Simple physical model for layer-number dependencies of proton stopping in ultra-thin films

Calculated proton stopping powers for a variety of ultra-thin films all show some simple scaling relationships with 1/N, where N is the number of film layers. The complexity of the calculations tends to obscure the physics underlying that scaling. We present a simple jellium model which exhibits the same scaling relationships and has the right order of magnitude for them. We also obtain the scaling dependence of the leading term in 1/N upon the kinetic energy and quantify the role of loss to surface excitations.