Vision and precision in radii estimations

Finite nuclear size effects play an increasingly important role in precision atomic and nuclear physics. For example, they have been found to strongly affect the determination of the V_ud matrix element of the CKM matrix (arXiv:2309.16893) Determining the absolute charge radius of some short-lived nucleus entails careful assembly of several pieces spanning different fields. Measurements include optical isotope shifts, muonic atom x-ray energies, electron scattering cross-sections, while theoretical calculations span high-field QED and nuclear structure effects in muonic atoms and many-body calculation of isotope shift factors in atomic systems. In this talk I will give an overview of the different pieces that go into a charge radius and discuss their current status and reliable uncertainty estimations. The talk will be biased towards medium mass numbers ($10<A<60$) relevant to the the study of mirror nuclei (arXiv:2409.08193).