  The inverse $\beta$-decay reaction, anti-nu_e + p --> e^+ + n, for low-energy
anti-neutrinos coming from nuclear reactors is of great current interest in
connection with high-precision measurements of the neutrino mixing angle
$\theta_{13}$. We have previously derived analytic expressions, up to
next-to-leading order in heavy-baryon chiral perturbation theory, for the
radiative corrections (RCs) and the nucleon-recoil corrections both for this
reaction and for the related neutron $\beta$-decay process. We investigate here
the numerical consequences of these analytic expressions. We show that the
recoil corrections are small for neutron $\beta$-decay, but for inverse
$\beta$-decay, the recoil corrections are comparable in size to the RCs for
typical energies of reactor anti-neutrinos, and they have opposite signs. It
turns out that the RCs and the recoil corrections exhibit very different
dependences on the neutrino energy.
