When a nucleus is bombarded with particles such as neutrons or protons, if a particle is absorbed, one has a new kind of nucleus: either a nucleus of a different element (if protons are used) or a different isotope (if neutrons are used). If the bombarding particles are photons, and have enough energy, they may cause a neutron or a proton to be ejected and one has a new kind of nucleus as above.
The new nucleus then decays (if it is radioactive) with its characteristic half-life. The radiation given off subsequent to this decay can be detected, if one wishes.
All these processes are thoroughly well understood.
Where I work we use this for chemical analysis in a technique called neutron activation analysis.
No siqnificant change in the half-life of any nuclide under anything like normal earth conditions has been accomplished. I have myself done research that attempted this. As has been pointed out to you, it would take a disastrous change in the basic physical constants to change half-lives. Such a change would likely destroy the earth or certainly leave notable evidence.
Accelerated decay is a complete non-starter. Anyone who claims that it happened has been lied to, or is lieing themselves.
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