As I understand it, an unstable nucleus is going to randomly fission because the forces binding it together are momentarily weaker than the electrostatic repulsion of the protons.
Given that some nuclei are really unstable, and others are stable for billions of years, is it true that so-called stable nuclei are actually theoretically able to fission through quantum tunnelling, just unlikely to do so? Have stable atoms ever been observed to spontaneously fission?
Additionally, will bombarding stable nuclei with particles split them? Can you hit a Carbon atom with a neutron and split it, or will it always add on or miss? Can a photon split a nucleus?