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A problem lays in the fact that you need them to go 319 m/s relative to each other. This means that we are rapidly approaching are detector or going away from it. Shooting something very fast at a sensitive detector would most certainly break something and to speed up something away from the detector is also difficult because the mechanism we used to launch it would block the system.
You could solve both problems with magnetic acceleration/deacceleration, but this would give lots of radiation that could interfere with the experiment itself.
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