After graduating from Cornell, O'Neill accepted a position as an instructor at Princeton University. There he started his research into high-energy particle physics. In 1956, his second year of teaching, he published a two-page article that theorized that the particles produced by a particle accelerator could be stored for a few seconds in a storage ring. The stored particles could then be directed to collide with another particle beam. This would increase the energy of the particle collision over the previous method, which directed the beam at a fixed target. His ideas were not immediately accepted by the physics community.