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 neutron skins of neutron-rich nuclei and the corresponding slope of the neutron equation of state near a value of 0.10 neutrons/fm$^{3}$. The neutron skin is important for constraining the neutron equation of state for use in astrophysics. The charge radii of several neutron-rich nuclei are already accurately measured to the accuracy of about 0.005 fm. Experiments at 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 neutron EOS at a density of 0.10 neutrons/fm$^{3}$.