Laser spectroscopy of radioactive isotopes: Role and limitations of accurate isotope-shift calculations

Nuclear mean-square charge radii of radioactive isotopes are obtained from isotope-shift measurements using laser spectroscopy. To extract the values of $\ensuremath{\delta}\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}$ the atomic field and mass shift factors need to be evaluated. We here summarize the currently available experimental and theoretical techniques for calculating the atomic field and mass shift factors for complex, open-shell atoms, including the $5{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}\ensuremath{-}4d5p{\phantom{\rule{4pt}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ and $4d5s{\phantom{\rule{4pt}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{2}\ensuremath{-}4d5p{\phantom{\rule{4pt}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transitions for singly charged yttrium ($Z=39$).