Electronic surface excitations of cavities in metals

Within the random-phase approximation (RPA), we have obtained the average surface-plasmon energy of voids and bubbles in nearly-free-electron metals using energy-weighted moments of the electronic response to operators of type ${\mathit{r}}^{\mathrm{-}(\mathit{L}+1)}$ ${\mathit{Y}}_{\mathit{L}0}$. We have used a local-density approximation of Slater and Wigner type for the exchange and correlation energies, respectively, and the jellium model for the positive ionic background. Compact expressions for the plasmon average energies are given, which allow one to discuss clearly the role played by the kinetic- and Coulomb energy contributions to the restoring force of the L modes. The effect of the electronic surface diffuseness is clarified. For the numerical applications, we have used an improved Thomas-Fermi-Weizsäcker model already emoloyed in similar studies on metal spheres. Using this model, we have also studied the static polarizability of voids. In the case of bubbles, the gas filling the cavity is modeled by a constant dielectric function whose effect is incorporated in the calculation of the electronic density and in the RPA response. A comparison with the experimental data is presented.