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We present a fully relativistic investigation of the radiative recombinationof a twisted electron with a bare heavy nucleus. The twisted electron isdescribed by the wave function which accounts for the interaction with thenucleus in all orders in $\alpha Z$. We use this wave function to derive theprobability of the radiative recombination with a single ion being shifted fromthe twisted electron propagation direction. We also consider more realisticexperimental scenarios where the target is either localized (mesoscopic) orinfinitely wide (macroscopic). The situation when the incident electron is acoherent superposition of two vortex states is considered as well. For thenonrelativistic case we present analytical expressions which support ournumerical calculations. We study in details the influence of the electrontwistedness on the polarization and angular distribution of the emitted photon.It is found that these properties of the outgoing photon might be verysensitive to the total angular momentum and kinematic properties of twistedbeams. Therefore, the recombination of the twisted electrons can serve as avaluable tool for atomic investigations as well as for the diagnostics of thevortex electron beams.

Radiative recombination of twisted electrons with bare nuclei: going beyond the Born approximation