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Nuclei spontaneously decay according to a certain decay rate. There are however different kinds of decay, alpha, beta, gamma... What causes then the nuclei, when they decay, to do so in one way of another? Is there a different decay rate for each kind of decay?

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It is conservation rules (mostly that of energy) that controls what decays are possible, and what channels are allowed (the strong interaction respected quark flavor, but the weak interaction does not). If the final state has higher energy than the initial state there can be no spontaneous process leading from one to the other.

The energy environment of a nucleus is a complicated place because it is affected by the strong nuclear force, electromagnetic forces and by the limits on state occupation imposed by Pauli exclusion. There are a lot of question already on the site about when various processes can proceed and related subjects

Your question about the case where a nucleus has multiple modes have different half-lives is tricky. The measured result is the same half-life for each mode, but we can ask "If we could magically block modes and study the isolated half-life of each mode, what would they be?" If you perform the (often approximate) calculation for that question you generally find different half-lives. The interesting part is the the branching fractions for each decay are related to ratios of the calculated "isolated" half-lives, so you are seeing the effect of the different probabilities when you look at the frequency of different decays.

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Thank you, perfectly explained. However I don't think I understood the final part.Do you mean that the decay rates influence one another? – carllacan Jan 19 '14 at 16:15

There is a different decay rate for each kind of decay. There is no specific "cause" for one decay versus the other. That is, given one nuclei, it is indeterminate what it will decay into after some given amount of time. However, we can determine the probabilities of what it will decay into. This is calculated using Quantum Field Theory.

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I see. Which characteristics of the isotopes determine then (through Quantum Field Theory calculations) which decays are "available" for a specific nucleus? – carllacan Jan 19 '14 at 16:18
Refer to dmckee's answer above – mcFreid Jan 19 '14 at 16:53

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