  We present a study of Mott scattering of polarized electrons in the presence
of a laser field with circular polarization using the helicity formalism and
the introduction of the well known concept of non flip differential cross
section as well as that of flip differential cross section. The results we have
obtained in the presence of a laser field are coherent with those obtained in
the absence of a laser field. We have studied the relativistic regime as well
as the non relativistic regime that are precisely defined in the text. Two
important consistency checks have been carried out successfully. The first one
is that the sum of both differential cross sections (one with spin up, the
other with spin down) always gives the unpolarized differential cross section.
The second one is that the relativistic unpolarized differential cross section
converges to the non relativistic differential cross section in the limit of
small velocities. Moreover, the results obtained using the sofware Reduce
\cite{8} gave rise to non contracted coefficients that have been dealt with
using the geometry chosen.
