Mirror Charge Radii and the Neutron Equation of State

The differences in the charge radii of mirror nuclei are shown to be proportional to the derivative of the neutron equation of state and the symmetry energy at nuclear matter saturation density. This derivative is important for constraining the neutron equation of state for use in astrophysics. The charge radii of several neutron-rich nuclei are already measured to the accuracy of about 0.005 fm. Experiments at isotope-separator and radioactive-beam facilities are needed to measure the charge radii of the corresponding proton-rich mirror nuclei to a similar accuracy. It is also shown that neutron skins of nuclei with $N=Z$ depend upon the value of the symmetry energy at a density of $0.10\mathrm{nucleons}/{\mathrm{fm}}^3$.

Figure 1

Neutron skins for ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ for 48 Skyrme functionals plotted versus the slope of the symmetry energy, $L$. The colors correspond to the constraints made for the neutron skin of ${}^{208}\mathrm{Pb}$: 0.12 fm (red), 0.16 fm (orange), 0.20 fm (green), and 0.24 fm (blue). The lines are to guide the eye.

Figure 2

Difference in the proton rms radii of the mirror nuclei ${}^{52}\mathrm{Ni}$ and ${}^{52}\mathrm{Cr}$ compared to the neutron skin of ${}^{52}\mathrm{Cr}$. Results are shown for the 48 Skyrme functionals discussed in the text but without the Coulomb interaction. The points are labeled according to their respective values for the neutron skin of ${}^{208}\mathrm{Pb}$ ranging from 0.12 to 0.24 fm.

Figure 3

Same as Fig. 2 but with the Coulomb interaction added.

Figure 4

The neutron skin of ${}^{52}\mathrm{Cr}$ (top) and $\mathrm{\Delta }{R}_{\mathrm{ch}}$ for ${}^{52}\mathrm{Ni}$ and ${}^{52}\mathrm{Cr}$ (bottom) plotted versus the slope of the symmetry energy, $L$.

Figure 5

The neutron skin of ${}^{54}\mathrm{Fe}$ (top) and $\mathrm{\Delta }{R}_{\mathrm{ch}}$ for ${}^{54}\mathrm{Ni}$ and ${}^{54}\mathrm{Fe}$ (bottom) plotted versus the slope of the symmetry energy, $L$.

Figure 6

The neutron skin of ${}^{56}\mathrm{Ni}$ plotted versus the slope of the symmetry energy, $L$, (left), and versus the value of the symmetry energy at a density of $0.10\mathrm{nucleons}/{\mathrm{fm}}^3$ (right).

Figure 7

$\mathrm{\Delta }{R}_{\mathrm{ch}}$ for ${}^{34}\mathrm{Ar}$ and ${}^{34}\mathrm{S}$ plotted versus the slope of the symmetry energy, $L$. The experimental result (see text) for $\mathrm{\Delta }{R}_{\mathrm{ch}}$ is shown by the black point with an error bar near the $y$ axis.