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 δr² 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 5s²4pt0ex¹-0.16em0exS₀-4d5p4pt0ex¹-0.16em0exP₁ and 4d5s4pt0ex³-0.16em0exD₂-4d5p4pt0ex³-0.16em0exP₁ transitions for singly charged yttrium ($Z=39$).