Transcript Chapter 5: Interaction of Radiation with Matter (輻射與物質的交互作用)

Chapter 5
Interaction of Radiation with Matter
KS Chuang
Interaction of Radiation with Matter
Interaction Cross Sections (作用截面)
Interaction Mechanisms (作用機制)
Energy Transfer
Review: Structures of Radiological Physics
X-ray Tube (X光管)
Radiation
Sources
(輻射源)
Radioactive Source (放射性射源)
Accelerator (加速器)
Radiation
Interactions
(輻射作用)
Photon Interactions (光子作用)
Electron Interactions (電子作用)
Medical Imaging (醫學影像)
Radiation
Applications
(輻射應用)
Radiation Therapy (放射治療)
Radiation Protection (輻射防護)
X-ray Interaction with Body Tissues
Photon energy transfers to electron
(光子能量轉移電子)
Electron energy imparts to matter
(電子能量給予物質)
Ionization, excitation, bond breaks
(游離、激發、分子鍵斷裂)
Physical effect (imaging)
Chemical effect (imaging)
Biological effect (therapy)
Interaction Cross Section
• Microscopic Cross Section (微觀截面)
– Atomic cross section (原子截面) / Atomic
attenuation coefficient (原子衰減係數)
– Electronic cross section (電子截面) /
Electronic attenuation coefficient (電子衰減
係數)
• Macroscopic Cross Section (巨觀截面)
– Linear attenuation coefficient (線性衰減係數)
– Mass attenuation coefficient (質量衰減係數)
Cross Section (截面)
Small cross section
Differential
cross section
Large cross section
The larger the cross
section, the larger is the
probability that you
score.
Atomic Cross Section (原子截面)
no interaction
interaction
photon
photon
Atomic c.s. = am
Unit = barn (10-24 cm2)
The probability of a photon-atom interaction is
proportional to the atomic cross section.
Electronic Cross Section (電子截面)
no interaction
interaction
photon
photon
Electronic c.s. = em
The probability of a photon-electron interaction is
proportional to the electronic cross section.
If every electron has the same cross section, am = Z em
Linear Attenuation Coefficient
(線性衰減係數)
Volume
photon
Linear attenuation coefficient = m = am  Na
Unit = cm-1
The number of photon-atom interactions in a unit (linear)
distance is proportional to the (linear) attenuation
coefficient.
Mass Attenuation Coefficient
(質量衰減係數)
Mass
photon
Mass attenuation coefficient = m/r = am  Na/r
Unit = cm2/g
The number of photon-atom interactions in a unit (mass)
distance is proportional to the (mass) attenuation
coefficient.
Atomic Cross Section (am)
Electronic Cross Section (em)
Interaction with an atom

photon
am
 P /
em
 P /
atom
Interaction with an electron

photon
electron
Macroscopic Cross Section or
Attenuation Coefficient: m and m/r
Interaction with all atoms in a unit volume
m a m  N a

photon
Na 
atoms
cm3
Interaction with all atoms in a unit mass

m / ra m  ( N a / r)
photon
Na / r 
atoms
kg
Photon Interaction Coefficients
Relations Among
Interaction Coefficients
N Ar number of atoms

A
volume
N r
number of electrons
Ne  A Z 
A
volume
N A  Avogardo' s number, r  density, Z  atomic number
Na 
 cm 2 
 1 
 atoms 
m   a m 
  Na 

 cm 
 cm 3 
 atom 
 cm 2 
 1 
 electrons 
m   e m 

N
 e

 cm 
 cm 3 
 electron 
m / r )  m / r
Linear Attenuation Coefficient, m
N=number of photons interact in x
 N / N fraction of photons that interact in x
m

x
x
N  N 0e  mx (exponenti al attenation law)
Energy Transfer Coefficient
(能量轉移係數)
N+N
N
N+N
E+E
E
Absorption
E
E+E
N
 N / N
m
x
 E / E
m tr 
x
Scattering
 E / E  N  h  h '

x
x N  h
 N / N h  h '
E

 m hk
x
h
m tr 
Half-Value Layer (HVL, 半值層)
N 0 / 2  N 0e  mxh
HVL  xh 
ln 2
m

0.693
m
Broad Beam (寬射束)
N  N 0e mx B( x , h, A, L)
B : buildup factor (增建因數)
Energy Transfer (能量轉移)
Energy Absorption (能量吸收)
interaction
h
Etr
Energy transfer (from x-ray
to electron)
interaction
h
Eab
bremsstrahlung
Energy imparted (from
electron to medium):
Energy absorbed
Energy Transfer Coefficient (能量轉移係數)
Energy Absorption Coefficient (能量吸收係數)
m tr / r )  m / r ) Etr
h
mab / r )  m / r ) Eab
h
0.26 MeV is radiated as
bremsstrahlung
Photoelectric Effect
h
photoelectron
x
E= h - B.E.
m pe   
Z 3r
( h ) 3
 Etr  Eab  h (for low Z material)
    tr  ab
 (cm2/atom)
Photoelectric Effect
water
h
lead
Summary of Photoelectric Effect
• Process involves bound electrons
• Prob of ejection is maximum if the photon has
just enough energy to knock the electrons
from its shell
• Cross section varies 1/E3
• Coeff per gram varies with Z3
Compton Effect
Θ=45o
△λ
λ’
Mo Kα
X Rays : λ=0.714
A

INTENSIRY
Θ=90o
△λ
Θ=135
o
Graphite Target
The Compton shift Δλ=λ- λ’
0.700
0.750
24
Compton Effect (康普吞效應)
h
Compton electron-
x
E = h - h ’
mce    r
Etr
 tr  
h

  for low energy photon
  for high energy photon
Compton Scattering with Free
Electron
mo v
hv hv'

cos  
 cos 
c
c
1  v2 / c2
mo v
hv'
sin  
 sin 
c
1  v2 / c2
Conservation of Energy


1


2
hv  hv'  E  mo c 
 1
2
2


 1 v / c

Compton Scattering
 (1  cos  )
E  hv 
1   (1  cos  )
1
hv'  hv 
1   (1  cos  )
hv

2
m0c
Emax: electron is
knocked straight
forward (photon 
=180)
Emin (=0 ): electron
ejected at right angle
(photon  = 0)
Compton Effect
Electronic Cross Section
 m2/electron)
不考慮B.E. (cross section determined
by Klein-Nishina formula)
考慮B.E.
h
Energy Transfer in a Compton Scattering
Very little energy is transferred in Compton scattering
for low energy photons
Ex: Determine the maximum energy of recoil electron
for (a) an incident photon of low energy and (b) an
incident of high energy
• incident photon with energy = 51.1 keV
  51.1 / 511  0.1
2
2  0.1
Emax  hv 
 51.1 
 8.5 keV
2  1
0.2  1
• High energy photon E=5.11 MeV
  5.11 / .511  10.
2
2  10.
Emax  hv 
 51.1 
 4.87 MeV
2  1
20  1
In a Compton collision between a very high energy
photon and an electron, show that the radiation (a)
scattered at right angle is approximately 0.511 MeV
and (b) scattered backward is 0.255 MeV
• (a) scattered at right angle  = 90o
hv'  hv 

hv

1
hv

1   (1  cos  ) 1  
 0.511 MeV
• (b) scattered backward  = 180o
hv'  hv 
1
hv

1   (1  cos  ) 1  2
hv

 0.255 MeV
2
 >> 1
Summary of Compton Process
•
•
•
•
Interaction between a photon and a free electron
Independent of atomic number
Decrease with increase in energy
In each collision some energy is scattered and some
absorbed depending on the collision angle of photon
energy
• Fraction of energy transferred to K.E. increase with
photon energy
• Most important for photon energy between 100keV
to 10MeV
Pair Production
E-
e-
hv
0.511 MeV
e+ E+
mpp    Zr
E  E  1.02  hv
h  1.02 MeV
 tr  
h
0.511 MeV
Triplet Production
 m2/atom)
Pair Production
Atomic Cross Section
h
Summary for Pair Production
•
•
•
•
Between a photon and the nuclear charge
Threshold for the process 1.02 MeV
Increase rapid with energy
Increase rapidly with atomic number Z2 per
atom
• Energy absorbed is (E-1.02) MeV
• Two annihilation photons (0.511 MeV)
produced
m/r m2/kg)
Total Attenuation Coefficient
h
Percentage
Relative Importance for Different Types of
Interactions
Photon Energy (MeV)