The dipole-dipole interaction between two adatoms viewed as a surface plasmon mediated interaction

The semi-classical dipole-dipole interaction law previously derived from the classical image force theory is rederived from a model hamutonian in which the dipole-dipole interaction between two adatoms is mediated by surface plasmons. From this approach it emerges that the semi-classical law is only valid in the adiabatic limit where image charges can quasi-instantaneously follow the charge fluctuations on the adsorbate. Connection with the second order perturbation theory of dipole-dipole interaction between two adatoms is also analysed.