Electromagnetic effects in the Surface Enhanced Raman Scattering from a molecule at a liquid Hg surface

In a previous publication the image enhancement effect and the enhanced radiation due to near field excitation of surface roughness were calculated for a finite-size molecule above a metal described by a nonlocal dielectric relation [Phys. Rev. Letters 44 (1980) 1774]. When applied to a roughened Ag surface these calculations led to a predicted Surface Enhanced Raman Scattering (SERS) gain of ~ 10³ due to each effect, yielding an overall gain ~ 10⁶, in agreement with experiment. Here these calculations are extended to the case of a liquid Hg surface, the roughness corresponding to thermally excited ripplons. The SERS gain due to image enhancement is reduced to ~ 10, due primarily to the ~ 24 times greater electron scattering rate in Hg over that in Ag. The roughness gain is reduced to ~ 2 at room temperature, due to the difference between the ripplon spectrum and that of the boss-like surface structures assumed for the solid surface. The predicted overall SERS gain for Hg is ~ 20, far less than reported in recent observations [R. Naanan et al., J. Phys. Chem. 84 (1980) 2692]. The discrepancy raises serious questions about the electromagnetic explanations of SERS.