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Protons and antiprotons, actually.
Jerk.
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Just protons and lead nuclei, actually. To get a reasonable amount of data you need millions of particles whipping by a point in very short periods of time so that a few thousand of them at best can actually collide. There is no known source that could supply enough antiprotons for that kind of action. Positrons maybe antiprotons not so much.
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So we're smashing neutrons together
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If only we could. You see neutrons having no charge are really really easy to smack into each other. (They tend not to push each other out of the way.) Unfortunately having no charge there really is no good way to accelerate them. (They don't respond much to magnetic or electric fields which is pretty much the only way of doing it.)