  The Mott scattering of high-energetic twisted electrons by atoms is
investigated within the framework of the first Born approximation and Dirac's
relativistic equation. Special emphasis is placed on the angular distribution
and longitudinal polarization of the scattered electrons. In order to evaluate
these angular and polarization properties we consider two experimental setups
in which the twisted electron beam collides with either a single well-localized
atom or macroscopic atomic target. Detailed relativistic calculations have been
performed for both setups and for the electrons with kinetic energy from 10 keV
to 1000 keV. The results of these calculations indicate that the emission
pattern and polarization of outgoing electrons differ significantly from the
scattering of plane-wave electrons and can be very sensitive to the parameters
of the incident twisted beam. In particular, it is shown that the angular- and
polarization-sensitive Mott measurements may reveal valuable information about,
both the transverse and longitudinal components of the linear momentum and the
projection of the total angular momentum of twisted electron states. Thus, the
Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.
