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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
Pair Production
γ
0.511 MeV
Photon Energy (MeV)
Atomic Number of Absorber
120
100
6.2 Interaction ofγ-Radiations withMatter
73
–
e
ray
-
Z
N
Fig. 6.6 Illustration of the pair production process. An energetic γ-ray with energy greater than
1.02MeV interacts with the nucleus, and one positive electron (e
are produced at the expense of the photon. The photon energy in excess of 1.02MeV appears as
the kinetic energy of the two particles. The positive electron eventually undergoes annihilation to
produce two 511-keV photons emitted in opposite directions
Fig. 6.7 Relative
contributions of the
photoelectric effect,
Compton scattering, and
pair production as a
function of photon energy
in absorbers of different
atomic numbers. (Adapted
with permission from
Hendee 1970a)
100
80
60
40
20
K
LM
0
0
0.1 110
e
+
) and one negative electron (e−)
Compto
+
0.511 MeV
n
–
e
+
e
scattering is predominant in intermediate Z absorbers at medium energies (~1MeV).
At higher energies (>10MeV), pair production predominates in all Z absorbers.
6.2.1.4 Raleigh Scattering
In Raleigh scattering, a γ-ray can interact with the atom as a whole atom instead of
individual orbital electrons, whereby the photon energy is spent for the atom to
oscillate in phase. The atom then releases the energy in the form of a γ-ray with
almost the same energy as the initial γ-ray, which is emitted at a slightly different
angle than the original γ-ray. This scattering is also termed coherent or classical
74
I Ie
t
x
0
.
6 Interaction ofRadiation withMatter
scattering. Since it occurs only with low-energy photons (<40keV) and as its overall probability of occurrence is low, it is of little signicance in nuclear medicine.
6.2.1.5 Photodisintegration
When the γ-ray photon energy is very high (>10MeV), the photon may interact with
the nucleus of the absorber atom and transfer sufcient energy to the nucleus such
that one or more nucleons may be emitted. This process is called the photodisinte-
gration reaction or photonuclear reaction and produces new nuclides. The (γ, n)
reactions on targets such as 12C and 14N have been used to produce 11C and 13N
radionuclides but now are rarely used to produce radionuclides.
6.3 Attenuation ofγ-Radiations
6.3.1 Linear andMass Attenuation Coefficients
γ-ray and x-ray photons are either attenuated or transmitted as they travel through
an absorber. Attenuation results from absorption of photons of various energies by
the photoelectric effect, Compton scattering, and pair production at higher energies.
Depending on the photon energy and the density and thickness of the absorber,
some of the photons may pass through the absorber without any interaction leading
to the transmission of the photons (Fig.6.8). Attenuation of γ-radiations is an important factor in radiation protection.
As shown in Fig.6.8, when a photon beam of initial intensity I0 passes through
an absorber of thickness x, then the transmitted beam It is given by the exponential
equation:
(6.4)
Fig. 6.8 Illustration of
attenuation of a photon
beam (I
) in an absorber of
0
thickness x. Attenuation
comprises a photoelectric
effect (τ), Compton
scattering (σ), and pair
production (κ). Photons
passing through the
absorber without
interaction constitute the
transmitted beam (I
t
‐
)
t
µ .
4
PHOTON ENERGY (MeV)
0
6.3 Attenuation ofγ-Radiations
75
where μ is the linear attenuation coefcient of the absorber for the photons of interest and has the unit of cm−1. The factor e
−μx
represents the fraction of the photons
transmitted. Because attenuation is primarily due to photoelectric, Compton, and
pair production interactions, the linear attenuation coefcient μ is the sum of photoelectric coefcient (τ), Compton coefcient (σ), and pair production coefcient
(κ). Thus,
(6.5)
Linear attenuation coefcients normally decrease with the energy of the γ-ray or
x-ray photons and increase with the atomic number and density of the absorber. The
relative contributions of photoelectric effect, Compton scattering, and pair production in water (equivalent to body tissue) at different energies are illustrated in
Fig.6.9.
An important quantity, µm, called the mass attenuation coefcient, is given by the
linear attenuation coefcient divided by the density ρ of the absorber
µ
m
(6.6)
The mass attenuation coefcient µm has the unit of cm2/g or cm2/mg. The mass
attenuation coefcients for fat, bone, muscle, iodine, and lead are given in Fig.6.10.
6.3.2 Half-Value Layer
The concept of half-value layer (HVL) of an absorbing material for γ- or x- radiations
is important in the design of shielding for radiation protection. It is dened as the
thickness of the absorber that reduces the intensity of a photon beam by one-half.
Thus, an HVL of an absorber around a source of γ-radiations with an exposure rate
Fig. 6.9 Plot of linear
attenuation coefcient of
γ-ray interaction in water
(equivalent to body tissue)
as a function of photon
energy. The relative
contributions of
photoelectric, Compton,
and pair production
processes are illustrated
1
c
0.1
0.01
0.001
0.01 0.1 1.0
Water
c
10 10
76
10
2
PHOTON ENERGY (keV)
H
0 693.
TV
= 332. HVL
Fig. 6.10 Attenuation
coefcients for fat, muscle,
bone, iodine, and lead as a
function of photon energy.
(Adapted with permission
from Hendee 1970b)
6 Interaction ofRadiation withMatter
bone
muscle
50
iodine
100
10
10
10
1
lead
0
fat
-1
0
of 150mR/h will reduce the exposure rate to 75 mR/h. The HVL depends on the
energy of the radiation and the atomic number of the absorber. It is greater for highenergy photons and smaller for high-Z materials.
For monoenergetic photons, the HVL of an absorber is related to its linear attenuation coefcient as follows:
150
VL
Because μ has the unit of cm−1, the HVL has the unit of cm. The HVLs of lead
for different radionuclides are given in Table6.2.
Another important quantity, tenth-value layer (TVL), is the thickness of an
absorber that reduces the initial beam by a factor of ten. It is given by
ln ..01
L
230
(6.7)
(6.8)
(6.9)
0 693 0 693
003
..
.
HVL
052
..
..
.
x
L
xc
mm
6.3 Attenuation ofγ-Radiations
77
Table 6.2
Half-value layers HVLs and tenth-value layers TVLs of lead, concrete, and water or
tissue for commonly used radionuclides in nuclear medicine
HVL, concrete
a
Radionuclides HVL, lead (cm)
137
Cs 0.72 4.8 2.18
18
F 0.50 1.51
131
I 0.27 2.93 6.3 0.99
123
I 0.007 0.11
99m
Tc 0.023 4.6 0.091
111
In 0.026 0.20
67
Ga 0.086 0.48
57
Co 0.03 0.085
60
Co 1.56 6.6 4.53
201
Tl 0.026 3.7 0.089
99
Mo 0.058 2.34
177
Lu 0.054 0.211
a
Adapted with permission from Smith and Stabin (2012)
(cm)
HVL, water or
tissue (cm) TVL, lead (cm)
Problem 6.2
If the HVL of lead for the 140-keV photons of
99m
Tc is 0.03cm of lead, calculate the linear attenuation coefcient of lead for the 140-keV photons and
the amount of lead needed to reduce the exposure of a point source of radiation by 70%.
Answer
a
23 1
1
.
cm
Because the initial beam is reduced by 70%, the remaining beam is 30%.
23 1
.
03 1
.
03 23 1
n
120231
0 052
.
x
e
x
x
m
Thus, 0.52mm of lead will reduce a beam of 140-keV photons by 70%.
78
6 Interaction ofRadiation withMatter
6.4 Interaction ofNeutrons withMatter
Because neutrons are neutral particles, their interactions in the absorber differ from
those of the charged particles. They interact primarily with the nucleus of the
absorber atom and very little with the orbital electrons. The neutrons can interact
with the atomic nuclei in three ways: elastic scattering, inelastic scattering, and
neutron capture. If the sum of the kinetic energies of the neutron and the nucleus
before collision is equal to the sum of these quantities after collision, then the interaction is called elastic. If a part of the initial energy is used for the excitation of the
struck nucleus, the collision is termed inelastic. In neutron capture, a neutron is
captured by the absorber nucleus, and a new excited nuclide is formed. Depending
on the energy deposited, an α-particle, a proton, a neutron, or γ-rays can be emitted
from the excited nucleus, and a new product nuclide (usually radioactive) is
produced.
6.5 Questions
1. (a) What is the difference between excitation and ionization? (b) How are δ-rays
produced? (c) How much energy is required on the average to produce an ion
pair in air by charged particles?
2. Dene specic ionization (SI), linear energy transfer (LET), and range (R).
3. Electromagnetic radiations and electrons have low LETs compared to heavy
particles (e.g., α-particles), which have high LETs. Explain.
4. The range of an α-particle is almost equal to the total path traveled, whereas the
range of an electron is less than the total path traveled by the particle. Explain.
5. Indicate how the range of a charged particle is affected by the following
conditions:
(a) As the mass increases, the range increases or decreases.
(b) As the energy of the particle increases, the range increases or decreases.
(c) As the charge of the particle increases, the range increases or decreases.
6. Dene Bragg ionization and straggling of ranges. Which has more straggling,
an α-particle or an electron? Explain.
7. How is bremsstrahlung produced? Does its production increase or decrease
with increasing kinetic energy of the electron and the atomic number of the
absorber? Explain why 32P is stored in plastic containers.
8. Discuss the mechanism of the photoelectric effect. Does this process increase
or decrease with increasing energy of the γ-ray and with increasing atomic
number of the absorber?
9. A 0.495-MeV γ-ray interacts with a K-shell electron by the photoelectric process. If the binding energy of the K-shell electron is 28 keV, what happens to the
rest of the photon energy?
10. (a) Explain the Compton scattering of electromagnetic radiations in the
absorber.
(b) Does it depend on the atomic number of the absorber?
(c) How is it affected by the γ-ray energy?
Suggested Readings
79
11. If a relatively high-energy γ-ray is scattered at 180° (backscattered) by the
Compton scattering, what is the maximum energy of the scattered photon?
12. (a) How does pair production occur?
(b) Why does pair production require a minimum of 1.02MeV for γ-ray energy?
(c) Is this process affected by the atomic number of the absorber and the pho-
ton energy?
13. Which electrons of the absorber atom are involved in the photoelectric and
Compton interactions of electromagnetic radiations?
14. (a) Discuss the attenuation of a photon beam passing through an absorber. (b)
Does it depend on the density and the atomic number of the absorber?
(a) Dene the half-value layer (HVL) of an absorbing material for a γ-
ray energy.
15. If 1 mCi of a radionuclide is adequately shielded by 5 HVLs of a shielding
material, how many HVLs are needed to provide equal shielding for (a) 5 mCi
and (b) 8 mCi?
16. A 1-mm lead apron will afford approximately twice as much protection as a
0.5-mm apron, or does this shielding depend on the energy of the radiation?
17. How many HVLs are approximately equivalent to three tenth-value layers?
18. Suppose 5% of the 364-keV photons of
a lead brick of 10-cm thickness, calculate the HVL of lead for
131
I are transmitted after passing through
131
I.
19. There is a 75% chance that a monoenergetic photon beam will be attenuated by
4mm of lead. What is the HVL of lead for the photon?
20. Which of the following radiations has the highest LET?
(a) 120-keV x-ray
(b) 100-keV electron (c) 5-MeV α-particle
(a) 10-MeV proton
(b) 14-MeV neutron
21. Dene Cerenkov radiation and Raleigh scattering.
Suggested Readings
Cherry SR, Sorensen JA, Philips ME. Physics in Nuclear Medicine. 4th ed. Philadelphia:
W.B.Saunders 2012.
Friedlander G, Kennedy JW, Macias ES, Miller JM. Nuclear and Radiochemistry. 3rd ed.
NewYork: Wiley; 1981
Knoll GF. Radiation Protection and Measurement. 4th ed. NewYork: Wiley; 2010.
Lapp RE, Andrews HL. Nuclear Radiation Physics
Hall; 1972.
Smith DS, Stabin MG.Exposure rate constants and lead shielding values for over 1,100 radionu-
clides. Health Phys. (2012); 102(3):271-291. https://doi.org/10.1097/hp.0b013e318235153a.
PMID: 22420019.
Hendee WR. Medical Radiation Physics.1st ed. Chicago: Year Book Medical Publishers, Inc;
1970a: 141
Hendee WR. Medical Radiation Physics. 1st ed. Chicago: Year Book Medical Publishers, Inc;
1970b: 221
. 4th ed. Englewood Cliffs, NJ: Prentice-
Gas-Filled Detector
7.1 Principles of Gas-Filled Detector
The operation of a gas-lled detector is based on the ionization of gas molecules by
radiation, followed by collection of the ion pairs as charge or current with the application of a voltage between two electrodes. The measured charge or current is proportional to the applied voltage and the amount and energy of radiation, and depends
on the type and pressure of the gas.
A schematic diagram of a gas-lled detector is shown in Fig.7.1. When an ionizing radiation beam passes through the gas, it causes ionization of the gas molecules and ion pairs are produced depending on the type and pressure of the gas.
When a voltage is applied between the two electrodes, the negative electrons will
move to the anode and the positive ions to the cathode, thus producing a current that
can be measured on a meter.
At very low voltages, the ion pairs do not receive enough acceleration to reach
the electrodes and may combine together to form the original molecule instead of
being collected by the electrodes. This region is called the region of recombination
(Fig.7.2). As the applied voltage is gradually increased, a region of saturation is
encountered, where the current measured remains almost the same over the range of
applied voltages. In this region, only the primary ion pairs formed by the initial
radiations are collected. Individual events cannot be detected; only the total current
passing through the chamber is measured. Because specic ionization differs for α-,
β-, and γ-radiations, the amount of current produced by these radiations differs in
this region. The voltage in this region is of the order of 50–300V.Ionization chambers such as dose calibrators are operated in this region.
When the applied voltage is further increased, the electrons and positive ions
gain such high velocities and energies during their acceleration toward the electrodes that they cause secondary ionization. The latter will increase the measured
current. This process is referred to as the gas amplication. This factor can be as
high as 10
6
per individual primary event depending on the design of the gas detector
7
© The Author(s), under exclusive license to Springer Science+Business Media, LLC,
part of Springer Nature 2025
G. B. Saha, Physics and Radiobiology of Nuclear Medicine,
https://doi.org/10.1007/978-1-0716-4816-2_7
81
82
V
T
+
–
Applied Voltage
Fig. 7.1 A schematic
diagram of a gas-lled
detector illustrating the
principles of operation
Fig. 7.2 A composite
curve illustrating the
current output as a result of
increasing voltages for
different radiations. (a)
Region of recombination,
(b) region of saturation, (c)
proportional region, (d)
region of limited
proportionality, (e) Geiger
region, and (f) continuous
discharge
7 Gas-Filled Detector
+
+
A B C D E
+
+
–
–
AIR OR GAS
–
+
+
+
–
+
+
+
α
β
+
+
CURREN
F
γ
and the applied voltage. In this region, the total current measured is equal to the
number of ionizations caused by the primary radiation multiplied by the gas amplication factor. Also, the current increases with the applied voltage in proportion to
the initial number of ion pairs produced by the incident radiation. Therefore, as in
the case of the region of saturation, the current amplication is relatively proportional to the types of radiations, for example, α-, β-, and γ-radiations. This region is
referred to as the proportional region (see Fig.7.2). Proportional counters are usu-
ally lled with 90% argon and 10% methane (P-10) at atmospheric pressure. These
counters can be used to count individual counts and to discriminate radiations of
7.2 Ionization Chamber
83
different energies, but are not commonly used for γ- and X-ray counting because of
poor counting efciency (<1%).
As the applied voltage is increased further, the current produced by different
types of radiation tends to become identical. The voltage range over which the current tends to converge is referred to as the region of limited proportionality. This
region is not practically used for detecting any radiation in nuclear medicine.
With additional increase in voltage beyond the region of limited proportionality,
the current becomes identical for all radiations, regardless of how many ion pairs
are produced by the incident radiations. This region is referred to as the Geiger
region (see Fig.7.2). In the Geiger voltage region, the current is produced by an
avalanche of interactions. When highly accelerated electrons strike the anode with
great force, ultraviolet (UV) light is emitted, which causes further emission of photoelectrons by gas ionization and from the chamber walls. The photoelectrons will
again strike the anode to produce more UV, and hence an avalanche spreads along
the entire length of the anode. The amplication factor can be as high as 1010. During
the avalanche, however, the lightweight electrons are quickly attracted to the anode,
whereas a sheath of slow-moving heavy positive ions builds up around the anode.
As a result, the voltage gradient falls below the value necessary for ion multiplication, and therefore the avalanche is terminated. All this occurs in less than 0.5μs,
and the counter is left insensitive and must recover before another event can be
counted.
Recovery begins with the migration of the positive ions toward the cathode (i.e.,
chamber wall) and takes about 200μs at a gas pressure of 0.1 atmosphere, which is
equal to the dead time of the counter that varies with gas pressure. As the positive
ions approach the cathode, secondary electrons may be emitted from the surface of
the cathode, which then set another discharge just about 200μs after the previous
one. Such repetitive discharges that are due to secondary electrons are independent
of the types and energy of radiation that the counter is intended to measure. The
emission of secondary electrons is suppressed by a technique known as quenching
to eliminate repetitive counter discharges (see later).
As the applied voltage is increased beyond the Geiger region, a single ionizing
event produces a series of repetitive discharges leading to what is called spontane-
ous discharge. This region is called the region of continuous discharge because the
gas may be ionized in the absence of radiation at this high voltage (see Fig.7.2).
Operation of a detector in this region may cause damage to the detector.
7.2 Ionization Chamber
Ionization chambers are operated at voltages in the saturation region that spans
50–300V.The detector is a cylindrical or rectangular chamber lled with air or a
gas, sometimes at high pressure. A central wire and the chamber act as the electrodes and the current is measured by an electrometer. The detection efciency of
the ionization chambers for X-rays and γ-rays is very low (<1%) and depends on the