Parity violating electron scattering can measure the neutron density of aheavy nucleus accurately and model independently. This is because the weakcharge of the neutron is much larger then that of the proton. The Parity RadiusExperiment (PREX) at Jefferson Laboratory aims to measure the root mean squareneutron radius of $^{208}$Pb with an absolute accuracy of 1% ($\pm 0.05$ Fm).This is more accurate then past measurements with hadronic probes, which allsuffer from controversial strong interaction uncertainties. PREX should clearlyresolve the neutron-rich skin. Furthermore, this benchmark value for $^{208}$Pbwill provide a calibration for hadronic probes, such as proton scattering,which can then be used to measure neutron densities of many exotic nuclei. ThePREX result will also have many implications for neutron stars. The neutronradius of Pb depends on the pressure of neutron-rich matter: the greater thepressure, the larger the radius as neutrons are pushed out against surfacetension. The same pressure supports a neutron star against gravity. The Pbradius is sensitive to the equation of state at normal densities while theradius of a 1.4 solar mass neutron star also depends on the equation of stateat higher densities. Measurements of the radii of a number of isolated neutronstars such as Geminga and RX J185635-3754 should soon improve significantly. Bycomparing the equation of state information from the radii of both Pb andneutron stars one can search for a softening of the high density equation ofstate from a phase transition to an exotic state. Possibilities include kaoncondensates, strange quark matter or color superconductors.
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