  Full one-loop radiative corrections are calculated for low energy
neutrino-nucleon quasi-elastic scattering, $\bar \nu_{e}+p \longrightarrow
e^{+} + n$, which involves both Fermi and Gamow-Teller transitions, in the
static limit of nucleons. The calculation is performed for both angular
independent and dependent parts. We separate the corrections into the outer and
inner parts {\` a} la Sirlin. The outer part is infrared and ultraviolet
finite, and involves the positron velocity. The calculation of the outer part
is straightforward, but that of the inner part requires a scrutiny concerning
the continuation of the long-distance hadronic calculation to the
short-distance quark treatment and the dependence on the model of hadron
structure. We show that the logarithmically divergent parts do not depend on
the structure of hadrons not only for the Fermi part, but also for the
Gamow-Teller part. This observation enables us to deal with the inner part for
the Gamow-Teller transition nearly parallel to that for the Fermi transition.
The inner part is universal to weak charged-current processes and can be
absorbed into the modification of the coupling constants up to the order of the
inverse proton mass $O(1/m_{p})$. The resulting $O(\alpha)$ corrections to the
differential cross section take the form $ [1+\delta_{\rm out}(E)] [
(1+\delta_{\rm in}^{\rm F}) < 1 >^2 +g_A^2 (1+\delta_{\rm in}^{\rm GT}) < {\mib
\sigma} >^2]$, where $<1 >$ and $<{\mib \sigma}>$ stand for the Fermi and
Gamow-Teller matrix elements; the outer correction $\delta_{\rm out}$ is
positron energy ($E$) dependent and takes different functional forms for the
angular independent and dependent parts. All factors are explicitly evaluated.
