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Say I had an unstable element ready to go through beta decay and I introduced it to high speed electrons: would this lessen the time needed for the product to go through beta decay?

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We see this kind of question a lot. My personal reaction is always 'I wouldn't describe that process as "decay"', but sure, you can forcibly dissociate nuclei. –  dmckee Aug 24 '13 at 17:29
    
    
Why electrons in particular? –  Ben Crowell Aug 25 '13 at 0:18
    
If you couldn't greatly increase the rate of decay by external radiation, we wouldn't have nuclear reactors or nuclear bombs. What you are asking is the difference between normal half-life decay and a chain reaction. –  Olin Lathrop Jan 28 at 23:20
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Hmmm, maybe not with electrons, but perhaps gamma rays....In nature there is evidence that 176Lu nuclei underwent accelerated decay in the early solar system by excitement to an unstable isomeric state. Search scholar for 176Lu-176Hf decay system in Angrite meteorites for more information

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Yes, with electrons. And with photons. Both processes have been considered for radioactive waste conversion, and both work, but not with the efficiency, scale and cost that would be needed. –  dmckee Sep 14 '13 at 3:07
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http://phys.org/news/2011-05-gamma-ray-laser-emit-nuclear.html
http://en.wikipedia.org/wiki/Induced_gamma_emission
Let us not forget Hf-178m2 media snit.

Nuclear decay of any kind must surmount an activation energy barrier or tunnel through it. Pump the barrier directly or wang the nucleus overall and it proceeds at a different rate. Electron capture additionally can be changed by reducing electron density (s,d orbitals) at the nucleus in high oxidation state fluorides or by inclusion within a fullerene. If that atom is fully ionized, no decay at all.

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