Charge Radius of Neutron-deficient $^{54}$Ni and Symmetry Energy Constraints Using the Difference in Mirror Pair Charge Radii

TL;DR

This study measures the charge radius difference between mirror nuclei $^{54}$Ni and $^{54}$Fe to constrain the symmetry energy slope parameter $L$, providing insights into neutron-rich matter and neutron star properties.

Contribution

It provides the first precise charge radius measurement of $^{54}$Ni and links mirror charge radii differences to symmetry energy constraints.

Findings

$ ext{L}$ is constrained between 20 and 70 MeV.

Results favor a soft neutron matter equation of state.

The neutron-skin thickness of $^{48}$Ca is estimated to be 0.15-0.19 fm.

Abstract

The nuclear root-mean-square charge radius of $^{54}$Ni was determined with collinear laser spectroscopy to be $R(^{54}$Ni) = 3.737\,(3)~fm. In conjunction with the known radius of the mirror nucleus $^{54}$Fe, the difference of the charge radii was extracted as $\Delta R_{\rm ch}$ = 0.049\,(4)~fm. Based on the correlation between $\Delta R_{\rm ch}$ and the slope of the symmetry energy at nuclear saturation density ($L$), we deduced $20 \le L \le 70$\,MeV. The present result is consistent with the $L$ from the binary neutron star merger GW170817, favoring a soft neutron matter EOS, and barely consistent with the PREX-2 result within 1$\sigma$ error bands. Our result indicates the neutron-skin thickness of $^{48}$Ca as 0.15\,-\,0.19\,fm.