One Final Special Relativity collision problem (no new particles created)

[cpfoxhunt]

Homework Statement

This is the last problem I'll trouble you guys with, I'm just completely stuck on it. Here it is.

In the jet of a quasar, an ultr&relativistic electron collides head-on with a very
low energy photon of the cosmic microwave background. No new particles are created.
Show that the energy of the photon after the collision is given by
E= (El + P1*C)E2
(El - Pl*C) + 2E2
where E1 and p1 are respectively the energy and the magnitude of the momentum of
the incident electron, and E2 is the energy of the initial photon.

Homework Equations

Call mass of the electron m

Obviously that e^2-p^2c^2 = 0 for a photon

The Attempt at a Solution

So far I've worked out that (E1 + E2)^2 - (p1 + E2/C)^2 = (from the cm frame invarient of the square of the resultant rest masses) (mC^2)^2 = E1^2 - (p1C)^2.

Very nice, but whenever I try to introduce a final value of E for the finishing energy of the photon, I get stuck, and cannot elimiate enough variables.
Any ideas?
Cheers
Cpfoxhunt

 

[Meir Achuz]

For the photon, E=p. (Please let c=1).
Write the equation for energy conservation and for momentum conservation.
The initial photon momentum (z component) is -E2 and its final momentum is +E.
Add and subtract these two eqs to get eqs for (E1-p1) and (E1+p1).
Multiply these two equations, using E^2-p^2=m^2 for the electron.
This gives a simple equation to solve for E..

 

[cpfoxhunt]

How did you get to the iinitial photon momentum being -e2? whereas the final momentum is positive?
And I still have a p3 i.e. the momentum of the electron after the collision floating around. Any ideas?