# Isn't positron capture theoretically possible?

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?

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