Neutron Drops and Skyrme Energy-Density Functionals

The $J^{\pi }{=0\mathrm{}}^{+}$ ground state of a drop of 8 neutrons and the lowest $1/2^{-}$ and $3/2^{-}$ states of 7-neutron drops, all in an external well, are computed accurately with variational and Green's function Monte Carlo methods for a Hamiltonian containing the Argonne $v_{18}$ two-nucleon and Urbana IX three-nucleon potentials. These states are also calculated using Skyrme-type energy-density functionals. Commonly used functionals overestimate the central density of these drops and the spin-orbit splitting of 7-neutron drops. Improvements in the functionals are suggested.