I can sense the direction in which this question is going...
To include nuclear/radioactivity as a food safety hazard in a
HACCP plan does not seem to be a big issue and makes sense in areas of this planet where there is a (real or perceived) risk of food being or becoming contaminated with radioactivity that is higher than the naturally occurring levels. 'Safe' levels of radioactivity are determined and corrobated by scientific evidence, although these limits are not necessarily interpreted equally around the world. Following the Fukushima accident, the EU has initially allowed much higer levels of radioactivity in foods than some other countries. You will have to find out about locally acceptable levels (or the levels that are acceptable in your target market).
To monitor the identified nuclear hazard as a
CCP is much more difficult and might be very cost-intensive.
For easy monitoring, it might be sufficient to rely on reported results of radioactivity in foods from national or independent surveillance programs (probably to be taken at face value) or to ask your suppliers to test for radioactivity and trust their evaluation (verified by regular supplier audits). If these two are not an option and you need control of radioactivity in your business, you'll have to purchase expensive analytical kit to carry our the relevant analysis yourself. In my opinion, this only makes commercial sense if there is a real and proven risk of foods entering your business that could be emitting dangerously high levels of radiation and there are no other ways available for you to reliably control this hazard.
I also agree with Dr. Ajay Shah that in factories where food is irradiated, the hazard of nuclear contamination must be controlled with a
CCP (national radiation legislation will probably require more stringent controls, though). - You'll know if that's the case in your business!
Nuclear and radioactive are two expressions for the same thing. I would see radiation as either physical contamination (i.e. because radioactive substances are attached to food) or chemical contamination (if radioactive elements have been incorporated into food). So - still only three groups of hazards.
This might become more relevant in the years to come.
Matt