Indirect long-range oscillatory interaction between adsorbed atoms

The oscillatory part of the indirect interaction between two adatoms on a metal surface, separated by a large distance R, is examined for the jellium as well as for the tight-binding model. The asymptotic form of the interaction is derived from the singularity of its Fourier transform at wave number q = 2k_F. For a substrate with a spherical Fermi surface, the interaction energy is proportional to $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^5$. The fall-off is faster than the corresponding oscillatory interaction between two impurities in the bulk, which varies as $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^3$. For substrates with a partially filled surface band, the interaction energy falls off much more slowly. Under simple assumptions, the interaction behaves as $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^2$. Comparisons are made with the numerical calculations by Einstein and Schrieffer. The experimental results of Tsong on Re atoms adsorbed on W using field-ion microscopy is also discussed.