The Compton Effect Introduction

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

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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: 
Ω
·
Ω
Ω
·
Ω
·
(6) 
The final form on the right uses the definitions 
ε
= E
0
/m
e
c
2 
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