  The elastic scattering of twisted electrons by neutral atoms is studied
within the fully relativistic framework. The electron-atom interaction is taken
into account in all orders, thus allowing us to explore high-order effects
beyond the first Born approximation. In order to illustrate these effects,
detailed calculations of the total and differential cross sections as well as
the degree of polarization of scattered electrons are performed. Together with
the analysis of the effects beyond the first Born approximation, we discuss the
influence of the kinematic parameters of the incident twisted electrons on the
angular and polarization properties of the scattered electrons.
