Nope, no can do. It's because electrons and protons are different animals. An electron can annihilate with a positron (anti-electron) and a proton can annihilate with an anti-proton, but not with each other. Very serious experiments have searched in vain for the disintegration of a proton into a positron plus pions or gamma rays, which would be equivalent to the inverse of proton-electron annihilation.
There is no fundamental reason for this, it's just a fact of life. In quantum field theory electrons interact with other charged particle via the virtual exchange of photons. They can also interact with neutrinos and other leptons such as muons via the exchange of W bosons. Protons, being charged, also interact with other charged particles as well as participate in strong interactions via exchange of so-called gluons.
Now life gets complicated here. Since we know that the neutron does decay into a proton plus an electron plus an anti-neutrino, you should ask why doesn't the reverse happen. It could, but the energetics are unfavorable. The possibility of such a reaction is due to the slight mixing of the electromagnetic and weak interactions.
Sigh... it's tough. There are no easy answers to your question.
LeeH
(published on 11/23/2011)
