Multidimensional King-plot analysis for accurate extraction of Cd nuclear charge radii: a challenge for nuclear structure theory

High-accuracy determination of isotope shift factors, which plays a crucial role in accurate extraction of nuclear charge radius, is well-known to be challenging experimentally and theoretically. Nonetheless, based on an accurate measurement of the isotope shifts for the Cd$^+$ $5s~^2S_{1/2}-5p~^2P_{3/2}$ and the Cd $5s^2~^1S_0-5s5p~^1P_1$ transition, a multidimensional King-plot analysis is performed to extract the atomic field shift and mass shift factors accurately. The results are further cross-checked against results from atomic structure calculations using a high-accuracy configuration interaction and many-body perturbation theory. Combined with previous isotope shifts, nuclear charge radii for $^{100-130}$Cd of the highest accuracy are reported. For the neutron-rich region, accuracies for the charge radii are improved by nearly one order of magnitude. This work provides a coherent and systematic extraction of Cd nuclear charge radii from isotope shifts. The results offer stringent testing and possible challenges to the latest advances in nuclear theory and excellent benchmarking to the atomic structure calculations.