The Compton Effect Introduction



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Bog'liq
compton

 
= .511 MeV).
 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.2
0.4
0.6
0.8


PHY 192 
Compton Effect Spring 2012 
10 
Since we will be measuring energy, it is of interest to rewrite this to give the probability of measuring 
electrons with a given kinetic energy T = E
e
- m
e
c
2
. We can get the expression plotted in figure 2 by 
substituting for the angle 
Θ
in Eq. (5) via Equations (2) and (3), and further by using the solid angle 
definition given below Eq. (5), and applying the relationship: 

·


·

·
(6) 
The final form on the right uses the definitions 
ε
= E
0
/m
e
c

and
t
= T
e
/ m
e
c
2

Energy dependence
The Klein-Nishina formula can be integrated over photon scattering angle (or electron recoil energy) 
to yield the total cross-section, which displays the dependence on the incident energy (shown in Fig 4) for the 
Compton process: 
2 · 2
(7) 
Fig. 4: Energy dependence of Compton scattering, vs. x = 
ε 
=Eo/ m
e
c
2

The Compton process is weakly energy dependent up until about .1 MeV, when it begins to decrease 
significantly; other processes become more important at higher energies. 
0.01
0.1
1
10
100
0.05
0.10
0.20
0.50
1.00

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