1. 輻射與物質的作用
Interaction of radiation with matter
林信宏 (Hsin-Hon Lin) Assistant Professor
Department of Medical Imaging and Radiological Sciences
Chang Gung University
2. 2
Interaction of Particles with Matter
1.0
Radioactive Decay
Produce particles
Nuclear fission neutron
Matter
Particle interaction
4. 1.1 β-Ray: Range–Energy Relationship (I)
Experimental arrangement for absorption
measurements on beta particles.
Absorption curve (aluminum absorbers)
of 210Bi beta particles.
Count per minute
Range
Background radiation
5. 1.1
Range–energy curves for
beta particles in various
substances.
• Areal density (electrons/cm2)
of electrons in the absorber (o)
• The atomic number of the
absorber (x)
◼ Areal density ∝ Density thickness
td (g/cm2) = ρ (g/cm3) × t1 (cm)
Maximum Range
Density
Low
High
β-Ray: Range–Energy Relationship (II)
6. 1.1
The quantitative relationship between beta energy and
range is given by the following experimentally
determined empirical equations:
Range:
R = 0.407E 1.38 E ≤ 0.8 MeV
R = 0.542E − 0.133 E ≥ 0.8 MeV
Energy:
E = 1.92R 0.725 R ≤ 0.3 g/cm2
E = 1.85R + 0.245 R ≥ 0.3 g/cm2
where
R = range, g/cm2 and
E = maximum beta energy, MeV.
β-Ray: Range–Energy Relationship (III)
8. 1.3
◼ Interaction between the electric fields of a beta particle and
the orbital electrons of the absorbing medium leads to
electronic excitation and ionization.
Ek = Et − φ
φ : the ionization potential of the absorbing medium
Et : the energy lost by the beta particle during the collision
Ek: the kinetic energy of the ejected electron e-
◼ Delta ray: the ejected electron (the order of 1 keV ) may receive a
considerable amount of energy, enough to cause it to travel a long
distance and to leave a trail of ionizations.
◼ The average energy expenditure per ion pair (w) in air: 34 eV/ip
β-Ray: Ionization and Excitation
9. 1.3
◼ Stopping power : The linear rate of energy loss = dE/dx
(KeV/cm)
◼ Specific Ionization (SI)
• The number of ion pairs formed per unit distance traveled by
the beta particle.
𝑆𝐼
𝑖𝑝
𝑐𝑚
=
d𝐸
dx
( Τ
eV cm)
𝑤 Τ
(eV ip)
• Used when attention is focused on the energy lost by the
radiation. W: the average energy expenditure per ion pair.
β-Ray: Specific Ionization (SI) (比游離)
Path
11. 1.3 β-Ray: Stopping Power(阻擋本領)
• Mass stopping power
S Τ
eV∙cm2 g =
Τ
𝑑𝐸 𝑑𝑥
𝜌
◼ Focused on the on the energy lost by the radiation.
• Linear Energy Transfer (LET)
LET( Τ
𝑘𝑒𝑉 μ𝑚)=
𝑑𝐸𝐿
d𝑙
◼ Focused on the energy absorption by the absorbing medium.
• Relative Mass Stopping Power
ρ𝑚 =
𝑆𝑚𝑒𝑑𝑖𝑢𝑚
𝑆𝑎𝑖𝑟
12. 1.4 β-Ray: Bremsstrahlung (制動輻射)
• X-rays emitted when high-velocity charged particles
undergo a rapid change in velocity.
◼ Bremsstrahlung has a continuous energy distribution.
• Fraction of incident β energy converted into photons (X-
rays):
𝑓𝛽=3.5×10−4𝑍𝐸𝑚
◼ Z = atomic number of absorber, Em= maximal β energy in MeV
Beta shields are therefore made with
materials of the minimum practicable
atomic number. In practice, materials of
>13 (Al) are avoided for β-ray shielding.
14. 1.5 β-Ray: X-ray Production
• Fraction of the mono-energetic energy in the electron beam is
converted into X-rays:
𝑓𝑒=1 × 10−3𝑍𝐸
◼ Z = atomic number of absorber
◼ E= energy of electron in MeV
17. 2.1 α-Ray: Range–Energy Relationship
• Range in air (at 0◦C and 760 mm Hg, STP):
Ra(cm) = 0.322E3/2 (MeV), for 2<E<8 MeV
• The number of alphas is not reduced until the approximate
range is reached.
Monoenergetic
18. 2.1 α-Ray: Range–Energy Relationship
• Range in other medium:
Rm × ρm × (Aa)0.5 = Ra × ρa × (Am)0.5
where
Ra and Rm = range in air and tissue (cm).
Aa and Am = atomic mass number of air and the medium.
ρa and ρm = density of air and the medium (g/cm3).
• Range in tissue: ( Aa ≈At )
Ra × ρa = Rt × ρt
where
Ra and Rt = range in air and tissue (cm).
ρa and ρt = density of air and the tissue (g/cm3).
19. 2.2 α-Ray: Energy Transfer
Bragg peak
◼ As the alpha particle undergoes
successive collisions and slows
down, its specific ionization
increases because the electric
fields of the alpha particle and
the electron have longer times
to interact, and thus more
energy can be transferred per
collision.
◼ An alpha particle loses energy at
an increasing rate as it slows
down until the Bragg peak is
reached near the end of its
range.
Bragg peak
This peak occurs because the cross section of
interaction increases immediately before the
particle come to rest.
20. 2.2 Why no Bragg peak occurs in electron/beta ?
Charged particles lose more energy per cm as they
slow down, so there’s a large dose enhancement
just before they stop. This “Bragg peak” is
sharper, the more massive the particle. The
electron peak is very broad because of the small
electron mass. (range straggling)
mass 273 times that of the electron Ne
20
10
Bragg Peak
21. 3.1 γ-Ray: Interaction Cross Section (作用截面)
Small cross section Large cross section
If the dart hits the target, you score. The larger the cross
section, the larger is the probability that you score.
22. 3.1 γ-Ray: Atomic Cross Section (原子截面)
Atomic c.s. = μa
Unit = barn (10-24 cm2)
The probability of a photon-atom interaction
is proportional to the atomic cross section.
photon
photon
interaction
no interaction
23. 3.2 γ-Ray: Linear Attenuation Coefficient
The probability of a photon-atom interaction is
proportional to the atomic cross section.
Linear attenuation coefficient = μl= μa N (unit = cm-1)
photon
Volume
24. 3.2 γ-Ray: Linear Attenuation Coefficient
• Microscopic cross section: (σ=μa)
σ(cm2/atom)= μl(cm-1)/N (atoms/cm3)
• Macroscopic (total) cross section: (Σ = μl)
Σ (cm-1)= σ(cm2/atom) × N (atoms/cm3)
• Attenuation coefficient for combined materials:
μl= (μa)A × NA +(μa)B × NB
26. 3.3 γ-Ray: Exponential Absorption (衰減吸收)
Incident photon intensity
collimator
Transmitted
photon intensity
Scattered photons
I
dx
I0
I = I0 × e-μt
Where
I0 = gamma-ray intensity at zero absorber thickness
t = absorber thickness
I = gamma-ray intensity transmitted through an absorber of thickness t
e = base of the natural logarithm system
μ = slope of the absorption curve = the attenuation coefficient (衰減係數).
t
27. 3.3 γ-Ray: Good geometry
Conditions:
• Well-collimated
• Large source-to-detector distance
• Thin absorber
• No scattering material in the vicinity of the detector
Narrow beam of radiation
monoenergetic beams
heterochromatic beam
30. 30
3.5 γ-Ray: Pair Production (成對發生)
• The photon interacts with the electromagnetic field of nucleus and gives
up all its energy to create an electron (e-) and a positron (e+)
• Eγ > 1.02 MeV = 2m0C2 for this interaction to happen.
• Kinetic energy transfer = (hf – 2m0C2) MeV.
• σpp(κ) ∝ log(E)(Z2)
Followed by annihilation radiation
31. Compton e-
(E)
(Eγ’)
(Ee-)
3.6 γ-Ray: Compton Scattering (康普吞散射)
• Incident photon interacts with a free electron
𝐸𝑒− = 𝐸
α(1−𝑐𝑜𝑠𝜃)
1+α (1−𝑐𝑜𝑠𝜃)
𝐸γ′ = 𝐸
1
1+α(1−𝑐𝑜𝑠𝜃)
where α =
𝐸
𝑚0𝐶2 =
𝐸
0.511
(E: MeV)
• Kinetic energy transfer = (hf –hf ’) = E – E’
• σcs(κ) ∝ Z/E
33. 3.7 γ-Ray: Photoelectric Absorption (光電吸收)
• Incident photon interacts with a bounded electron
• Kinetic energy transfer = hf – 𝜙 = Eγ – 𝜙 (𝜙: binding energy)
• σpe(κ) ∝ Z4-5/E3
• Predominant for low-energy γ-rays
34. 3.7 γ-Ray: K, L, or M edges
lead
water
Eγ
σ
pe
(cm
2
/atom)
88 keV
K,L edge
Characteristic x-ray
Auger electron
35. 3.8 γ-Ray: Photonuclear reaction (光核反應)
• Also called photodisintegration (光蛻變)
• A(γ,n) B reactions
• Threshold reactions (低限反應)
• Important for very high energy γ-rays
◼ 9Be(γ , n)8Be (>1.67 MeV)
39. 39
4.0 Types of ionizing radiation
◼ Direct ionizing radiation
Direct interactions via the Coulomb force along a particles track
• Charged particles
• Electrons
• Positrons
• Protons
• heavy charged particles
◼ Indirectly Ionizing Radiation
Uncharged particles that must first transfer energy to a charged
particle which can then further ionize matter
• Two step process
• Electromagnetic radiations: x- or γ-rays
• Neutrons
40. Charged particle interaction: Electron/Beta/alpha
◼ Elastic, resulting in no loss of energy
◼ Inelastic, where the kinetic energy of the incident
electron changes
• Inelastic collisions with orbital electrons
excitation
Ionization
• Inelastic collisions with the nucleus
bremsstrahlung
40
4.0 Review: Particle interaction
41. 4.1 Neutron: Classification according to energy
41
Different energy ranges of neutrons:
Ultracold: E < 10-6 eV
Cold and very cold: E = (10-6 eV – 0.0005 eV)
Thermal neutrons: E= (0.002 eV – 0.5 eV) neutrons are in thermal
equilibrium with neighborhood [≈ 0.025 eV ]
Epithermal neutrons and resonance neutrons: E = (0.5 eV – 1000 eV)
Slow neutrons: E < 1 keV
Neutrons with middle energies: E = (1 keV – 500 keV)
Fast neutrons: E = (0.5 MeV – 20 MeV) [ > 0.1 MeV ]
Neutrons with high energies: E = (20 MeV – 100 MeV)
Relativistic neutrons: E= (0,1 – 10 GeV)
Ultrarelativistic neutrons: E > 10 GeV
10-6 eV
ENERGY RANGE
5×10-4 eV
0.5 eV
1000 eV
1 keV
0.5 MeV
20 MeV
100 MeV
10 GeV
43. 43
4.3 Neutron: Elastic Scattering
Elastic Scattering (n, n)
(彈性碰撞)
• Most for fast neutron and low-Z absorbers
(e.g., H)
• Kinetic energy
Scattering neutron: 𝐸 = 𝐸0
𝑀−𝑚
𝑀+𝑚
2
Target nucleus: 𝐸0 − 𝐸 = 𝐸0 1 −
𝑀−𝑚
𝑀+𝑚
2
• For H, (E0-E)max =E0
(E0,m)
M
44. 44
4.4 Neutron: Inelastic Scattering
Inelastic Scattering (n, nγ)
(非彈性碰撞)
• Neutron can excite the nucleus, then
emitted γ-rays
• Most for high-E neutrons and high-Z
materials
• Impossible for H
γ- rays
45. 45
4.5 Neutron: Absorption
Neutron Capture (n,x) (中子捕獲)
• Most for thermal neutrons
• Absorption (neutron-capture) cross section:
𝜎 ∝
1
𝐸
∝
1
𝑣
(one-over-law)
• 113Cd and 10B are good neutron
absorbers
Neutron absorption cross
sections for boron, showing
the validity of the 1/v law
46. 46
4.5 Neutron: Absorption
Non-elastic reactions: Transmutation (n, x)
A nucleus may absorb a neutron forming a compound nucleus, which then de-energizes by
emitting a charged particle, either a proton or an alpha particle. This produces a nucleus of
a different element. Such a reaction is called a transmutation.
Neutron-Proton
Reaction (n, p)
Neutron-Alpha
Reaction (n, α)
47. 47
4.6 Neutron: Neutron Attenuation
• It is customary to designate only the microscopic cross
section σ for the absorbing material
I = I0 × e -Nσt =I0 × e-Σt
Where Σ is the neutron attenuation coefficient and Σ =Nσ (N is
the atomic density (atoms/cm3), the number of nuclei per unit
volume)
• Neutron cross sections are strongly energy dependent
