SURFACE-MODES IN METAL-CLUSTERS AND CAVITIES

Solving the hydrodynamical equations by means of a variational princip le, we obtain a simultaneous description of the surface and volume mod es of the valence electrons in a metal. This variational scheme, which has been previously used in the context of nuclear fluid dynamics, is applied to describe the dynamics of the valence electrons in a spheri cal metal cluster and of the valence electrons in the metal surroundin g a spherical cavity (void). The eigenmodes fulfil the linear energy-w eighted sum rule (m(1)), the inverse energy-weighted sum rule(m(-1)) a nd orthogonality relations. The surface modes predicted by Mie (in clu sters) and by Natta (in cavities) appear in this model as natural solu tions of the equations of motion and boundary conditions. We have cons idered a stabilized spherical jellium model. The parameters of the eff ective interaction are obtained by means of a variational method takin g into account the experimental values of the density, compressibility and bulk energy. In the present model we have ignored the diffuseness of the equilibrium electron density, taking into account, however, th e surface degrees of freedom of the valence electrons and thus allowin g them to penetrate into the vacuum (outside of the jellium) when unde rgoing collective oscillations. The spectra of the excitation energies , and the electronic transition currents and transition densities are obtained for spherical clusters and voids.