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Electric dipole absorption by ballistic electrons in small metal spheres

We describe a semiclassical approach to estimating the absorption of electromagnetic radiation by small conducting spheres, in which the motion of the charge carriers is ballistic. The results are strikingly different between the cases of rough and smooth walled particles. For a rough walled particle the absorption coefficient is proportional to omega 2 in the low-frequency limit. For a smooth walled sphere the absorption coefficient has a low-frequency cut-off at omega c, the angular frequency of a circumferential 'whispering gallery' classical orbit of a carrier at the Fermi surface. At frequencies above omega c the spectrum consists of a sequence of overlapping resonance bands which combine to give an absorption coefficient proportional to omega 2 only for omega >> omega c.