[Physics FAQ] - [Copyright]
Updated January 2022 by Dan Watts.
Original by Bill Johnson, with an early update by Scott Chase.
"I've had this idea for making radioactive nuclei decay faster/slower than they normally do. You do [this, that, or the other thing]. Will this work?"
Short Answer: possibly, but probably not usefully.
Long Answer: "One of the paradigms of nuclear science since the very early days of its study has been the general understanding that the half-life, or decay constant, of a radioactive substance is independent of extranuclear considerations". (Emery, cited below.) Like all paradigms, this one is subject to some interpretation. Normal decay of radioactive stuff proceeds via one of four mechanisms:
Gamma decay often occurs from the "daughter nucleus" of one of the other decay modes. We neglect very exotic processes like C-14 emission or double beta decay in this analysis.
Beta decay happens most often to a nucleus with a neutron excess, which decays by converting a neutron to a proton:
n ---> p + e− + anti-nue ,where n means neutron, p means proton, e− means electron, and anti-nue means an anti-neutrino of the electron type. The type of beta decay that involves destruction of a proton is not familiar to many people, and so deserves some elaboration. Either of two processes may occur in this kind of decay:
p ---> n + e+ + nue ,where e+ means positron and nue means electron neutrino; or
p + e− ---> n + nue ,where the electron is captured from the neighborhood of the nucleus undergoing decay. These processes are called "positron emission" and "electron capture" respectively. A given nucleus that has too many protons for stability may undergo beta decay through either, and typically both, of these reactions.
"Conversion electrons" are produced by the process of "internal conversion", in which the photon that would normally be emitted in gamma decay is virtual and its energy is absorbed by an atomic electron. The absorbed energy is usually sufficient to eject the electron from the atom.
Now for the tie-in to decay rates. Both the electron-capture and internal conversion phenomena require an electron somewhere close to the decaying nucleus. In any normal atom, this requirement is satisfied in spades: the innermost electrons are in states such that their probability of being close to the nucleus is both large and insensitive to environmental influences. The decay rate depends only very weakly on the electron wave functions, i.e., on how much of their time the inner electrons spend very near the nucleus.
But this general rule has its exceptions. The most notable is the astrophysically important isotope beryllium-7. Be-7 decays purely by electron capture (positron emission being impossible because of inadequate decay energy) with a half-life of somewhat over 50 days. It has been shown that differences in chemical environment result in half-life variations of the order of 0.2%, and high pressures produce somewhat similar changes. Also, a 2004 paper (see the references) measures a 0.8% reduction in half-life for Be-7 atoms enclosed in carbon-60 cages. Other nuclei in which decay-rate changes are known to occur are zirconium-89 and strontium-85, also electron capturers; technetium-99m ("m" implying an excited state), which decays by both beta and gamma emission; and various other "metastable" isotopes that decay by gamma emission with internal conversion. With all of these other cases the magnitude of the effect is less than is typically the case with Be-7.
What makes these cases special? The answer is that one or more of the usual starting assumptions (such as insensitivity of electrons near the nucleus to external forces, or availability of the innermost electrons for capture/conversion) are not completely valid. Atomic beryllium has only 4 electrons to begin with, and so the "innermost electrons" are also practically the outermost ones, and are thus much more sensitive to chemical effects than is usual. With most of the other cases, the foibles of nuclear structure produce very little energy from the decay: as little as a few electron volts, as compared with most radioactive decays, which release hundreds or thousands of kiloelectron volts. In these low-energy cases, the innermost electrons can't undergo internal conversion. Remember that converting an electron requires dumping enough energy into it to expel it from the atom (more or less); "enough energy" is typically some tens of keV, and so they don't get converted at all in these cases. Conversion therefore works only on some of the outer electrons, which again are more sensitive to the environment.
A real anomaly is the beta emitter rhenium-187. Its decay energy is only about 2.6 keV, practically nothing by nuclear standards. "That this decay occurs at all is an example of the effects of the atomic environment on nuclear decay: the bare nucleus rhenium-187 [i.e., stripped of all orbital electrons] is stable against beta decay [but not to bound-state beta decay, in which the outgoing electron is captured by the daughter nucleus into a tightly bound orbital], and it is the difference of 15 keV in the total electronic binding energy of osmium [to which it decays] and rhenium [...] which makes the decay possible" (Emery).
A 1996 paper (see the references) discusses this bound-state decay of bare-nucleus rhenium-187. Whereas neutral rhenium-187 has a half-life of 42 × 109 years, the authors measured fully ionised rhenium-187 to have a half life of just 33 years! They discuss the cosmological implications of the altered half life of rhenium-187 in various degrees of ionisation in stellar interiors, and what that implies for our knowledge of galactic ages.
Alpha decay and spontaneous fission might also be affected by changes in the electron density near the nucleus, for a different reason. These processes occur as a result of penetration of the "Coulomb barrier" that inhibits emission of charged particles from the nucleus, and their rate is very sensitive to the height of the barrier. Changes in the electron density could, in principle, affect the barrier by some tiny amount. But calculations show that the magnitude of the effect is very small. For a few alpha emitters, the change has been estimated to be of the order of 1 part in 107 or less (!), which is not measurable, given that the alpha emitters' half lives aren't known to that degree of accuracy to begin with.
All told, the existence of changes in radioactive decay rates due to the environment of the decaying nuclei is on solid grounds, both experimentally and theoretically. But the magnitude of the changes is nothing to get very excited about, except for the case of neutron bombardment. Controlled neutron bombardment is the basis for nuclear reactors (and exponentially increasing nuclear bombardment is the basis of a nuclear fission bomb).
In the country of Gabon in mid-western Africa lies a uranium deposit known as Oklo. This is the only known natural self-sustaining nuclear fission site.  As discussed in a 1989 paper (see the references), its uranium-235 concentration is 0.48% to 0.68% of the total uranium present, in contrast to the 0.72% concentration that is normally found in uranium. This depletion is consistent with the effects of nuclear fission.
Although Oklo is the only such natural reactor site known, the generation of neutrons by lightning discharge has been reported since at least 1985; so if you leave fissionable material out in a storm, its fission rate might be temporarily increased by lightning-induced neutrons.
Perhaps the best review article on this subject is G. T. Emery, Perturbation of Nuclear Decay Rates, Annual Review of Nuclear Science 22, pg 165 (1972). Papers describing specific experiments are cited in that article, which contains considerable arcane maths but also gives a reasonable qualitative feel for what is involved.
The recent work on Be-7 enclosed in C-60 cages is in Ohtsuki et al., Enhanced Electron-Capture Decay Rate of Be-7 Encapsulated in C-60 Cages. Phys. Rev. Lett. 93, 112501 (2004).
The discussion of the half life of fully ionised rhenium-187 is found in Bosch et al., Observation of Bound-State β− Decay of Fully Ionized 187Re: 187Re—187Os Cosmochronometry, Phys. Rev. Lett. 77, 5190 (1996).
The discussion of the Oklo natural reactor can be found in F. Gauthier-Lafaye and F. Weber, Natural Fission Reactors of Oklo, Economic Geology 84, 2286 (1989)
A few papers discussing neutron production in thunderstorms are: