Laser spectroscopy of neutron-rich tin isotopes: A discontinuity in charge radii across the $N=82$ shell closure

The change in mean-square nuclear charge radii $\delta \left \langle r^{2} \right \rangle$ along the even-A tin isotopic chain $^{108-134}$Sn has been investigated by means of collinear laser spectroscopy at ISOLDE/CERN using the atomic transitions $5p^2\ ^1S_0 \rightarrow 5p6\ s^1P_1$ and $5p^2\ ^3P_0 \rightarrow 5p6s^3 P_1$. With the determination of the charge radius of $^{134}$Sn and corrected values for some of the neutron-rich isotopes, the evolution of the charge radii across the $N=82$ shell closure is established. A clear kink at the doubly magic $^{132}$Sn is revealed, similar to what has been observed at $N=82$ in other isotopic chains with larger proton numbers, and at the $N=126$ shell closure in doubly magic $^{208}$Pb. While most standard nuclear density functional calculations struggle with a consistent explanation of these discontinuities, we demonstrate that a recently developed Fayans energy density functional provides a coherent description of the kinks at both doubly magic nuclei, $^{132}$Sn and $^{208}$Pb, without sacrificing the overall performance. A multiple correlation analysis leads to the conclusion that both kinks are related to pairing and surface effects.