Understanding Relativistic Kinematics for Proton-Photon Collisions

[jdstokes]

Hi all,

I would be very grateful if anyone would be willing to check my understanding of this stuff as it has been several years since I used it in undergrad calculations.

If a proton and a photon collide head-on with known energies, then the energy in the center of mass frame will be given by the invariant mass $E_\mathrm{com} = W$. Thus $E_\mathrm{com} = \sqrt{(E_\gamma+ E_p)^2-(p_\gamma + p_p)^2} = \sqrt{(E_\gamma+ E_p)^2-\left(E_\gamma + \sqrt{E_p^2 - m_p^2}\right)^2}$.

Does this sound reasonable?

 

[malawi_glenn]

sure why not, remember that you should have vector p's in the first expression:

$$E_\mathrm{com} = \sqrt{(E_\gamma+ E_p)^2-(\vec{p}_\gamma + \vec{p}_p)^2}$$

Just for completeness, then use the fact that they are 'head on'

 

[pam]

That means you need a minus sign in your last term.