhydrogenous material of equal
mass.

3.2.3 The Photoelectric Effect

In the photoelectric effect, all of the incident photon energy is transferred to an electron, which is
ejected from the atom. The kinetic energy of the ejected photoelectron (Epe) is equal to the
incident photon energy (Eo) minus the binding energy of the orbital electron (Eb) (Fig. 3-9, left).

In order for photoelectric absorption to occur, the incident photon energy must be greater than or
equal to the binding energy of the electron that is ejected. The ejected electron is most likely one
whose binding energy is closest to, but less than, the incident photon energy. For example, for
photons whose energies exceed the K-shell binding energy, photoelectric interactions with K-
shell electrons are most probable. Following a photoelectric interaction, the atom is ionized, with
an inner-shell electron vacancy. This vacancy will be filled by an electron from a shell with
lower binding energy. This creates another vacancy, which, in turn, is filled by an electron from
an even lower binding energy shell. Thus, an electron cascade from outer to inner shells occurs.
The difference in binding energy is released as either characteristic x-rays or Auger electrons.
The probability of characteristic x-ray emission decreases as the atomic number of the absorber
decreases, and thus, characteristic x-ray emission does not occur frequently for diagnostic energy
photon interactions in soft tissue. The photoelectric effect can and does occur with valence shell

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electrons such as when light photons strike the high Z materials that comprise the photocathode
(e.g., cesium, rubidium, and antimony) of a photomultiplier tube. These materials are specially
selected to provide weakly bound electrons (i.e., electrons with a low work function), so when
illuminated the photocathode readily releases electrons. In this case, no inner shell electron
cascade occurs and thus no characteristic x-rays are produced.

FIGURE 3-9 Photoelectric absorption. Left: The diagram shows that a 100-keV
photon is undergoing photoelectric absorption with an iodine atom. A. In this case, the K-
shell electron is ejected with a kinetic energy equal to the difference between the incident
photon energy and the K-shell binding energy (100 keV – 33 keV = 67 keV). B. The
vacancy created in the K shell results in the transition of an electron from the L shell to
the K shell. The difference in their binding energies (i.e., 33 keV – 5 keV) results in a 28-
keV Kα characteristic x-ray. This electron cascade will continue, resulting in the production
of other characteristic x-rays of lower energies. Note that the sum of the characteristic x-ray
energies equals the binding energy of the ejected photoelectron (33 keV). C. An alternative
(competing) process that can occur is the transfer of the difference in binding energy
(transition energy), that would otherwise have been emitted as a characteristic x-ray (in this
case the 28 keV) to an electron in the same atom whose binding energy is less than the
transition energy. The figure shows the 28-keV Kα transition energy being transferred to an
“M” shell electron that is ejected from the atom as an Auger electron with a kinetic energy
equal to the transition energy minus its binding energy (28 keV – 1 keV = 27 keV). The
probability of Auger electron emission increases relative to characteristic x-ray emission as

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 the transition energy decreases.

EXAMPLE: The K– and L-shell electron binding energies of iodine are 33 and 5 keV,
respectively. If a 100-keV photon is absorbed by a K-shell electron in a photoelectric interaction,
the photoelectron is ejected with a kinetic energy equal to Eo – Eb = 100 – 33 = 67 keV. A
characteristic x-ray or Auger electron is emitted as an outer-shell electron fills the K-shell
vacancy (e.g., L to K transition is 33 – 5 = 28 keV). The remaining energy is released by
subsequent cascading events in the outer shells of the atom (i.e., M to L and N to M transitions).
Note that the total of all the characteristic x-ray emissions in this example equals the binding
energy of the K-shell photoelectron (Fig. 3-9, right).

Thus, photoelectric absorption results in the production of

 A photoelectron
 A positive ion (ionized atom)
 Characteristic x-rays or Auger electrons
The probability of photoelectric absorption per unit mass is approximately proportional to Z3/E3,
where Z is the atomic number, and E is the energy of the incident photon. For example, the
photoelectric interaction probability in iodine (Z = 53) is (53/20)3 or 18.6 times greater than in
calcium (Z = 20) for a photon of a particular energy.

The benefit of photoelectric absorption in x-ray transmission imaging is that there are no
scattered photons to degrade the image. The fact that the probability of photoelectric interaction
is proportional to 1/E3 explains, in part, why image contrast decreases when higher x-ray
energies are used in the imaging process. If the photon energies are doubled, the probability of
photoelectric interaction is decreased eightfold: (½)3 = 1/8.

Although the probability of the photoelectric effect decreases, in general, with increasing photon
energy, there are exceptions. For every element, the probability of the photoelectric effect, as a
function of photon energy, exhibits sharp discontinuities called absorption edges (see Fig. 3-10).
The probability of interaction for photons of energy just above an absorption edge is much
greater than that of photons of energy slightly below the edge. For example, a 33.2-keV x-ray

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photon is about six times as likely to have a photoelectric interaction with an iodine atom as a
33.1-keV photon.

As mentioned above, a photon cannot undergo a photoelectric interaction with an electron in a

particular atomic shell or subshell if the photon’s energy is less than the binding energy of that
shell or subshell. This causes a dramatic decrease in the probability of photoelectric absorption
for photons whose energies are just below the binding energy of a shell. Thus, the photon energy
corresponding to an absorption edge is the binding energy of the electrons in that particular shell
or subshell. An absorption edge is designated by a letter, representing the atomic shell of the
electrons, followed by a roman numeral subscript denoting the subshell (e.g., K, LI, LII, LIII). The
photon energy corresponding to a particular absorption edge increases with the atomic number
(Z) of the element. For example, the primary elements comprising soft tissue (H, C, N, and O)
have absorption edges below 1 keV. The element iodine (Z = 53), commonly used in
radiographic contrast agents to provide enhanced x-ray attenuation, has a K-absorption edge of
33.2 keV (Fig. 3-10). The K-edge energy of the target material in most x-ray tubes (tungsten, Z =
74) is 69.5 keV.

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