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My textbook says that electron capture is when an electron is 'captured' by a proton in the nucleus which causes them to turn into a neutron and an electron neutrino. The name kind of suggests it only works in the nucleus though.

Is there a term for electron capture happening between just a lone proton and electron?

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The energetic requirements of $$e^- + p \longrightarrow n + \nu_e$$ are such that the electron needs around $1.4\,\mathrm{MeV}$ kinetic energy relative the proton for the reaction to proceed in free space (because of the difference in mass between the proton and the neutron). And even then this is a weak-mediated interaction, and so have a very small cross-section.

There are relatively few places where these conditions obtain (none that are friendly to unprotected humans). Where they do (mostly in the heart of stars) the reaction will be in equilibrium with the reverse reaction (beta decay of the neutron) with proton-neutron fusion removing nucleons from the equilibrium, and because of the small cross-section and the fleeting nature of moments when the preconditions are met the actual rate is trivial even compared to the very slow process of proton-proton fusion (if this event were common in the sun we'd see it in solar neutrino experiments, but we don't).

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The process can be called neutronization or sometimes inverse beta decay (though this can refer to a proton anti-neutrino interaction too).

It occurs between free protons and electrons in the cores of collapsing stars immediately prior to a supernova and as an equilibrium process in the neutron fluid region of a neutron star.

Since others have talked about the unlikelihood of the reaction, I'll point out that the energy threshold is lower than it is to create a neutron inside a nucleus (at least while the free neutrons are non-degenerate) and it is the most important reaction in the creation of neutron stars and their subsequent cooling (along with beta decay).

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If you have a lone proton - then that single proton is the nucleus, thus it is still electron capture, however, this rarely happens for a single proton, because a free neutron has a half life of about 10 minutes, after which it decayse back into a proton, electron and anti neutrino.

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I believe your questions derive from the inclusion of "... in the nucleus..." in the textbook statement. If this part is removed, you get "..."electron capture" is when an electron is captured by a proton..." Therefore, if the proton is by itself, or surrounded by other particles, it makes no difference. If the proton is by itself, it is the nucleus! If it is surrounded by other particles, it still is the nucleus. Therefore the same term "electron capture" is applicable to both situations, and there are no other terms.

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