  We present a semi-relativistic model for the description of the ionization
process of atomic hydrogen by electron impact in the first Born approximation
by using the Darwin wave function to describe the bound state of atomic
hydrogen and the Sommerfeld-Maue wave function to describe the ejected
electron. This model, accurate to first order in $Z/c$ in the relativistic
correction, shows that, even at low kinetic energies of the incident electron,
spin effects are small but not negligible. These effects become noticeable with
increasing incident electron energies. All analytical calculations are exact
and our semi-relativistic results are compared with the results obtained in the
non relativistic Coulomb Born Approximation both for the coplanar asymmetric
and the binary coplanar geometries.
