Multipolar response of small metallic spheres: Nonlocal theory

The multipolar response of a small metallic sphere is studied with use of a nonlocal dielectric function. Results obtained with the hydrodynamic and Lindhard-Mermin models are presented and compared to those given by the local Drude model. We find an enhancement of the imaginary part of the multipole polarizabilities at low frequencies and pole order l<$l_c$, where $l_c$ is a cutoff order that corresponds to excitations at the high-wave-vector edge of the electron-hole pair continuum. The absorption coefficient for two very close spheres is calculated and the effect of nonlocality on the number and position of the multipolar absorption peaks is discussed.