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Pi-Bond
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Homework Statement
Homework Equations
Zero-momentum frame is defined as the frame in which total momentum is zero.
The Attempt at a Solution
(a) In terms of the zero momentum variables, (e1 and e1 are to distinguish the two resultant particles)
[itex] \vec{p'}_{HE} + \vec{p'}_{CBR} = \vec{p'}_{e1} + \vec{p'}_{e2} = 0 [/itex]
This says that the photons have equal and opposite momenta in the zero-momentum frame, and so do the resultant particles. So the energy of both photons is equal, say to E'.
[itex] E'_{HE} + E'_{CBR} = 2E' = E_{e1} + E_{e2} = 2m_0c^2 [/itex]
I'm not sure if this right...I think this follows from the fact that we are dealing with the minimum photon energy situation, so the resultant particles would be stationary in the zero-momentum frame. Or is this the equation for the other frame in the question? (With the energies replaced)
(b) Based on the information given,
[itex] E_{HE} = \frac{1}{\Gamma} E'_{HE} [/itex]
And similar for the CMB photons.
I'm not sure how to write energy and momentum for the resultant particles in this frame. I'm guessing I have to substitute the above photon energy into the answer of part (a). But then I still don't know the energies/momenta of the resultant particles.
Feeling very confused now! Any help would be appreciated.
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