  We report elastic scattering theory for surface electron waves in quantum
corrals defined by adatoms on the surface of noble metals. We develop a
scattering-matrix technique that allows us to account for a realistic smooth
potential profile of the scattering centers. Our calculations reproduce
quantitatively all the experimental observations, which is in contrast to
previous theories (treating the adatoms as point scatterers) that require
additional inelastic channels of scattering into the bulk in order to achieve
the agreement with the experiment. Our findings thus indicate that surface
states are not coupled to the bulk electrons.
