# Can the decay rate of nuclear decay be proportional to the second/third exponent of number of nuclei?

A equation we all come across in high-school physics:

$$\frac{-dN}{dt}= kN$$ where N is number nuclei left

Is this always true for spontaneous nuclear decays? In chemistry, we find second, third order reactions. Similarly, has anyone found spontaneous decay where the decay rate is proportional not to the first exponent of remaining nuclei, rather to second or third exponent?

• Closely related: physics.stackexchange.com/questions/178233/… – Emilio Pisanty Jul 9 '17 at 13:05
• It's not the same @Emilo Pisanty – Mockingbird Jul 9 '17 at 13:07
• ... which is why I said it's related instead of a duplicate. Nevertheless, it does mean that you need to ask a sharper question: if your question is whether there are observations of decay that does not follow the simple exponential, then yes there are, as detailed in the link above. If you're asking whether there are observations of nuclear decay that specifically has the population derivative equal to a higher power of the population, then the answer is no, but you should make that clearer in the question. – Emilio Pisanty Jul 9 '17 at 13:13
• See my edit. Want to suggest something? – Mockingbird Jul 9 '17 at 13:55
• If you want to make an analogy with chemical reactions, then you should probably be considering nuclear reactions, rather than spontaneous nuclear decay. For example, you could consider the cross-section for neutron or proton transfer reactions as a function of the number of nucleons (mass number) in the target and projectile. – Ben Crowell Jul 9 '17 at 15:34

## 1 Answer

The nuclear forces responsible for radioactive decay are short ranged and so isolated from other forces (such as the much weaker E\$M forces) that this results in the exponential decay law. I believe there have been experiments that demonstrate that these decays can be slightly affected by exposure to very strong E&M fields, but this is a special circumstance that normally does not occur. I would have to Google to find references to those experiments. I believe the experiments were conducted on nuclear isomers.

Edit: The experiments that I was remembering took place between 1998 and 2007, but a Google search reveals that those experiments have now been discredited. You may read about this episode here. The search terms that I used were: nuclear, isomer, decay, stimulated. If you follow the links resulting from this search, you may find the original sources.

• So what did you find? – Mockingbird Jul 10 '17 at 3:41
• @Mockingbird See my edit, – Lewis Miller Jul 11 '17 at 18:37