  The behavior of the surface barrier that forms at the metal-vacuum interface
is important for several fields of surface science. Within the Density
Functional Theory framework, this surface barrier has two non-trivial
components: exchange and correlation. Exact results are provided for the
exchange component, for a jellium metal-vacuum interface, in a slab geometry.
  The Kohn-Sham exact-exchange potential $V_{x}(z)$ has been generated by using
the Optimized Effective Potential method, through an accurate numerical
solution, imposing the correct boundary condition. It has been proved
analytically, and confirmed numerically, that $V_{x}(z\to \infty)\to -
e^{2}/z$; this conclusion is not affected by the inclusion of correlation
effects. Also, the exact-exchange potential develops a shoulder-like structure
close to the interface, on the vacuum side. The issue of the classical image
potential is discussed.
