Neutron Radii in Nuclei and the Neutron Equation of State

The root-mean-square radius for neutrons in nuclei is investigated in the Skyrme Hartree-Fock model. The main source of theoretical variation comes from the exchange part of the density-dependent interaction which can be related to a basic property of the neutron equation of state. A precise measurement of the neutron radius in ${}^{208}\mathrm{Pb}$ would place an important new constraint on the equation of state for neutron matter. The Friedman-Pandharipande neutron equation of state would lead to a very precise value of $0.16\pm 0.02\mathrm{fm}$ for the difference between the neutron and the proton root-mean-square radius in ${}^{208}\mathrm{Pb}$.