Neutrons are produced in two ways, first is from nuclear fission and the second is from spallation – where you fire a proton beam into a target material like tungsten, which then causes a reslease of neutrons. Muons are actually present in cosmic rays, but to produce them on a large scale we fire protons at a graphite target creating pions, which then decay into muons (you’ll have to believe on this one).
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