Laser spectroscopy on the heavy ion beams

In the presented report the perspectives of the study of the electric charg e and current space distributions in the nuclei by laser spectroscopy metho ds on the beams of the fast multiple charged ions are discussed. The calcul ations of both the level energies and widths in the H-like and He-like ions and of the isotopic shifts and hyperfine splitting in the optical spectra of these ions are performed. The project of the experimental set-up for the se measurements is considered.