Is it possible for an atom to emit a neutron or a proton?
ThanksIn short, yes.
Now, when you produce nuclei via fusion, you tend to produce them with high excitation where their level densities are very high - these are called "hot compound nuclei". Nuclei in this state will release energy by evaporating one or more nucleons. Heavy compound nuclei emit neutrons, and light compound nuclei will also emit protons and other charged particles (e.g. alphas).