Anna gives an excellent description of fission by neutron capture, and I'd guess that is what you were asking about. However I thought it worth adding that nuclei can also undergo spontaneous fission, though only very heavy nuclei do this. In principle uranium (235 and 238) can undergo spontaneous fission but it's very slow compared to alpha or beta decay.
In spontaneous fission the idea of a potential barrier is important for obvious reasons. The energy of a U238 nucleus is greater than the energy of it's fission products, so it's energetically favourable for the nuclei to split. If there were no potential barrier U238 nuclei would all fission instantly and there wouldn't be any left. However in order to split the U238 nucleus has to go through an intermediate state with a higher energy, and this creates the potential barrier, just like the diagram you draw.
Well, your diagram isn't really correct for fission because fission is a quantum process and the nucleus splits by tunneling through the barrier. It's not like a chemical reaction where you have a Boltzmann distribution of energies in the reagents so a proportion of the reacting molecules do have enough energy to get over the barrier. Still, the end result is much the same.
According to http://www.eng.fsu.edu/~dommelen/quantum/style_a/ntcsf.html the activation energy for spontaneous fission of a uranium nulceus is 6.5MeV.