Theory of absorption of electromagnetic radiation energy by fine metal particles

Temperature and frequency dependences of the cross section of absorption of an external alternating electromagnetic field by a small metal particle was evaluated using the kinetic equation for the electron distribution function. It is assumed that the particle radius $R$ satisfies the inequality $l_{ee}\ll R\ll\lambda$, where $l_{ee}$ is the electron mean free path and $\lambda$ is the electromagnetic radiation wavelength. A general expression for the absorption cross section is obtained for an arbitrary ratio between the linear particle size and the skin layer thickness. The effect of particle temperature variation under the action of the external alternating electromagnetic field on the absorption cross section was studied. It is proved that for $R\ll\lambda$ and $R\ll l_{ee}$, the absorption cross section should be calculated using the quantum mechanical principles and considering the electron temperature equal to zero. Under these conditions, it is not correct to introduce the electron distribution function and the absorption cross section is a rather complicated function of the frequency of the external field.