The Matter Radius of 132Sn and the CREX-PREX Dilemma

Abstract

The density dependence of the nuclear symmetry energy remains a central open problem in nuclear physics. Parity violating electron scattering experiments have provided largely model-independent determinations of the neutron skin thickness of both 48Ca and 208Pb, whose consistent theoretical interpretation remains challenging. A new measurement of the matter radius of the unstable, doubly magic nucleus 132Sn provides an important additional constraint. Using a representative set of covariant energy density functionals spanning a wide range of isovector properties, we show that at least one of these models can simultaneously reproduce the charge and matter radii of132Sn. When interpreted together with the PREX and CREX results, the new measurement--much like CREX--favors a relatively soft symmetry energy. These findings underscore the need for an independent confirmation of the PREX result, such as the anticipated MREX campaign at the MESA facility.

Figures (4)

• Figure 1: Theoretical predictions for the charge and matter radii of ${}^{132}$Sn. The probability distribution functions were generated with FSUGarnet Chen:2014mza and the experimental data are from ISOLDE LeBlanc:2005ik and RIKEN Hijikata:2026xwa, respectively.
• Figure 2: (a) Proton, neutron, and matter densities of ${}^{132}$Sn predicted by the three covariant energy density functionals used in this work, together with densities extracted from experiment using two-parameter Fermi distributions. (b) Corresponding matter form factors. Because protons probe primarily the nuclear surface, model differences appear only at large momentum transfer, where the form factor has already fallen by more than two orders of magnitude.
• Figure 3: Predicted correlation between the neutron skin thickness of $^{208}$Pb, $^{132}$Sn, and $^{48}$Ca from a set of covariant energy density functionals. The PREX, CREX, and RIKEN constraints are also shown. Indicated with red circles are the predictions from FSUGarnet, RMF022, and FSUGold2. The tight correlation illustrates the challenge of reconciling the neutron skins of these three nuclei within a single theoretical description.
• Figure 4: Statistical correlations between neutron skin thicknesses obtained from the covariance analysis of the FSUGarnet and FSUGold2 energy density functionals. The neutron skins of $^{208}$Pb, $^{132}$Sn, and $^{48}$Ca exhibit nearly perfect correlations, underscoring the difficulty of simultaneously reproducing all experimental constraints within a single model.