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note
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max = l/R for a thick film. Thus the interaction is mediated by surface plasmon of wave vectors larger than 1/R and retardation effects in the nanoparticle/film problem can be neglected for small nanospheres.
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note
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The effect of a background polarizability of the metal is a screening of the surface charges associated with the surface plasmons. This effect can be modeled using a lower conduction electron density. In the application to metallic structures of gold, we therefore use an effective bulk plasmon frequency of 4.6 eV which corresponds to the experimental value of 2.6 eV for the dipolar sphere plasmon in a vacuum.
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