Vlasov theory of Mie resonance broadening in metal clusters

Dynamical electromagnetic properties of metal clusters with radii R <10 nm have been theoretically considered in the dipole approximation in a jellium model taking into exact account the spatial dispersion of free electron gas. The Vlasov equation for the plasma electron distribution function inside a spherical cluster exposed to a low-intensity external electromagnetic field is solved analytically in the linear response approximation for the cases of both diffuse and mirror reflection of electrons from the cluster boundary. The solution found is used to obtain the non-local relation between the current density and the electric field inside the cluster, which is substituted into the Maxwell equations and boundary conditions for the electromagnetic field. In the diffuse reflection case the complete set of field equations is reduced to a single integral equation which has been solved numerically to obtain the distributions of both the electric field and the electron density inside the cluster, as well as the cluster dynamical electric polarizability and the photoabsorption and photoscattering cross sections. It has been found, from the cluster photoabsorption spectra calculated, that in the considered model the width of the dipole Mie resonance is mainly due to the electron reflection from the cluster boundary, it slightly depends on the permittivity 0 of the environment, and in the case of clusters in vacuum it is described with a good accuracy by the conventional expression ( R ) = + bv F / R with b 1.0, v F being the electron Fermi velocity.