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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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