# Compton Scattering Using Mandel-Stam Variables

1. Mar 6, 2008

### americanforest

1. The problem statement, all variables and given/known data

Not homework, just for fun. I want to derive Compton Scattering equations using Mandel-Stam variables as opposed to the way that I have done it in class using the usual energy and momentum conservation

2. Relevant equations

$$(p_\mu+p_{ei}_\mu)^2=(p'_\mu+p_e_\mu)^{2}=s$$
p is the momentum of incoming photon and pei is of initially stationary electron. p' is final photon and p_e_\mu is final electron.

3. The attempt at a solution

I'm going to try to do the right side in the CMS frame and the left side in the lab frame for convencience.

$$Em_e=2EE_e_$$
...skip a few easy steps using
$$E=\sqrt{p^{2}+m^{2}}$$
$$E^{2}-E'^{2}=\frac{p_e_^2}{me^{2}}$$

Which isn't right. What's wrong here?

Last edited: Mar 6, 2008
2. Mar 7, 2008

### pam

You have to do both in the lab system because you need the photon energies in the lab system. Your first equation can't be right. You can't use the same E in each system.
Stanley's name is Mandelstam. He is only one person.

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