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Is there any way to alterate weak interaction and thus the rate of beta decay by making it slower or faster? If yes, how? Would radiating some extra bosons or neutrinos, perhaps in a focused beam, change the rate somehow?

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No nuclear reaction rates can be altered as far as we know, other than by the well-known method of hitting the nuclei with neutrons.

Having said that, some people keep reporting correlations with solar activity, possibly related to some undetermined neutrino-based reactions

some not so recent articles with links to papers on the subject:

https://copaseticflow.blogspot.com/2013/05/solar-neutrinos-and-radioactive-decay.html

https://en.wikipedia.org/wiki/GSI_anomaly

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    $\begingroup$ This is not really right, since electron capture is a counterexample. Please see the question that this one duplicates (but note that the accepted answer is wrong). $\endgroup$
    – user4552
    Commented Nov 17, 2019 at 0:04

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