Dependence of the stopping power on the surface response function

We have calculated the stopping power of protons moving parallel to a metal surface using two different models of surface response function: A fully quantum mechanical model (QMM) and the specular reflection model (SRM). Although the surface electronic structure is described by means of a smooth potential barrier in the former and by an infinite barrier in the latter, they yield nearly the same results at relatively high velocities, whereas for low velocities very different results are obtained. These differences are explained in terms of the wavelength of the modes excited by the ion.