Landau damping and wall dissipation in large metal clusters

Abstract

In analogy with nuclear many-body studies, the discrete-matrix random phase approximation (RPA) is used to describe the photoabsorption of large, spherical metal clusters. In this limit, the single-peak, classical Mie regime is valid and the matrix-RPA equations can be solved analytically. The RPA yields a closed formula for the width, Γ, of this peak due to Landau damping. This width is inversely proportional to the radius R of the cluster, in agreement with experimental observations for large silver and gold clusters embedded in a host medium. The RPA proportionality coefficient is unequivocally determined, and the reasons for the uncertainty in its value arising from disagreements among previous theoretical approaches are discussed. Specifically, Γ = λg( h ̷ Ω sp ε F ) v R , where λ is the multipolarity of the plasma vibration, Ω sp is the frequency of the surface plasmon, and ε F is the Fermi energy of the conduction electrons. The function g varies from unity to zero as the frequency of the surface plasmon increases from zero to infinity. It is shown that the frequency dependence of g for a spherical shape is identical to that of a cubical boundary. v = ( 3v F 4 ){1 + ( π 2 6 )( T ε F ) 2} is the average speed of a Fermi gas at temperature T. This result indicates a very small dependence on temperature, a trend in agreement with the observation. A classical interpretation of this result is proposed based on the similarities with the onebody, wall-dissipation theory familiar from nuclear physics. According to this interpretation, the surface of the cluster is viewed as a moving wall whose interaction with the conduction electrons mimicks the multipole transitions induced by the electric field of the plasmon. This interpretation expresses Γ as the ratio, Γ = γ B , of a surface friction coefficient, γ, over an inertia mass, B. The 1 R dependence results from the fact that the inertia mass is proportional to the volume, whereas the friction coefficient is proportional to the surface of the cluster.