Long-ranged adsorbate-adsorbate interactions mediated by a surface-state band

The adsorbate-adsorbate interaction mediated by Shockley surface states on, for example, the (1 1 1) faces of noble metals, yields an oscillatory form modulated by a 1/d(2) envelope at asymptotic adsorbate separations d. For this interaction we obtain a non-perturbative analytical estimate, specified by experimentally accessible Shockley-state parameters and the finite Fermi-level phase shift delta(F) not equal 0, which characterize the standing-wave patterns observed in scanning tunnelling microscopy (STM) images. We provide explicit interaction results for the phase shift value delta(F) = -pi/2 suggested by the STM measurements of sulphur adsorbates on Cu(111), and we attempt to relate our results to the corresponding observations of correlations in the adsorbate distribution function.