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## Homework Statement

In a fixed target experiment a particle of mass M and kinetic energy T strikes a stationary particle of mass M. By evaluating s, t and u in the laboratory frame and using the above relation, or otherwise, show that the kinetic energy T' of the particle scattered elastically at an angle θ is given by

T' = T cos^2 θ / (1 + ((T/2M)*sin^2 θ))

## Homework Equations

We know that:

We define P1 as the four momentum of the incoming proton:

P1 = (T+M,0,0,T)

P2 as the stationary proton:

P2 = (M,0,0,0)

P3 as the initially incoming proton after the scattering event:

P3 = (T'+M, 0, T'sinθ, T'cosθ)

P4 as the initially stationary proton after the scattering event:

P4 = (E4+M, P4) where P4 in the bracket is a 3 vector not 4.

We also know:

s = (P1 + P2)

^{2}, t = (P1 − P3)

^{2}and u = (P1 − P4)

^{2}

and

s + t + u = ∑ m

_{i}

^{2}= 4m

^{2}

## The Attempt at a Solution

I have attempted this multiple times over a few days, I realize that P4 and therefore u need to be eliminated as they aren't in the solution but I am unsure how.

Any help/ suggestions would be appreciated. Thanks, John.