makes me wonder how nobody had the idea to take a ridiculously unshielded nuclear power generator, put it on top of a tank, give the tank loadsa lead armor (not to stop projectiles but to stop the crew from dying too fast) and make it shoot lasers then send all that into enemy territory
shoot tank -> tank explodes -> fallout on your own land, gg no re
not shoot tank -> tank wrecks your shit -> your shit is wrecked, gg no re
hell you could install a selfdestruct mechanism in case it got stuck in a trench ror
As far as shooting at it, you might get an explosion, but the most you'll get is a dirty bomb; unless you put enough nuclear material to go supercritical in there and rig it to do so under sudden shocks like getting shot at (in which case you now have to worry about it doing so if you, say, hit a sharp bump in the road), there really isn't much point to it when you can just go Davy Crockett and keep the tank chassis intact.
Also, really, why would you want to put it on a tank?
Nuclear ramjets are where it's at. Load it up with nukes, set it up so you can open the shielding if you want to make the exhaust itself radioactive (or don't; it'd be complex, prone to failure, and just ramming it into the ground at supersonic speeds should scatter radioactive material across enough terrain), and watch the fireworks. And, without people on board, you never need to land the thing to take on food or water, so it can just sit in the stratosphere for years, watching and waiting. ^_^