The current theoretical formulations of optical absorption by small metal particles are critically reviewed. Several inconsistencies of the usual dielectric-function calculations are noted, and an improved expression is proposed. The results indicate that optical spectra should have a bearing on the difficult question of the level distribution in small particles. Finite ionization potential effects are shown to be important for small particles and are included in the dielectric formulation. The new results agree with hydrodynamic theories that state that the position of the anomalous absorption peak essentially depends on the degree of diffuseness of the metal-particle surface.
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