On van der Waals friction. II: Between atom and half-space

We calculate the frictional resistance experienced by an atom, modelled as a harmonic oscillator, moving with constant velocity u at a fixed distance zeta outside and parallel to the surface of a Drude-modelled half-space. Our method applies in the nonrelativistic/nonretarded/electrostatic regime, where u is far below c, and u/zeta is far below any important natural frequency of the atom or of the material. For a dissipative (e. g. for an ohmic) half-space and for the low values of u least unlikely to be of practical interest, this force is dominated by a term proportional to u/zeta(8), found perturbatively to fourth order in the interaction between atom and half-space. It appears to depend rather sensitively on how line shapes are handled.