I think what you are asking is about 'neutrinos', not neutrons. Neutrinos were first proposed in 1930's by pauli to explain the missing energy in beta-decay. From the conservation principles it was inferred that it should be a massless spin-1/2 particles. With experiments it appeared that if electron-neutrinos interacts with matter, it produces electron only. The same is true for mu- and tau- neutrinos. So, the neutrinos appear to conserve their 'flavor', i.e. its electron-ness or muon-ness. But a few years back 'neutrino-oscillation' were observed. That is, if you start with a pure muon-neutrino beam , after sometime some tau-neutrinos appear, as if from nowhere. This can only mean one thing that, the neutrinos we see in our real world is not those which like to maintain their 'flavor". In a more technical language, the 'flavor' eigenstates and the 'mass' eigenstates are different. According to QM this can only happen if the neutrinos have a finite mass (more precisely, mass difference). There are several lecture notes in the internet on neutrino oscillation, if you are interested and have a basic knowledge of QM, you will understand them.
What you see as a particular neutrino in an experiment is actually the superposition of different neutrino states. The apparent conversion that u see is actually due to variation of phase of different mass states at different rates.
The neutrino states are a combination of mass states and type (or flavor) (electron neutrino, mu neutrino and tau neutrino). The neutrinos change flavors when propagating as they have different masses. This arises because phases of different masses advance at different rates . Therefore if you start with a particular flavor of neutrino initially after some distance it will be a combination of different flavors.