Download Interactions of X and *?radiations

Interactions of Ionizing Radiation
Chung-Chi Lee, PhD
References:
1. Faiz M. Khan, The Physics of Radiation Therapy, 3rd ed.2003
2. Frank H. Attix, Introduction to Radiological Physics and Radiation Dosimetry, 1986
Interactions of x and  radiations
Photon Beam Attenuation
dN  Ndx dI   Idx
xL
dN   Ndx I L dI
   dx

I
I  I0
x 0

ln I |II 0L   x |0xL
I = I0e- x

 (cm -1)


I ( xL )  I 0e   xL
linear attenuation coefficient
Half value layer

HVL = 0.693 / 
I
I0
 1 / 2  e HVL
Photon Beam Attenuation

Attenuation of a monoenergetic beam

An exponential function
Photon Beam Attenuation

Transmission of a beam with a spectrum of
photon energies

deviate from an
exponential expression
Coefficients

Linear attenuation coefficient (cm-1)


Dependent on photon energy & the nature of
material 
Mass attenuation coefficient (cm2/g)


Division of  by  takes away the dependence
on density

Thickness expressed by  x

Coefficients
function of material & photon energy
Coefficients

Electronic attenuation coefficient
 1
2



(
cm
/ electron )
e
 N0


NA  Z
N0 
AW
N0: number of electrons per gram
Atomic attenuation coefficient
 Z
2



(
cm
/ atom)
a
 N0
Coefficients

Energy transfer coefficient (cm-1)

fraction of photon energy transferred into kinetic
energy of charged particles per unit thickness of
absorber
E tr
tr 

h

E tr : the average energy tra nsferred into kinetic
energy of charged particles per interactio n
Mass energy transfer coefficient (cm2/g)
tr E tr 


 h 
Coefficients

Energy absorption coefficient (cm-1)
en  tr (1  g )


g : the fraction of the energy of secondary charged
particles that is lost to bremsstrahlung in the
material
Mass energy absorption coefficient (cm2/g)
en tr

(1  g )


Coefficients

useful reference source:



AAPM TG-21 protocol
Table A-3 from “The Physics of Radiology”, 1983, 4th
by Johns & Cunningham
NIST (National Institute of Standards & Technology)

http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html
Summary
# of photons passing a material with
thickness x without any interaction
# of attenuated photons passing a
material with thickness x
the energy of a photon beam
transferred to charged particles
within a material of thickness x
the absorbed energy of a photon
beam by a material with thickness x
: I  I0  e
(  )(  x )

: I  I 0  (1  e
:tr 0  e
(
:en 0  e
(  )(  x )

tr )(  x )

(
en )(  x )

)
Interactions of x and  radiations
Interactions of a photon beam

I.
Photo Disintegration
•
II.
III.
IV.
V.
Only for very high energy photons
Coherent Scattering
Photoelectric Effect
Compton Scattering
Pair Production
Interactions of x and  radiations

Coherent Scattering



also known as classical or Rayleigh scattering
no energy absorption involved
scattering of the photon at small angles
Interactions of x and  radiations

Photoelectric Effect


a photon interacts with an atom and ejects an atomic
electron with kinetic energy h - EB
the photon was completely disappeared
EB: binding energy of
the orbital electron
Interactions of x and  radiations

Photoelectric Effect

interaction byproducts: characteristic x-rays and Auger
electrons
Interactions of x and  radiations

Photoelectric Effect

interactions can take place with electrons in the K, L, M,
N shells but most probably in the K shell
Interactions of x and  radiations

Photoelectric Effect

interaction probability
: /  Z3/E3
Absorbing edge
Interactions of x and  radiations

Compton Effect

a photon interacts with a “free” electron
Interactions of x and  radiations

Compton Effect

applying conservation laws of energy and momentum
E  h 0
 (1  cos  )
1   (1  cos  )
1
h   h 0
1   (1  cos  )
cos  (1   ) tan  / 2
where   h 0 / m0c 2
Interactions of x and  radiations

Compton Effect

Special cases—direct hit
   0,   180
2
Emax  h 0
1  2
1
  h 0
h min
1  2

Special cases—grazing hit
   90,   0
E  0 & h   h 0
Interactions of x and  radiations

Compton Effect

Interaction of a low-energy photon
 Ex. h0 = 51.1 keV
  h 0 / m0c 2  51.1 / 511  0.1
2(0.1)
 8.52 keV
1  2(0.1)
1
  51.1 (keV)
h min
 42.58 keV
1  2(0.1)
Emax  51.1 (keV)

The scattered photon has almost the same energy as
the incident photon
Interactions of x and  radiations

Compton Effect

Interaction of a high-energy photon
 Ex. h0 = 5.11 MeV
  h 0 / m0c 2  5.11 / 0.511  10
2(10)
 4.87 MeV
1  2(10)
1
  5.11 (MeV)
h min
 0.24 MeV
1  2(10)
Emax  5.11 (MeV)

The scattered photon carries away only a small
fraction of the initial energy
Interactions of x and  radiations

Compton Effect
Compton scatter at   90 and   180
 of special interest in designing radiation protection
barriers
   90 &  >> 1 (very high energy photons)
h 0 h 0
1
h  

 m0c 2  0.511 MeV
1   (1  cos  )
1


h   h 0

  180 &  >> 1 (very high energy photons)
h 0
h
h  
 0  m0c 2 / 2  0.255 MeV
1  2 2
Interactions of x and  radiations

Compton Effect

interaction probability



independent of atomic number Z
dependent only on electron density (# of electrons per gram)
decreases with increasing energy
Interactions of x and  radiations

Pair Production

a photon interacts with a nucleus to create e-, e+ pair
Interactions of x and  radiations

Pair Production


threshold energy: 1.02 MeV (rest mass of e- + e+)
total kinetic energies for e- + e+ pair: h -1.02 MeV
Interactions of x and  radiations

Pair Production


near the end of e+ range, it combines with one
electron and annihilation process occurs
create two annihilation photons, each having energy
of 0.511 MeV
Interactions of x and  radiations

Pair Production


interaction probability increases with Z2 per atom, Z
per electron and Z per gram
probability increases with increasing energy
Interactions of x and  radiations

Total Mass Attenuation Coefficient
(  /  )total  ( /  )coherent  ( /  ) photoelectric
 ( /  )Compton  ( /  ) pair
Interactions of x and  radiations

Relative importance
Interactions of x and  radiations
Interactions of x and  radiations
Interactions of x and  radiations
Interactions of x and  radiations

Relative importance
Interactions of x and  radiations

Relative importance
Interactions of x and  radiations
Interactions of Charged Particles
Introduction
Photons


loss energy in one or a few catastrophic events
Charged Particles




interact with one or more e- or nucleus of practically
every atom it passes
most of the interactions individually transfer only
minute fractions of its kinetic energy
1 MeV charged particle would undergo ~105
interactions to lose all its KE
Interaction Types
I. Ionization
II. Excitation
III. Bremsstrahlung production
Interactions of Charged Particles

mediated by Coulomb force between
the electric field of the traveling
particle and electric fields of orbital
electrons and nuclei of atoms of the
material
Types of Coulomb Force Interactions

Soft collision



b~a
Interactions with external
nuclear field


b >> a
Hard (knock-on) collisions

b << a
Nuclear interactions by
heavy charged particle


e-
e-
high enough KE
b < nucleus radius
e-
nucleus
+
+ ++
++
a
ee-
eb
Undisturbed trajectory
a: atomic radius
b: classical impact parameter
Interactions of Charged Particles
Soft collisions (b >> a)




interact with an atom as a whole
transfer only a small amount of
energy (a few eV)
causing excitation & infrequently
ionization
Interactions of Charged Particles
Hard (knock-on) collisions (b ~ a)






interact with a single atomic electron
causing ejected delta rays to dissipate energy
to form tracks of their own
few in number but comparable energy loss to
soft collision
accompanied with characteristic X-ray or
Auger electron emission
causing ionization of material atoms
Interactions of Charged Particles
Coulomb-Force interactions with the
external nuclear field (b << a)

Elastic Scattering (97-98%)



cross section  Z2
thin foil of high Z as scatter
Interactions of Charged Particles
Coulomb-Force interactions with the
external nuclear field (b << a)

Bremsstrahlung (2-3%)





cross section  Z2
insignificant for low Z material (tissue like) for
electron <10 MeV
cross section  1/M2 for constant v
insignificant for particles other than electron
Interactions of Charged Particles
Stopping Power


the expectation value of the rate of energy
loss per unit of path length x by a charged
particle of type Y and kinetic energy T, in a
medium of atomic number Z
dT
( )Y ,T , Z in MeV/cm or J/m
dx
Interactions of Charged Particles
Mass stopping power

dT
MeV  cm 2
J  m2
(
)Y ,T ,Z in
or
dx
g
kg
Can be subdivided into



Mass Collision Stopping Power
Mass Radiative Stopping Power
dT
dT
dT
(
)c  (
)r
dx
dx
dx
Stopping Power Tables

useful reference sources:



ICRU reports 35 & 37 for electrons
ICRU report 49 for proton and alpha particles
NIST (National Institute of Standards & Technology)

http://physics.nist.gov/PhysRefData/Star/Text/contents.html