effect of Compton scattering and its application

1. OPTICAL MATERIALS
COMPUTON EFFECT
Prepared by:
Anteneh Andualem Tsegaye

2. COMPUTON EFFECT
(SCATTERING)

3. Contents
 Introduction
 General Formalism
 The mathematical description of Compton effect ( scattering )
 Practical application areas of Compton effect
 Compton scatter densitometer (CSD) ,
 Compton scatter imaging (CSI)
 Compton profile analysis (CPA )

4. Introduction
 The wave theory : we can understand that charged particles would
interact with the light since the light is an electromagnetic wave.
 If we consider the photon idea of light, some of the photons would
“hit” the charged particles and “bounce off”. The laws of
conservation of energy and momentum should then predict the
scattering ( particle property of light)
 Compton effect: Quantum theory of light states that a photon
behaves as a relativistic particle with zero rest mass.

5. The classical vs Quantum model
, ,f I t 
Compton showed that
Depends only on the
scattering angle.

6. General Formalism
 and be the wavelengths of the incident and scattered x rays.1 2
P of scattered photon
Initial P of photon
Consider an x-ray photon colliding with a single electron at rest

7. Mathematical Description
Conservation of momentum
1 1
1
1
........................1
E hf h
p
c c 
  
2 2
2
2
........................2
E hf h
p
c c 
  
1 2 1 2
2 2 2
1 2 1 22 .
e e
e
p p p p p p
p p p p p
    
  
 Energy and momentum conservation can be used to analyze
the problem

8. Conservation of energy
 Energy of electron before collision
2 2 2
1 2 1 22 cos .....................3ep p p p p   
P of electron after collision and θ is scattering angle of
the photon
2
oE mc

9.  Energy of electron after collision
 Then conservation of energy
 Transposing p2c and squaring
 
1/2
2 2 2
o eE p c
 
1/2
2 2 2
1 2 .................4o o ep c E p c E p c   
 1 22 2 2
1 2 1 2
2
2 ...................5o
e
E p p
p p p p p
c

   

10.  Compair equation 3 and 5
 Multiplying each term by
 Equation 7 is called Compton equation
 
 1 2
1 2 1 cos ................6oE p p
p p
c


 
1 2
,
o
hc h
p p E p
 
 2 1 ..................1 co ..s . 7
h
mc
      
Compton wave length =2.4 x 10-12nm

11.  The greater the angle of the scatter ,the more energy is lost by
the photon
 Loss of Energy = Increase in Wavelength.
 2 1 1 cos
h
mc
       
2 hc
E mc hf

  
The Physical Interpretation

12. Bound and free Electrons
 In considering the Compton effect, how would you compare the
scattering of photons from bound and free electrons?
 If electrons are bound to an atom, the whole atom recoil
,carrying away most of the energy into the collision thus
change of wave length is small even not detectable.
 1 cos
h
mc
  

13.  For free electron , mass of electron giving very large
change in wave length, thus Compton effect is likely to
be easily observable for free electron.
 1 cos
h
mc
  
Free electron

14. Compton Effect Spectra examples
Forward scattered spectrum shows
only peak at input wave length λ
At scattering angle θ > 0 a
Compton peak appears at the
scattered wavelength λ`
θ > 0 a peak remains at the
incident wave length due to
scattering from more strongly
bound electron ( high effective
mass of electron due to strong
binding to nucleus)
0o
 
45o
 
90o
 

15. Compton vs Photoelectric Effect
 E.g. An X-ray photon has sufficient energy to overcome the work
function. What determines whether the photoelectric or Compton
effect takes place?
 If the electron is free ,both Compton and photoelectric effect are
equally likely to occur. If the electron is bound ,Compton
scattering will be come less noticeable.
 1 cos
h
mc
  

16. Application of Compton effect
Compton scatter densitometer (CSD)
 The electron density in certain volume of an object can be obtained
by applying Compton scattering.
 Where dN is the number of counts per second; ϕ0 is the photon
flux of the incident beam ; f1 and f2 are respectively the
exponential attenuation factors of the primary beam and the
scattered beam; ρe is the electron density of the tested material.
 
 1 2 ,KN
o e
d
dN f f dV S q z
d
 
 


17.  Is the Klein-Nishina differential cross section with σKN as the total
cross section and θ the scattered angle; S(q ,Z) is the incoherent
atomic scatter function that accounts for electron binding energy
effects with q being the photon momentum transfer.
 KNd
d
 


18.  For a certain incident photon energy and flux in a fixed geometry
(θ , f1 and f2 are fixed), the count rate dN depends only on the
electron density of the tested material.

19.  Therefore, with the CSD, the physical density of scattered objects
can be measured.
 The objects can be also tested by CSD even if they have defects
like flaws, impurity or bubbles.
 Practically, the technique is used very widely in industry,
agriculture, and other fields.

20. Compton scatter imaging (CSI)
 Theoretically: used to obtain the information of a volume element
by a detector at the scatter angle in the energy spectrum of a
scatter.
 Records the scatter signal from a certain volume element.
 Advantages : ability to provide quantitative 3D images of the
electron density distribution of an object without the need for all-
round access to the object.
 Disadvantage : relatively low scanning rate.

21. Compton profile analysis (CPA )
 CPA is based directly on the dependence of the Compton scattered
photon energy spectrum (Compton profile) upon the elemental
composition of the scattering material.
 The spectrum is usually measured by using a high-resolution
detector and is related directly to the composition parameters of a
small Z element material.
 CPA offers good discrimination between materials such as water or
organic compounds and inorganic material of low Z elements

22. General use
In physics
 Measurement of electron distribution of the scattered and electron
momentum.
In chemistry
 The type of chemical bonds between electrons.
 Characterizing mineral density in the bone and composition in the
tissue and measuring ash in coal and solid loading fraction in
slurry

23. Conclusion
 Compton disproof the classical theory of scattering
 The wavelength shift of x-rays scattered at a given angle is
absolutely independent of the intensity of radiation and the length
of exposure, and depends only on the scattering angle.
 Compton scattering is more observable for free electron.
 Compton effect uses for application such as electron and mineral
density measurement in certain volume of an object, type of
chemical bonds , Measurement of electron distribution and
momentum.

24. Home Massage
 Does the photon can transfer all of its
energy to a free electron ?
 Why and how to proof it?
 Hint: Energy and momentum must be conserved.

25. Reference
1. LUO Guang1,2,a, ZHOU Shang-qi1, HAN Zhong3, CHEN Shuang-kou4 ,
applications of Compton scattering Vol. 5 No. 4.
2. Raymond a. Serway; Modern Physics third Edition.
3. Holt R S, Cooper M J, Jackson D F. Gamma-ray scattering techniques for non-
destructive testing and imaging [J]. Nucl Instr and Meth.
4. J.M. Sharaf , Practical aspects of Compton scatter densitometry, Applied
Radiation and Isotopes 54 (2001) 801- 809.

27. Answers
Question one
 Conservation of momentum
 Total energy of electron
2 2
.
.
o o
e
hf m c m c K E
hc
K E hf p c

  
  
   
2 22
2 0
e o
o e
E m c pc
m cp
 
 

28.  Which implies momentum of electron should be zero. Not
possible because it corresponds to
 Photon can not be transfer all of its energy to a free electron .
   
2 22
2 0
e o
o e
E m c pc
m cp
 
 
0,e
h
p 

   

29. Reference formula
 Relativistic expressions for energy and momentum
2
2
2
1
c
v
mc
E


2
2
1
c
v
mv
p

 Energy of stationary
particle = mc2
   2222
pcmcE 
A relativistic particle is a particle which moves with a relativistic
speed; that is, a speed comparable to the speed of light. This is
achieved by photons to the extent that effects described by special
relativity are able to describe those of such particles themselves.