  A still open issue in many-body theory is the asymptotic behavior of the
exchange-correlation energy and potential in the vacuum region of a metal
surface. Here we report a numerical study of the position-dependent
exchange-correlation energy for jellium slabs, as obtained by combining the
formally exact adiabatic-connection-fluctuation-dissipation theorem with either
time-dependent density-functional theory or an inhomogeneous
Singwi-Tosi-Land-Sj\"olander approach. We find that the inclusion of
correlation allows to obtain well-converged semi-infinite-jellium results
(independent of the slab thickness) that exhibit an image-like asymptotic
behavior close to the classical image potential $V_{im}(z)=-e^2/4z$.
