Collective multipole excitations in small metal particles: Critical angular momentum lcr for the existence of collective surface modes.

Abstract

The electronic multipole response properties of small metal particles are investigated within the frame of a self-consistent spherical jellium model. The method used is the time-dependent local-density approximation (TDLDA), which was used before in a study of the dipole response [W. Ekardt, Phys. Rev. Lett. 52, 1925 (1984)]. On comparing the TDLDA response with the response of a system of noninteracting electrons, we see clearly how the electron-electron interaction is switched off rather suddenly around a critical angular momentum ${l}^{\mathrm{cr}}$. It is shown that the value of ${l}^{\mathrm{cr}}$ can be obtained from the equation ${q}^{\mathrm{cr}={l}^{\mathrm{cr}/\mathrm{R}}}$, where R is the radius of the jellium background and ${q}^{\mathrm{cr}}$ is the critical wave vector of the planar jellium surface. This result is consistent with a result found earlier for l=1 [W. Ekardt, Phys. Rev. B 31, 6360 (1985)]: A spherical surface behaves across the jellium edge like a patch of a planar jellium surface.