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I've heard of $\beta^-$ decay,

$$n \rightarrow p^+ + e^- + \bar \nu_e$$

$\beta^+$ decay,

$$p^+ \rightarrow n + e^+ + \nu_e$$

and electron capture,

$$p^+ + e^- \rightarrow n + \nu_e$$

but every time I've googled "positron capture," which I assume would probably happen as

$$n + e^+ \rightarrow p^+ + \bar \nu_e$$

I've never found any reliable results that mention anything about it other than a footnote on some website that mentions that a positron would annihilate with an electron in the cloud surrounding a nucleus before it even came close to the nucleus. However, if all of the electrons surrounding the nucleus were removed, then I see no reason why this reaction would not be possible at least in theory.

Is positron capture theoretically possible? If not, why not? If so, what nuclei could allow for this process to occur?

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Positron capture is not possible, and here is why: The "capture" part refers to the fact that the electron is taken from its atomic orbit around the nucleus containing the proton with which it reacts. Since a positron cannot for a bound state with a nucleus--it can't be captured.

Nevertheless, $e^+p(n, \bar{\nu}_e)$, is a perfectly good scattering reaction.

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  • $\begingroup$ of course if we just stick to "positron capture" one could imagine in an anti atom ( with antiprotons and antineutron and postitrons around) capturing the positron and turning into an antineutron. They have only managed to create antihydrogen, home.cern/about/engineering/storing-antimatter $\endgroup$ – anna v Dec 23 '17 at 5:12
  • $\begingroup$ One could direct a positron beam onto a neutron beam to force the situation. The cross-section would then by typical of low-energy weak interaction (i.e. terrible), but it ought to be possible to observe the reaction the OP proposes (counting missing momentum as exposing the neutrino). A heck of a lot of time, energy, and money for little obvious gain. $\endgroup$ – dmckee Dec 23 '17 at 8:46
  • $\begingroup$ @dmckee You may know this already, but helium-3 makes a good neutron stand in (it's stable, polarizable), and DESY has a positron beam (for storage lifetime vs. electrons), and that experiment was done: www-hermes.desy.de. $\endgroup$ – JEB Dec 23 '17 at 18:21

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