Elastic scattering theory for electronic waves in quantum corrals

Recent scanning-tunneling-microscopy studies on the (111) faces of noble metals have directly imaged electronic surface-confined states, and dramatic standing-wave patterns have been observed in geometrically arranged quantum corral structures formed by Fe adatoms on Cu(lll). We present a coherent elastic scattering theory for the electronic states in these ''leaky'' confining structures by seeking solutions of the two-dimensional Schrodinger equation compatible with Sommerfeld radiation conditions. A direct comparison to the reported experimental data reveals excellent agreement with our elastic-scattering theory. We are led to the conclusion that the Fe adatoms are well modeled by finite-height potential barriers, as opposed to ''black dot'' absorbing scatterers, and that the adatoms do not significantly couple the surface-state electrons to the bulk metallic states.