# How to Change Nuclear Decay Rates


"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) Like all paradigms, this one is subject to some interpretation. Normal decay of radioactive stuff proceeds via one of four mechanisms:

• Alpha decay: the emission of an alpha particle (a helium-4 nucleus) which reduces the number of protons and neutrons present in the parent nucleus by two each;
• Beta decay: encompassing several related phenomena in which a neutron in the nucleus is replaced by a proton, or a proton is replaced by a neutron, along with some other things involving electrons, positrons, neutrinos, and antineutrinos. These other things are, as we shall see, at the bottom of several questions involving perturbation of decay rates;
• Gamma decay: the emission of one or more gamma rays — very energetic photons — that take a nucleus from an excited state to some other (typically ground) state; some of these photons may be replaced by "conversion electrons", of which more shortly;
• Spontaneous fission: in which a sufficiently heavy nucleus simply breaks in half. Most of the discussion about alpha particles will also apply to spontaneous fission.

$$\gamma$$ 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 into a proton:

$\underset{\beta \text{ decay}}{n \rightarrow p^+ + e^- + \bar{\nu_e}} \label{1}$

where

• $$n$$ is a neutron
• $$p$$ is a proton
• $$e^-$$ is an electrons and
• $$\bar{\nu_e}$$ is an antineutrono of the electron type.

The type of beta decay that involves destruction of a proton is not familiar to many people, so deserves a little elaboration. Either of two processes may occur when this kind of decay happens:

$\underset{\text{positron emission}}{p^+ \rightarrow n + e^+ + \nu_e} \label{2}$

where $$e^+$$ is a positron (anti-electron) and $$\nu_e$$ is the electron neutrino; or

$\underset{\text{electron capture}}{p^+ + e^- \rightarrow n + \nu_e} \label{3}$

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", whereby 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 sufficient to unbind the electron from the nucleus (ignoring a few exceptional cases), and it is ejected from the atom as a result.

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 things in the environment. 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. For most nuclides that decay by electron capture or internal conversion, the probability of grabbing or converting an electron is usually also insensitive to the environment, as the innermost electrons are the ones most likely to get grabbed/converted.

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. However, the magnitude of the changes is nothing to get very excited about.