# Inverse Compton scattering in SR

1. Sep 23, 2009

### diazona

This is actually for a graduate course but it's a basic special relativity problem, i.e. undergraduate-level material, so I'm posting it here...

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

2. Relevant equations
$$U^{\mu} = (1, 0, 0, 0)$$ (in the observer's rest frame)
$$V^{\mu} = (\gamma, \gamma \vec{v})$$
$$P^{\mu} = (E, \vec{p})$$

3. The attempt at a solution
I got parts (a) and (b) easily enough by evaluating 4-vector products in the observer's rest frame,
(a) $$\gamma = -U^{\mu} V_{\mu} \gg 1$$
(b) $$E = U^{\mu}P_{\mu}$$
The problem is with part (c). We're supposed to express P' in terms of U, V, and P, but it doesn't seem to be possible without knowing the angle at which the scattered photon exits (or the angle at which the charged particle exits). Am I missing something, or is this actually impossible?

2. Sep 23, 2009

### gabbagabbahey

What quantity is conserved during the scattering event?

3. Sep 23, 2009

### diazona

Momentum, I know... P + mV = P' + mV', where V' is the final four-velocity of the charged particle. But I still don't see how that helps... I don't know V'.

4. Sep 23, 2009