  We examine first-order perturbative results based on jellium for the surface
energy of slabs of simple metals, using various local pseudopotentials
(Ashcroft, Heine-Abarenkov and evanescent core). The difference between the
pseudopotential and the jellium potential is averaged along the plane parallel
to the surface. We compare these perturbative results with those of the
stabilized jellium model (a modification of the regular jellium model in which
the perturbation appears in the energy functional right from the outset) and
with the output of other perturbative and non-perturbative calculations.
