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 jelliu m model taking into exact account the spatial dispersion of free electron g as. The Vlasov equation for the plasma electron distribution function insid e a spherical cluster exposed to a low-intensity external electromagnetic f ield is solved analytically in the linear response approximation for the ca ses of both diffuse and mirror reflection of electrons from the cluster bou ndary. The solution found is used to obtain the non-local relation between the current density and the electric field inside the cluster, which is sub stituted into the Maxwell equations and boundary conditions for the electro magnetic field. In the diffuse reflection case the complete set of field eq uations is reduced to a single integral equation which has been solved nume rically to obtain the distributions of both the electric field and the elec tron 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, tha t in the considered model the width of the dipole Mie resonance is mainly d ue to the electron reflection from the cluster boundary, it slightly depend s on the permittivity epsilon(0) of the environment, and in the case of clu sters in vacuum it is described with a good accuracy by the conventional ex pression gamma (R) = gamma(infinity) + bv(F)/R with b approximate to 1.0, v (F) being the electron Fermi velocity.