  We propose a procedure to analyze the relation between the exact
factorization of the electron-nuclear wave function and the Born-Oppenheimer
approximation. We define the adiabatic limit as the limit of infinite nuclear
mass. To this end, we introduce a unit system that singles out the dependence
on the electron-nuclear mass ratio of each term appearing in the equations of
the exact factorization. We observe how non-adiabatic effects induced by the
coupling to the nuclear motion affect electronic properties and we analyze the
leading term, connecting it to the classical nuclear momentum. Its dependence
on the mass ratio is tested numerically on a model proton- coupled electron
transfer in different non-adiabatic regimes.
