Electron-Proton Fusion?

A 'free' neutron is unstable with respect to beta decay, i.e. a neutron by itself will decay into a proton, beta and anti-neutrino, so the reverse action is unlikely. I suspect that electron capture may occur very rarely.

EC does happen in certain proton-rich (neutron deficient) radionuclides, and typically it is a K-electron which is absorbed. In plasmas, the ions and electrons have kinetic energies much, much greater than the binding energy of electrons (in the light elements). At lower energies, electrons recombine with ions to form neutral atoms, which then leak out of plasmas.

Protons (or more generally ions) and electrons interact in plasma, mostly by scattering or producing bremsstrahlung radiation, the latter of which results in energy loss from the plasma.

Fusion plasmas are likely to be D+D or D+T. D+³He would be preferable since it's an aneutronic reaction, but it requires higher temperatures (with concommitant pressure for a given particle density) and ³He is extremely rare (and thus very expensive). He-3 can be obtained from the beta decay of T (H-3).

Proton-proton fusion has a very low cross-section, and is the basis of one fusion process in stars - PP fusion or PP-chain.
http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

Otherwise, there are more exotic reaction like p + ¹¹B -> 3 ⁴He, but that requires significantly higher temperature than D+D or D+T.

p + p -> d + e⁺ + 1.4 MeV, but
p + d -> ³He + gamma + 5.5 MeV

 

http://www.nndc.bnl.gov/chart/ has a listing of all radionuclides and decay modes. Click on a location on the chart and select Zoom 1 at the top right of the chart.

The isotopes above or to the right of the black squares (stable elements) are proton-rich (neutron deficient) and preferentially decay by EC (electron capture, or K-capture), or in some cases positron emission. The further away the radionuclide is from the line of stability (black squares) the more rare it is, and usually it has a very short half-life.

Electron capture is dependent on nuclear properties, and should not be dramatically affected by the chemical form (BEC), i.e. BEC would not increase probability of EC in H, or D, or whatever.