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 $\delta ⟨r^2⟩$ along the even-$A$ tin isotopic chain ${}^{108-134}\mathrm{Sn}$ has been investigated by means of collinear laser spectroscopy at ISOLDE/CERN using the atomic transitions $5p^2{{}^{1}S}_0\to 5p6s{{}^{1}P}_1$ and $5p^2{{}^{3}P}_0\to 5p6s{{}^{3}P}_1$. With the determination of the charge radius of ${}^{134}\mathrm{Sn}$ 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 ${}^{132}\mathrm{Sn}$ 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 ${}^{208}\mathrm{Pb}$. 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, ${}^{132}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$, without sacrificing the overall performance. A multiple correlation analysis leads to the conclusion that both kinks are related to pairing and surface effects.

Figure 1

Optical spectra of even neutron-rich Sn isotopes for the determination of the isotope shift in the $5p^2{{}^{1}S}_0\to 5p6s{{}^{1}P}_1$ (SP) transition. The number of photomultiplier events is plotted as a function of the Doppler-tuned frequency relative to the resonance center of ${}^{124}\mathrm{Sn}$. The red line represents the fitted Voigt profile. For ${}^{128,130}\mathrm{Sn}$, the contribution of an isomer (dashed, blue line) and the $I=0$ ground state (dotted, olive line) are plotted individually, with a significantly smaller isomer-to-ground-state ratio in ${}^{128}\mathrm{Sn}$.

Figure 2

Evolution of the nuclear charge radii along the tin isotopic chain from the experiment (circles) and from DFT calculations using the SV-min (triangles) and $\mathrm{Fy}(\mathrm{\Delta }r,\mathrm{HFB})$ (dots) functionals. The experimental and predicted charge radii at the kink at ${}^{208}\mathrm{Pb}$ are shown in the inset. Experimental data for ${}^{204-212}\mathrm{Pb}$ are taken from Ref. [27].

Figure 3

Multiple correlation coefficient of the radius kinks ${\mathrm{\Delta }}_{2n}^{(3)}r$ in ${}^{132}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ with groups of model parameters (left) and groups of odd-even staggerings in binding energy, ${\mathrm{\Delta }}_1^{(3)}E$, and charge radii, ${\mathrm{\Delta }}_1^{(3)}r$, (right) calculated with SV-min and $\mathrm{Fy}(\mathrm{\Delta }r,\mathrm{HFB})$. For details, see Supplemental Material [61].