Compton Scattering
المؤلف:
Sidney B. Cahn And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 38
13-7-2016
1940
Compton Scattering
In the Compton effect, a γ-ray photon of wavelength λ strikes a free, but initially stationary, electron of mass m. The photon is scattered an angle θ, and its scattered wavelength is 
The electron recoils at an angle φ (see Figure 1.1).
Figure 1.1
a) Write the relativistic equations for momentum and energy conservation.
b) Find an expression for the change 
in the photon wavelength for the special case θ = π/2.
SOLUTION
a) From momentum and energy conservation we can write
(1)
where 
are the momenta and energies of the photon before and after the scattering, respectively, 
are the final momentum and energies of the electron, and εe is its initial energy. We have for the electron
and for the photon
So we can rewrite (1) in the form
(2)
b) To solve these equations we can express the momentum of the recoil electron pe in two ways
(3)
from (2).
and for a special case θ = π/2, cosθ = 0. We have
Dividing this equation by 
we get
Taking into account that p = h/λ, we obtain the final result:
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