Relativistic H/-H in a neutral beam accelerator

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danR
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A beam of hydrogen and antihydrogen atoms is accelerated to relativistic velocities by means of a neutral beam accelerator.

Identical photodetectors gather and record the photon energies of annihilating H and -H at both ends of the accelerator: where the atoms start; and at the end of the apparatus, where the velocity of the atoms is maximum.

Comparing the spatial and spectral distribution of the energies of the photons at either end, how do they compare? Can the momentum component of the measured energies be separated out? Can the non-photon (let's call it 'waste') energy be calculated? Assume the budget is large and the detectors are wide enough to capture all the decay products as photons, but if that's confused wording, do your best with what came before.

I'll tell you the motivation this question, but I want to be paid, before I say what I want to buy.
 
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I'll have to ask around the university here. They have some CERN researchers.