- #1

shwouchk

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Just wanted to say that this is my first post here, and I thank in advance anyone who spends time on this. Hopefully I will be able to return the favor someday.

Anyway...,

I thought I knew how to do this, but apparently I was wrong... I need to analyze the collision of a photon at an electron.

## Homework Statement

A photon hits an electron in it's rest system. After the collision, the photon's direction is perpendicular to it's prior direction, having half the starting energy (first it was going x+, now it is going y+).

After the collision, the electron is traveling at some speed v at an angle -a to the x-axis (i.e. x+ y-)

1. write the relevant preservation equations.

2. Find the hitting photon's energy

... (if I'll understand these I'll do fine with the rest)

The "knowns" are C - the speed of light and E0 - the electron's rest energy.

## Homework Equations

## The Attempt at a Solution

I have to say that I'm new to using the Lorentz transformation and it's consequences so I likely made a few mistakes, but..:

I had the conservation of energy as:

(E1 is the photon's starting energy)

E_0 + E_1 = E_0 * \omega + (E1 / 2);

I wrote the conservation of momentum as follows:

(E_1 / C) = (E_0 / C) * \beta * cos a (X axis)

0 = (E_1 / 2C) - (E_0 / C) * \beta * sin a (Y axis)

Then (after hours of thought and tackling this) I realized that E=pc is only true for particles traveling very close to (or at) the speed of light, and revised it to:

P_1 = P_e * cos a (X axis)

0 = P_2 - P_e sin a (Y axis)

and used:

(E_1 / 2) = P_2 * C

P_2 = ([P_e]^2 + [m_e]^2 * C^2)^(1/2)

However, it got somewhat messy and then I got an impossible answer, so I suspect something is wrong here as well...

I would really appreciate if someone explains the general way of solving this kind of problems (or rather how to treat the momentum conservation, I guess) and/or what is wrong about my way.

Thanks in advance,

Shwouchk.