  A fully relativistic approach is presented for the calculation of the
bremsstrahlung emitted by an electron scattered off an ionic target. The ionic
target is described as a combination of an effective Coulomb potential and a
finite-range potential induced by the electronic cloud of the ion. The approach
allows us to investigate the influence of the electronic structure of the
target on the properties of the emitted radiation. We calculate the double
differential cross-section and Stokes parameters of the bremsstrahlung of an
electron scattered off uranium ions in different charge states, ranging from
bare to neutral uranium. Results on the high-energy endpoint of the electron
bremsstrahlung from Li-like uranium ions ${\rm U}^{89+}$ are compared to the
recent experimental data. For this process, it is found that taking into
account the electronic structure of the target results in modification of the
cross-section on the level of 14%, which can, in principle, be seen in
present-day experiments.
