Exact one-dimensional pair correlation functions of a monolayer/substrate system

We have derived an exact expression for the one-dimensional atomic pair correlation function of the combined overlayer and substrate system in the very first stages of epitaxy. The overlayer can have an arbitrary island size distribution. This pair correlation function is then used to evaluate the widths and shapes of low-energy (or high-energy) electron diffraction intensity profiles. Several model calculations have been computed and the diffraction profiles resemble the recent molecular beam epitaxy measurements of Si/Si(111) and W/W(110) systems reported by Henzler and co-workers.