Fixed-node diffusion Monte Carlo computations for closed-shell jellium spheres

Fixed-node diffusion Monte Carlo computations are used to determine the ground state energy and electron density for jellium spheres with up to $N=106\mathrm{}$ electrons and background densities corresponding to the electron gas parameter $1<~r_s<~\mathrm{5.62.}$ We analyze the density and size dependence of the surface energy, and we extrapolate our data to the thermodynamic limit. The results agree well with the predictions of density functional computations using the local density approximation. In the case of $N=20,$ we extend our computation to higher densities and identify a transition between atomic- and jelliumlike nodal structures occurring at the background density corresponding to $r_s=\mathrm{0.13.}\mathrm{}$ In this case the local density approximation is unable to reproduce the changes in the correlation energy due to the discontinuous transition in the ground state nodal structure. We discuss the relevance of our results for nonlocal approximations to density functional theory.