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

The nuclear root-mean-square charge radius of ${}^{54}\mathrm{Ni}$ was determined with collinear laser spectroscopy to be $R({}^{54}\mathrm{Ni})=3.737(3)\mathrm{fm}$. In conjunction with the known radius of the mirror nucleus ${}^{54}\mathrm{Fe}$, the difference of the charge radii was extracted as $\mathrm{\Delta }{R}_{\mathrm{ch}}=0.049(4)\mathrm{fm}$. Based on the correlation between $\mathrm{\Delta }{R}_{\mathrm{ch}}$ and the slope of the symmetry energy at nuclear saturation density ($L$), we deduced $21\le L\le 88\mathrm{MeV}$. 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 ${}^{48}\mathrm{Ca}$ as 0.15–0.21 fm.

Figure 1

Resonance spectra for ${}^{54}\mathrm{Ni}$ (left) and ${}^{60}\mathrm{Ni}$ (right) relative to the rest-frame transition frequency of ${}^{60}\mathrm{Ni}$. The solid line is the fit to the data.

Figure 2

$\mathrm{\Delta }{R}_{\mathrm{ch}}$ as a function of $L$ at ${\rho }_0$. The experimental result is shown as a horizontal gray band. The solid circles are results of Skyrme EDF and the crosses are for the CODF calculations. The dashed lines indicate theoretical error bounds. The upper figure shows comparison with the GW170817 and the PREX-2.

Figure 3

“Data-to-data” relation between $\mathrm{\Delta }{R}_{\mathrm{ch}}$ and $\mathrm{\Delta }{R}_{\mathrm{pn}}({}^{48}\mathrm{Ca})$. The same marks and color coding are used as Fig. 2.