# When is emitting a particle (e.g. neutrino) the same as absorbing an antiparticle?

I've read that Pauli first proposed the neutrino to explain energy and momentum conservation in this equation:

$$n \to p^+ + e^- + \overline\nu_e$$

But it is also written differently here:

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

Is there a difference between the two equations? If not, does it mean we ascribe a negative energy to one of $$\overline\nu_e$$ or $$\nu_e$$?

Nor can you even guarantee that this kind of reversal preserve the possibility of the reaction. For instance $$p^- \to \bar{n} + e^- + \bar{\nu}_e$$ has the same isospin and lepton quantum numbers quantum numbers as your top reaction but it is strictly forbidden by energy considerations (the final state is heavier than the initial state).
Also things like $$\bar{p} + n \to e^- + \bar{\nu}_e$$ are allowed by quantum numbers but are vanishingly unlikely in practice. It would take some cleverness just to exhibit a Feynmann diagram at the quark-gluon-lepton level that totals up to the process exhibited here are the hadron-lepton level.