It depends on how they actually describe it in game, and how much artisitic license you're willing to use. I have a list of alternate ways you could roleplay the respec based on AT.
Science: easy enough, the radiation warps your powers into something. Your powers are already from wierd science.
Mutation: Also easy. Your new powers are a sign of evolution. If this was from the radiation or not, your call.
Technology: For robots and tech-suits, the radiation could either fry some hardware calling for replacement parts. You you acquired the new gear from the power plant.
Natural: Since the respec requires you to complete a trial mission, this is something that takes courage, skill, and a lot of planning. Any hero would succeeds gained a greater perspective on teamwork, fighting finesse, and their greater potental. The experience had changed them, and they learned something from it. Since I plan to swap teleport foe to gain access to the leadership, this is how I look at the respec.
Magic: This is a little harder, since now magic does not fit anywhere near a nuclear reactor. How, your magical powers can evolve much like a mutants can. Spells can be learned. Or, maybe after the great act of heroism you've pleased your gods or ascended to a new plane of understanding. Work with it.
Just my two bits of influence.
wow Triple R, well played. Heh. Good suggestions.
If you dont wanna be typical Tech or Magic.
Tech-The radiation doesn't fry your internal systems, but instead (if you have an energy fuel system, gas, energy,electric) the radiation effects your fuel. The molecules in the fuel metamorphasises, after running through your systems, it seems its 'alive' and re-wires all your interenal systems.
Magic-(You have to be magic by spells for this). Your magic isnt effected by the radiation, but instead your memory is wiped, you loose all the memories of most of your enchanments, this means you must re-study all your spells. Some come back to you easy and others dont, meaning you must replace them.
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Magic-(You have to be magic by spells for this). Your magic isnt effected by the radiation, but instead your memory is wiped, you loose all the memories of most of your enchanments, this means you must re-study all your spells. Some come back to you easy and others dont, meaning you must replace them.
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Getting smacked down by a dozen waves of Tank Smashers will do that to your noddle. 
Other than that, good advice.
Are you sure the reactor is all technological? Something that provides power to an entire city might have magical components as well...
How is it that intense radiation changes your character and you end up anything other than Mutation Archtype? This is an especially odd question for characters who are robots.
Speed Bandit.