It's a bit like the nuclear analogue of a chemical mixture which is thermodynamically unstable but kinetically stable.
The excited nuclear state is thermodynamically unstable with respect to it's lower energy ground state, but it has to overcome various strong internal interactions in order to reconfigure. The irradiation gives it the boost it needs to overcome the initial barrier.
In a similar way, a mixture of hydrogen and oxygen is extremely thermodynamically unstable - it would be a much lower energy configuration as water. However, it will sit around indefinately because energy is required to break up the existing molecules such that they can recombine. It doesn't yet have the energy it needs to overcome this - it's kinetically stable.
Now, throw a spark in there and watch it go...