- #1
physmurf
- 27
- 0
So, I am reading about a compton scattering problem, and I don't understand part of the derivation of a formula. I will explain my confusion.
If a gamma photon with energy [tex]E_{\gamma}[/tex], undergoes compton scattering with an electron which is at rest, how does one arrive at the following expression?
[tex]E^{'}_{\gamma}=\frac{E_{\gamma}}{1+(2E_{\gamma}/m_{o}c^{2})}[/tex]
So far it says we start with the conservation of energy and momentum:
[tex]E_{\gamma}=E^{'}_{\gamma}+E_{e} \ \ (eqn 1)[/tex]
[tex]\frac{E_{\gamma}}c=P_{e}-\frac{E^{'}_{\gamma}}{c}\ \ (eqn 2)[/tex]
From eqn 2 we get:
[tex]E_{\gamma}+E^{'}_{\gamma}=p_{e}c=\sqrt{(E_{e}+m_{o}c^{2})^{2}-(m_{o}c^{2})^{2}}[/tex]
This is where I am confused. I don't understand where the term inside of the radical comes from. Any ideas?
If a gamma photon with energy [tex]E_{\gamma}[/tex], undergoes compton scattering with an electron which is at rest, how does one arrive at the following expression?
[tex]E^{'}_{\gamma}=\frac{E_{\gamma}}{1+(2E_{\gamma}/m_{o}c^{2})}[/tex]
So far it says we start with the conservation of energy and momentum:
[tex]E_{\gamma}=E^{'}_{\gamma}+E_{e} \ \ (eqn 1)[/tex]
[tex]\frac{E_{\gamma}}c=P_{e}-\frac{E^{'}_{\gamma}}{c}\ \ (eqn 2)[/tex]
From eqn 2 we get:
[tex]E_{\gamma}+E^{'}_{\gamma}=p_{e}c=\sqrt{(E_{e}+m_{o}c^{2})^{2}-(m_{o}c^{2})^{2}}[/tex]
This is where I am confused. I don't understand where the term inside of the radical comes from. Any ideas?