commonly written free neutron decay (Beta - decay) formula

N --> P + e + antineutrino

commonly written Beta + decay

P --> N + e+ + neutrino

let us rewrite them so it makes more sense

Neutrino + neutron --> P + e

Electron + proton --> neutron + neutrino

We can do this because the positrion e+ is the opposite of the electron e. The neutrino is the opposite of the antineutrino. Both can be placed on the other side of the equation mark by changing them in their so called opposite / antimatter..

Now the equation make much more sense and shows how it is reversible! It also shows that the neutrino must be an energetic input that causes the reaction (beta -) and the reversed is the Beta + that release energy as a result of electron capture.

See neutron page for further explanation of the energetic state of the electron / atom.