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## Homework Statement

Hi Physics forum members,

The following is questions on how to use 4 momentum and momentum 4 vector conservation. From what I've learned of it, it is essentially the same as classical momentum conservation. However, I'm still not quite sure what you can, and should, be able to do with it given initial conditions.

The question in particular is if a particle like an electron, (moving relativistically so it's energy can be approximated as momentum), scatters of a proton initially at rest, say you're given the initial energy of the electron, from which obviously you could find it's initial momentum.

Keeping it simple by having the proton initially moving only along the x-axis, the electron and proton scatter at angles 0e and 0p relative to the axis. If you only know the initially electron energy and momentum, along the x axis, before it scatters and the angle 0e of the electron after, is it possible to use 4 momentum conservation to find the scattering angle of the proton, Op and in addition the final momenta of the electron and proton after scattering? Or is more info needed?

Keeping it simple by having the proton initially moving only along the x-axis, the electron and proton scatter at angles 0e and 0p relative to the axis. If you only know the initially electron energy and momentum, along the x axis, before it scatters and the angle 0e of the electron after, is it possible to use 4 momentum conservation to find the scattering angle of the proton, Op and in addition the final momenta of the electron and proton after scattering? Or is more info needed?

## Homework Equations

I started simply using 4 momentum vectors, (E/c, px, py, pz) For initial and final momentum. Then, for the electron, I had thought the 4 momentum was [Pe, Pe, 0,0] with momentum Pe in the x axis and, for the electron moving relativistically, E estimated to be Pe, the same as momentum, (the electron's mass is neglegible). The 4 momentum of the proton at rest is [Mp, 0, 0, 0], i.e. simply the mass of the proton-and yes, this is in c=1 units.

The 4 momentum of the electron after collision is then [((Me^2) + (Pef^2))^.5, Pef * Cos(0e), Pef * Sin(0e), 0] and for the proton is [((Mp^2) + (Ppf^2))^.5, Ppf * Cos(0p), Ppf * Sin(0p), 0]. Pef is the final momentum of the electron, Ppf is the final momentum of the proton, Oe and Op are scattering angles of electron and proton , (Me and Mp are electron and proton mass).

## The Attempt at a Solution

I had thought that by equating the each of the 4 components for the total momentum before and after the collision you could find 0p, scattering angle of proton, along with the final momenta Pef and Ppf of electron and proton after collision, knowing only Pe, the initial electron momentum and 0e, the scattering angle of the electron. But it hasn't worked very well, and I was wondering if there's some subtle aspect to 4 momentum conservation I'm missing or something I'm overlooking.