Spatial variation of the electron mean free path near a surface

The electron plasmon-emission-mean-free-path in semi-infinite Jellium is evaluated as a function of position, and of electron emergence angle. The usual assumption that this free path is spatially non-varying inside the “metal” is found to be a reasonable approimation to reality by virtue of the fact that the surface plasmon emission probability increases where that of the bulk plasmon decreases (and vice-versa). The inverse mean free path, however, does not fall to zero for an appreciable distance (on the order of angstroms) outside the surface defined by the vanishing of the electron density.