chapter 5 interactions of ionizing radiation. ionization the process by which a neutral atom...
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Chapter 5Interactions of Ionizing Radiation
Ionization• The process by which a neutral atom acquires a
positive or a negative charge• Directly ionizing radiation
– electrons, protons, and particles– sufficient kinetic energy to produce ionization ray• excitation
• Indirectly ionizing radiation– neutrons and photons– to release directly ionizing particles from matter when
they interact with matter
Photon beam description
• Fluence ()
• Fluence rate or flux density ()
• Energy fluence ()
• Energy fluence rate, energy flux density, or intensity ()
da
dN
dtda
dN
dt
d
da
dE fl
dtda
dE
dt
d fl
Photon beam attenuation
• x–the absorber thickness (cm) –linear attenuation coefficient (cm-1)
• I–intensity
dxNdN
dxNdN
xeIxI
dxIdI
0)(
Half-value layer (HVL)
• x=HVL I/I0=1/2 6930.
HVL
A mono-energetic beam A practical beam produced by an x-ray generator
Coefficients (1)
• Linear attenuation coefficient (, cm-1) – Depend on the energy of the photons
the nature of the material
• Mass attenuation coefficient (/, cm2/g)– Independent of density of material– Depend on the atomic composition
Coefficients (2)
• Electronic attenuation coefficient (e, cm2/electron)
• Atomic attenuation coefficient (a, cm2/atom)0
1
Ne
0N
Za
w
A
A
ZNN
0
Z the atomic number
N0 the number of electrons per gram
NA Avogradro’s number
AW the atomic weight
Coefficients (3)
• Energy transfer coefficient (tr)
– When a photon interacts with the electrons in the material, a part or all of its energy is converted into kinetic energy of charged particles.
h
E trtr
The average energy transferred into kinetic energy of charged particles per interaction
trE
Coefficients (4)
• Energy absorption coefficient (en)
– Energy loss of electrons• Inelastic collisions lossesionization and excitation
• Radiation lossesbremsstrahlung
en= tr(1-g)
– g fraction energy loss to bremsstrahlung• increses with Z of the absorber
the kinetic energies of the secondary particles
Etr = ? Een=?
1 MeV
(Initial Energy ofCompton Electron, Ee) (Bremsstrahlung)
(Scattered Photon)0.3 MeV
0.7 MeV
0.2 MeV
(Incident Photon, h)
Energy imparted of photon
Interactions of photons with matter
• Photo disintegration (>10 MeV)
• Coherent scattering (coh) Photoelectric effect ()
• Compton effect (c)
• Pair production ()
nXX AZ
AZ
10
1
Coherent scattering
• Classical scattering or Rayleigh scattering– No energy is changed into electronic motion– No energy is absorbed in the medium– The only effect is the scattering of the photon at
small angles.
• In high Z materials and with photons of low energy
K
LM
Photoelectric effect (1)
• A photon interacts with an atom and ejects one of the orbital electrons.
h-EB
Photoelectric effect (2)
/ Z3/E3
• The angular distribution of electrons depends on the photon energy.
15 keV
L absorption edge
88 keV
K absorption edge
Compton effect (1)
• The photon interacts with an atomic electron as though it were a “free” electron.– The law of conservation of energy
– The law of conservation of momentum
1
1
122
200
cvcmhh
/'
sin/
sin'
cos/
cos'
22
0
22
0
1
1
cv
vm
c
hcv
vm
c
h
c
h
K
LM
h
h’
Free electron
Compton electron
…………(1)
………(2)
…...…………(3)
Compton effect (2)
= h0/m0c2 = h0/0.511
)cos()cos(
11
10hE
)cos('
11
10hh
h0
h’
Free electron
E
By (1), (2), (3)
Special cases of Compton effect
• The radiation scattered at right angles (=90°) is independent of incident energy and has a maximum value of 0.511 MeV.
• The radiation scattered backwards is independent of incident energy and has a maximum energy of 0.255 MeV.
Dependence of Compton effect on energy
• As the photon energy increase, the photoelectric effect decreases rapidly and Compton effect becomes more and more important.
• The Compton effect also decreases with increasing photon energy.
Dependence of Compton effect on Z
• Independent of Z• Dependence only on the number of electrons per
gramelectrons/g
Pair production
• The photon interacts with the electromagnetic field of an atomic nucleus.
• The threshold energy is 1.02 MeV.
• The total kinetic energy for the electron-positron pair is (h-1.02) MeV.
h
E-
E+
+-
0.51 MeV
0.51 MeV
Positron annihilation
The probability of pair production
Z2/atom
PE effect
Compton effect
PP production
h
h
h
Ee
E+
E-
tr
h
hh
h
Etr
'
h
h
h
EEtr
021.
The relationships between and tr
PE effect
Compton effect
PP production
h
h
h
Ee
E+
E-
)1( gtren
)1( gtren
)1( gtren
The relationships between tr and en
The comparison between and en
Interactions of charged particles
• Coulomb force– Collisions between the particle and the atomic electrons
result in ionization and excitation.
– Collisions between the particle and the nucleus result in radiative loss of energy or bremsstrahlung.
• Nuclear reactions• Stopping power (S) =
• Mass stopping power (S/, MeV cm2/g)
lengthpath
lossenergykinetic
Heavy charged particles
• The particle slows down
energy loss ionization or absorbed
dose
2
2
(velocity)
charge)particle(theS
Bragg peak
Electrons
• Multiple changes in direction during the slowing down process smears out the Bragg peak.
Ionization
Excitation
Bremsstrahlung
Interactions of neutrons
• Recoiling protons from hydrogen and recoiling heavy nuclei from other elements– A billiard-ball collision
– The most efficient absorbers of a neutron beam are the hydrogenous materials.
• Nuclear disintegrations– The emission of heavy charged particles, neutrons,and rays
– About 30% of the tissue dose
Comparative beam characteristics (1)
• Neutron beams nBBeH 10
105
94
21
Comparative beam characteristics (2)
• Heavy charged particle beams
Comparative beam characteristics (3)
• Electron beams & protons
Thank you…Thank you…