Comment on Gor'kov and Eliashberg's theory for far-infrared absorption by small metallic particles

Numerous errors exist in Gor'kov and Eliashberg's expressions for the electric susceptibility χ(ω) of a small metallic particle. We have reevaluated the integral for χ(ω) for Dyson's circular ensembles and use the results to examine the dependence of the far-infrared absorption coefficient α( ̃ \~ν) and its derivative dαd ̃ \~ν on particle size and the geometric standard deviation σ of a log-normal distribution of sizes. We conclude that experimental observation of the oscillations characteristic of quantum-size effects by far-infrared absorption requires use of derivative spectroscopy and a distribution of particles with σ1.05 for the symplectic ensemble, which is the most favorable case. Thus, experimental verification of the applicability of the Gor'kov-Eliashberg theory is unlikely with currently available methods of sample preparation.