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  nucleons/fm^{3}.