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Charge Radii Measurements of Exotic Tin Isotopes in the Proximity of $N=50$ and $N=82$

F. P. Gustafsson, L. V. Rodríguez, R. F. Garcia Ruiz, T. Miyagi, S. W. Bai, D. L. Balabanski, C. L. Binnersley, M. L. Bissell, K. Blaum, B. Cheal, T. E. Cocolios, G. J. Farooq-Smith, K. T. Flanagan, S. Franchoo, A. Galindo-Uribarri, G. Georgiev, W. Gins, C. Gorges, R. P. de Groote, H. Heylen, J. D. Holt, A. Kanellakopoulos, J. Karthein, S. Kaufmann, Á. Koszorús, K. König, V. Lagaki, S. Lechner, B. Maass, S. Malbrunot-Ettenauer, W. Nazarewicz, R. Neugart, G. Neyens, W. Nörtershäuser, T. Otsuka, P. -G. Reinhard, N. Rondelez, E. Romero-Romero, C. M. Ricketts, S. Sailer, R. Sánchez, S. Schmidt, A. Schwenk, S. R. Stroberg, N. Shimizu, Y. Tsunoda, A. R. Vernon, L. Wehner, S. G. Wilkins, C. Wraith, L. Xie, Z. Y. Xu, X. F. Yang, D. T. Yordanov

Abstract

We report nuclear charge radii for the isotopes $^{104-134}$Sn, measured using two different collinear laser spectroscopy techniques at ISOLDE-CERN. These measurements clarify the arch-like trend in charge radii along the isotopic chain and reveal an odd-even staggering that is more pronounced near the $N=50$ and $N=82$ shell closures. The observed local trends are well described by both nuclear density functional theory and valence space in-medium similarity renormalization group calculations. Both theories predict appreciable contributions from beyond-mean-field correlations to the charge radii of the neutron-deficient tin isotopes. The models, however, fall short of reproducing the magnitude of the known $B(E2)$ transition probabilities, highlighting the remaining challenges in achieving a unified description of both ground-state properties and collective phenomena.

Charge Radii Measurements of Exotic Tin Isotopes in the Proximity of $N=50$ and $N=82$

Abstract

We report nuclear charge radii for the isotopes Sn, measured using two different collinear laser spectroscopy techniques at ISOLDE-CERN. These measurements clarify the arch-like trend in charge radii along the isotopic chain and reveal an odd-even staggering that is more pronounced near the and shell closures. The observed local trends are well described by both nuclear density functional theory and valence space in-medium similarity renormalization group calculations. Both theories predict appreciable contributions from beyond-mean-field correlations to the charge radii of the neutron-deficient tin isotopes. The models, however, fall short of reproducing the magnitude of the known transition probabilities, highlighting the remaining challenges in achieving a unified description of both ground-state properties and collective phenomena.

Paper Structure

This paper contains 3 sections, 1 equation, 3 figures, 3 tables.

Table of Contents

  1. Supplemental Material
  2. VS-IMSRG calculations
  3. Experimental methodology and the determination of nuclear charge radii

Figures (3)

  • Figure 1: (a) The absolute root-mean-square radii obtained using $R_c \left({}^{124}\text{Sn}\right) = 4.675\,(1)$ fm 50-Sn. (b) Differential mean-square charge radii of tin isotopes with respect to $^{124}$Sn. (c) The odd-even staggering $\Delta^{(3)}_{R}=1/2(R_{A+1}+R_{A-1}-2R_{A})$. Experimental results are compared to VS-IMSRG and DFT results (for details see text). The statistical uncertainties for Fy(IVP) are indicated by dark yellow bands and the systematic uncertainties (mainly ground-state correlations) by light yellow bands.
  • Figure 2: (a) Residual differential mean-square charge radii $\delta \left\langle r_{\mathrm{res}}^2 \right\rangle$ obtained by the subtraction of a linear trend which intersects at the magic numbers $N=50, 82$ (see Ref. Karthein2024 for details). Experimental results are compared with DFT Fy(IVP) calculations, with systematic uncertainties shown as a yellow error band (darker shade represents the influence of ground-state correlations) and VS-IMSRG calculations using different Hamiltonians and different valence spaces (for details see text). The experimental and calculated $B(E2)$ values are shown in panel (b). Experimental $B(E2)$ values were taken from Refs. Rosiak2018aradford2003nuclearguastalla2013doornenbal2014Ekstrom2008allmond2011coulombvarner2005coulombstelson1970staticback2013transitionsiciliano2020pairingBEENE2004471RADFORD2005264, shown with a 1-$\sigma$ error band from NNDC in Ref. pritychenko2016tables.
  • Figure 3: Sample spectra of the even-even tin isotopes acquired with the $5s^{2}5p^{2} \; ^{3\!}P_{2} \rightarrow 5s^{2}5p6s \; ^{3\!}P_{2}$ (284 nm) transition. The spectra are fitted using Lorentzian profiles with free linewidth as indicated with red lines.