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We use properties of doubly-magic nuclei and ab-initio calculations oflow-density neutron matter to constrain Skyrme equations of state forneutron-rich conditions. All of these properties are consistent with a Skyrmefunctional form and a neutron-matter equation of state that depends on threeparameters. With a reasonable range for the neutron-matter effective mass, thevalues of the two other Skyrme parameters are well constrained. This leads topredictions for other quantities. The neutron skins for $^{208}$Pb and$^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Otherresults including the dipole polarizability are discussed.

Constraints on Skyrme Equations of State from Properties of Doubly Magic Nuclei and Ab-Initio Calculations of Low-Density Neutron Matter