- #1
Nusc
- 760
- 2
Homework Statement
photon scatter angle is theta, electron recoil angle is phi
prove
tan(phi) = (1+hf/mc^2)^-1 cot(theta/2)
Homework Equations
The Attempt at a Solution
Conservation of energy is the same as in here:
http://en.wikipedia.org/wiki/Compton_scattering
Conservation of Momentum
In x :
p_gamma = p_gamma' cos(theta) + p_e' cos(phi)
In y:
0 = p_gamma' sin(theta) - p_e' sin(phi)
p_gamma'=p_e' sin(phi)/sin(theta)
Let's solve for p_e'^2 since we can directly substitute it in the energy term.
p_e'^2 = p_gamma^2 sin^2(theta)/ [sin^2(phi)cos^2(theta) + 2 sin(phi)cos(theta)sin(theta)cos(phi) + sin^2(theta)cos^2(phi)]
I'm not sure where the cot(theta/2) comes from which we want to show.