Not really sure. Protons would interact with everything around them as they are charged and I don’t think it would last very long. The way protons are normally used I experiments is keeping them in a beam in ultra high vacuum. Electromagnetic forces are used to make sure they don’t contact the walls of the vacuum chamber.
The neutron on the other hand I am less sure about. I suspect it would end up interacting with the nucleus of another atom – there is no electrostatic repulsion to keep it away and nuclear interactions will take over. We do use neutrons for some experiments – we have one such facility in the UK called ISIS and the EU are just starting to build a new one in Sweden so it is possible but I don’t know how they do it. I would need to look it up
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